University of Southern California Dissertations and Theses

Dissociation energy and dynamics of water clusters

(USC Thesis Other)

Dissociation energy and dynamics of water clusters

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content DISSOCIATION ENERGY AND DYNAMICS OF WATER CLUSTERS by Lee Chiat Ch’ng A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CHEMISTRY: CHEMICAL PHYSICS) August 2013 Copyright 2013 Lee Chiat Ch’ng ii Acknowledgments My graduate career has been a wonderful and rewarding experience. I have been fortunate to interact with a group of amazing people. I am also grateful for the constant supports of my friends and family. First and foremost I would like to thank my graduate research advisor, Professor Hanna Reisler for being a great advisor and mentor. I appreciate her time and care that have guided me throughout my graduate career. She has helped me build my confidence and inspired me to do my best. She cares about me both as a scientist and a person, and I have great admiration and respect for her. She is simply awesome! I would like to thank Drs. Andrew Mollner and Blithe Rocher. Many of my lab skills were passed down from them. They were wonderful teachers both in the lab and outside of the lab. In addition to technical and scientific knowledge, I learned American language and culture from them. They were incredibly patient teachers and they have set a foundation for my graduate career. Later in my graduate career, I was fortunate to have the opportunity to work with Dr. Amit Samanta. His kindness and cheerfulness made it a pleasure to go to work every day. He shared with me knowledge gained from his graduate experiences and helped in progressing my research. He’s a great team member, enthusiastic teacher and a valuable asset of our group. I would like to thank Drs. Chirantha Rodrigo, Mikhail Ryazanov and Igor Fedorov who generously shared their knowledge and experiences with me. I am iii appreciative of the time they have taken to help me. I also wish to thank the former group members and members of the other groups at the Seaver Science Center, whom I had an opportunity to interact with: Drs. Boris Karpichev, Laura Edwards, Jordan Fine, Luis Gomez, Sergey Malyk, Russell Sliter, Bill Schroeder, Chris Nemirow, and Oscar Rebolledo-Mayoral, and Ms. Jaimie Stomberg and Stephanie McKean. I would like to thank Professors Curt Wittig who gave me an opportunity to attend USC; Stephen Bradforth, who was an inspiring teacher; Anna Krylov, whom I had a chance to work with as a teaching assistant; and Andrei Vilesov, Surya Prakash and Kathy Shing who were willing to serve as my committee members. I would like to thank Professors Kathleen Allen and Steven Mednick from the Marshall School of Business for their teaching and guidance. I would like to thank Michele Dea, Heather Meunier-Connor, Valerie Childress, Katie McKissick and Jackie Yu for providing assistance on administrative aspects of my projects and classes. I would like to thank my undergraduate lecturer Dr. Laurel Kimura who helped me to transfer to Linfield College from Malaysia. And Professor Jim Diamond from Linfield College who recommended me to continue my graduate studies at USC. Last but not least, I would like to thank my family and friends for their support. I am especially grateful to my father, who emphasized the importance of education when I was growing up and supported my studies in the United States. I would also like to thank my friends, Dewi Sri Hartati and Bo Young Yoon, who accompanied me throughout my journey and many friends who made my life at Los Angeles enjoyable. iv Abstract The state-to-state vibrational predissociation (VP) dynamics of water clusters were studied following excitation of a vibrational mode of each cluster. Velocity-map imaging (VMI) and resonance-enhanced multiphoton ionization (REMPI) were used to determine pair-correlated center-of-mass translational energy distributions. Product energy distributions and dissociation energies were determined. Following vibrational excitation of the HCl stretch fundamental of the HCl- H 2 O dimer, HCl fragments were detected by 2 + 1 REMPI via the f 3 ∆ 2 ( ν' = 0) ← X 1 Σ + ( ν'' = 0) and V 1 Σ + ( ν' = 11 and 12) ← X 1 Σ + ( ν'' = 0) transitions. REMPI spectra clearly show HCl from dissociation produced in the ground vibrational state with J'' up to 11. The fragments’ center-of-mass translational energy distributions were determined from images of selected rotational states of HCl and were converted to rotational state distributions of the water cofragment. All the distributions could be fit well when using a dimer dissociation energy of bond dissociation energy D 0 = 1334 ± 10 cm -1 . The rotational distributions in the water cofragment pair-correlated with specific rotational states of HCl appear nonstatistical when compared to predictions of the statistical phase space theory. A detailed analysis of pair- correlated state distributions was complicated by the large number of water rotational states available, but the data show that the water rotational populations increase with decreasing translational energy. H 2 O fragments of this dimer were detected by 2 + 1 REMPI via the 1 B 1 (000) ← 1 A 1 (000) transition. REMPI clearly v shows that H 2 O from dissociation is produced in the ground vibrational state. The fragment’s center-of-mass translational energy distributions were determined from images of selected rotational states of H 2 O and were converted to rotational state distributions of the HCl cofragment. The distributions gave D 0 = 1334 ± 10 cm -1 and show a clear preference for rotational levels in the HCl fragment that minimize translational energy release. The usefulness of 2 + 1 REMPI detection of water fragment is discussed. The hydrogen bonding in water is dominated by pair-wise dimer interactions, and the predissociation of the water dimer following vibrational excitation is reported. The measured D 0 values of (H 2 O) 2 and (D 2 O) 2 , 1105 and 1244 ± 10 cm -1 , respectively, are in excellent agreement with the calculated values of 1103 and 1244 ± 5 cm -1 . Pair- correlated water fragment rovibrational state distributions following vibrational predissociation of (H 2 O) 2 and (D 2 O) 2 were obtained upon excitation of the hydrogen bonded OH and OD stretch fundamentals, respectively. Quasiclassical trajectory calculations, using an accurate full-dimensional potential energy surface, are in accord with and help to elucidate experiment. Experiment and theory find predominant excitation of the fragment bending mode upon hydrogen bond breaking. A minor channel is also observed in which both fragments are in the ground vibrational state and are highly rotationally excited. The theoretical calculations reveal equal probability of bending excitation in the donor and acceptor subunits, which is a result of interchange of donor and acceptor roles. The rotational distributions associated with the major channel, in which one water fragment has one quantum of bend, and the minor channel with both vi water fragments in the ground vibrational state are calculated, and are in agreement with experiment. The predissociation dynamics of the water trimer following excitation of the hydrogen bonded OH-stretch fundamental were investigated. The D 0 for the (H 2 O) 3 → H 2 O + (H 2 O) 2 dissociation channel is determined from fitting the speed distributions of selected rovibrational states of the water monomer fragment using velocity map imaging. The experimental value, D 0 = 2650 ± 150 cm -1 , is in good agreement with the previously determined theoretical value, 2726 ± 30 cm -1 , obtained using an ab initio full-dimensional potential energy surface (PES) together with Diffusion Monte Carlo calculations [Wang and Bowman, J. Chem. Phys., 2011, 135, 131101]. Comparing this value to D 0 of the dimer places the contribution of non-pairwise additivity to the hydrogen bonding at 450- 500 cm -1 . Quasiclassical trajectory (QCT) calculations using this PES help elucidate the reaction mechanism. The trajectories show that most often one hydrogen bond breaks first, followed by breaking and reforming of hydrogen bonds (often with different hydrogen bonds breaking) until, after many picoseconds, a water monomer is finally released. The translational energy distributions calculated by QCT for selected rotational levels of the monomer fragment agree with the experimental observations. The product translational and rotational energy distributions calculated by QCT also agree with statistical predictions. The availability of low-lying intermolecular vibrational levels in the dimer fragment is likely to facilitate energy transfer before dissociation occurs, leading to statistical-like product state distributions. vii Table of Contents Acknowledgments ii Abstract iv Chapter 1: Introduction 1 1.1 Hydrogen Bond 3 1.2 Vibrational Predissociation 6 1.3 Theoretical Studies 8 1.4 Experimental Studies 13 Chapter 2: Theoretical and Statistical Models of Vibrational Predissociation of Water Clusters 21 2.1 Ewing Model 22 2.2 Phase Space Statistical Theory 29 Chapter 3: Experimental Techniques 35 3.1 Experimental Arrangement 36 3.2 Infrared Action Spectra and Energetics 42 3.3 Resonance-enhanced Multiphoton Ionization (REMPI) of Water Fragments 50 3.4 Velocity Map Imaging 55 3.5 Technical Challenges in Studying Water Clusters 60 3.5.1 Minimizing Background Water in the Vacuum 60 Chamber 3.5.2 IR Absorption of Atmospheric Water 62 3.5.3 Optimization of Water Fragment Detection 64 Efficiency 3.5.4 Optimization of Molecular Beam Conditions 65 Laser Conditions, and Laser Timings 3.6 Image Fitting and Analysis 71 3.7 Simulations of Fragment Energy Distributions using Phase Space Theory 81 3.7.1 Dissociation of Dimers 81 3.7.2 Dissociation of the Water Trimer 85 3.7.2.1 Angular Momentum Constraints on Rotational Populations 86 3.7.2.2 Treatment of Rotational Quantum Numbers of an Asymmetric Rotor 87 3.7.2.3 Comparison of Speed Distributions Simulated by PST and Quasiclassical Trajectory Calculations 88 viii 3.7.2.4 Comparison of PST and Quasiclassical Trajectory Calculations 90 Chapter 4: Hydrogen Chloride-Water Dimer 97 Part 1: Detection of HCl Fragments 4.1 Introduction 98 4.2 Experimental Details 104 4.3 Results and Analysis 4.3.1 Infrared Action Spectra 107 4.3.2 REMPI Spectroscopy of HCl Fragments 109 4.3.3 Ion Imaging Results and Analysis 111 4.4 Discussion 4.4.1 Infrared Spectrum of HCl-H 2 O 115 4.4.2 Dissociation Energy of the HCl-H 2 O 116 4.4.3 Fragments’ Rotational State Populations 117 4.4.4 Comparison of Rotational Distributions with Phase Space Theory (PST) 119 4.4.5 Comparison with rotational Energy Distributions in Other Dimers 122 4.5 Summary 126 Part 2: Detection of H 2 O Fragments 4.6 Introduction 127 4.7 Experimental Details 130 4.8 Results and Discussion 4.8.1 Infrared Action Spectra 132 4.8.2 REMPI Spectroscopy of Water Fragments 134 4.8.3 Ion Imaging Results and Analysis 135 4.8.4 Fragments’ Translational and Rotational Energy Populations 139 4.9 Discussion and Conclusions 143 Chapter 5: Water Dimer 151 5.1 Introduction 152 5.2 Experimental Methods 154 5.3 Computational Methods 156 5.4 Results and Discussion 157 5.5 Conclusion 169 Chapter 6: Water Trimer 174 6.1 Introduction 175 6.2 Experimental Methods 179 6.3 Theoretical Methods 182 6.4 Results and Discussion 184 6.5 Summary and Conclusions 199 ix Chapter 7: Future Work 207 7.1 Extended Studies on Dimers 208 7.1.1 Hydrogen Chloride Water Dimer 208 7.1.2 Ammonia Water Dimer 210 7.2 Methanol-Water Dimer 211 Appendix A: REMPI spectroscopy of Water using a REMPI Cell 220 Introduction Introduction 1 Chapter 1: Introduction Water is essential to all forms of life and hydrogen bonding gives it its special properties. Thus, understanding hydrogen bond networks in water has generated much interest. These exceedingly complicated hydrogen bond networks, which are dominated by pairwise and nonpairwise intermolecular interactions, are not yet completely understood. Without hydrogen bonding, there would be no life on earth. Therefore, intense research has been directed toward understanding the hydrogen bond nature, strength and dynamics. Figure 1.1 Water is the most abundant elements on the surface of earth and it is essential to all forms of lives. As the smallest water unit with a hydrogen bond and a network of hydrogen bonds, the water dimer and trimer serve as prototypes for understanding the complex nature of larger water networks, such as liquids, solids, water chains, etc. Surprisingly, despite much effort in theoretical studies, it is not until recently that the hydrogen bond dissociation energy was measured accurately. The absence of experimental measurement is due to technical challenges in detecting internally Introduction Introduction 2 excited water molecules. Our successful development of a detection method for water molecules during the study of the hydrogen chloride-water dimer paved the ways for many interesting experiments. In this Dissertation, experimental dissociation energies and dynamics of the hydrogen chloride-water dimer, water dimer and water trimer are presented (Figure 1.2). Further experiments are proposed and described in Chapter 7. Figure 1.2 Mixed water cluster (hydrogen chloride-water) and water clusters (dimer and trimer) discussed in this Dissertation. Introduction Hydrogen Bond 3 1.1 Hydrogen Bond Water possesses particular physical and chemical properties that make it central to life-processes. These unique properties are mainly due to its hydrogen bond and the network of hydrogen bonds that hold water molecules together. Therefore, a fundamental understanding of hydrogen bonds nature, strength and dynamics remains an important goal of physical chemistry. It was found that a slight difference in hydrogen bond strengthening or weakening would have major consequences for life. What is a hydrogen bond and what makes it unique? The hydrogen bond was first reported in 1920 by Latimer and Rodebush 1 and has been an area of intense research efforts ever since. 2-6 This distinct bond that connects water molecules together has unique characteristics that cannot be described by the known chemical bondings—covalent, ionic and van der Waals. It is stronger than the van der Waals bond and approximately two orders of magnitude weaker than covalent and ionic bonds. It was later described by Pauling that the hydrogen bond occurs when an atom of hydrogen is attracted by rather strong forces to two atoms instead of only one. 3 Therefore, it can be found not only in water, but also mixed water clusters and certain molecules that include hydrogen atoms. Recently, the definition of a hydrogen bond has been revised as follows: 7 “The hydrogen bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment XH in which X is more electronegative than Introduction Hydrogen Bond 4 H, and an atom or a group of atoms in the same or a different molecule, in which there is evidence of bond formation.” A typical hydrogen bond is depicted as XH-YZ, where the dash denotes the hydrogen bond, XH is the hydrogen bond donor and YZ is the acceptor. X is an electronegative atom, most commonly O, N, F, Cl, etc. Hydrogen bond strengths cover a large range of energies from around 2 to 167 kJ/mol (175 – 14,000 cm -1 ). 8,9 The weakest hydrogen bonds resemble van der Waals bond (e.g. CH-O, OH-π, NH-π), while the strongest hydrogen bonds are closer in strength to covalent bonds (e.g. XH-X - , X + H-X). Much theoretical and experimental effort was devoted to revealing the components that give rise to hydrogen bonds. In a bottom up approach, physical chemists study a single hydrogen bond in dimers, such as (HF) 2 , (HCl) 2 , HCl-H 2 O, NH 3 -H 2 O, (H 2 O) 2 , (NH 3 ) 2 , etc. These systems represent hydrogen bonded dimers of different bond strengths. Proceeding to the next level, hydrogen bonded trimers that contain multiple hydrogen bonds, such as (HCl) 3 , (H 2 O) 3 , (NH 3 ) 3 , are investigated to elucidate the many body interactions that form a hydrogen bond network. These interactions are responsible for strengthening the hydrogen bond in the network, which partly explains the unusual high boiling point and other special properties of water. These are referred to by the names nonadditive, cooperative, or nonpairwise interactions, and have attracted intense research. Close collaborations between theory and experiment are needed to refine our knowledge of the major contributors toward the hydrogen bond and its networks. The theoretical and Introduction Hydrogen Bond 5 experimental studies conducted previously can be found in Sections 1.3 and 1.4, respectively. As we know that hydrogen bonding is responsible for the unique properties of water and its clusters, it is therefore crucial to examine the mechanisms that lead to making and breaking of this bond. Particularly, we are interested in learning what happens when a certain amount of energy is given to hydrogen bonded clusters. We can easily imagine that the hydrogen bond breaks when the energy deposited in the system exceeds the bond strength. But what happens to the excess energy? Conservation of energy dictates that the excess energy has to be disposed; in this case, it is transferred to the translational, rotational and/or vibrational motions of the fragments. The pattern of how the hydrogen bond breaks and excess energy is distributed is the focus of our study. In this Dissertation, we describe 1) accurate measurements of hydrogen bond strength [measured in terms of bond dissociation energy (D 0 )] in water and mixed water clusters, and 2) energy flow mechanisms in clusters leading to dissociation. The systems shown in Figure 1.2, HCl-H 2 O, (H 2 O) 2 , (D 2 O) 2 and (H 2 O) 3 are investigated and presented. Bond dissociation is achieved via vibrational predissociation of hydrogen bonded clusters, as described in the next section. As expected, HCl-H 2 O has a stronger hydrogen bond than the water dimer. As shown in Figure 1.2, HCl is the hydrogen bond donor and H 2 O is the acceptor, because HCl is a stronger acid than H 2 O. The hydrogen bond dissociation energy of Introduction Vibrational Predissociation 6 (D 2 O) 2 is similar to (H 2 O) 2 , but slightly higher because of the difference in zero point energy. These hydrogen bonds exhibit nearly linear structures. As shown in Figure 1.2, (H 2 O) 3 has a cyclic equilibrium geometry, where each H 2 O molecule acts as both donor and acceptor. Theory predicts that this interconnected hydrogen bond network enhances the hydrogen bond strength, which means that it requires more than twice as much energy to break two of the three hydrogen bonds of the trimer, compared to the dimer. 1.2 Vibrational Predissociation The dissociation energy (D 0 ) for breaking one hydrogen bond in dimers such as HCl-H 2 O and (H 2 O) 2 is in the range of 13 – 17 kJ/mol (1100 – 1400 cm -1 ). Therefore, these dimers have potential curves with a shallow minimum. The bond can be easily broken by vibrational excitation. The vibrational excitation of an intramolecular mode can be transferred to the hydrogen bond by vibrational coupling, leading to dissociation of the cluster. Figure 1.3 shows a simplified drawing where an excitation of v =1 vibrational level (intramolecular vibrational mode) of HCl in HCl-H 2 O leads to dissociation by coupling with the hydrogen bond coordinate through intermolecular modes. This type of vibrationally induced indirect dissociation through coupling processes is commonly called vibrational predissociation. Introduction Vibrational Predissociation 7 Figure 1.3 Predissociation of HCl-H 2 O, by vibrational excitation of the HCl v = 0 → 1 intramolecular mode. Note that energy is not to scale. Since knowledge of the potential energy surfaces (PES) was incomplete and the experimental results were unavailable in the early days were lacking, understanding vibrational predissociation of weakly bound complexes was difficult. After publication of gas phase vibrational relaxation results of hydrogen bonded dimers, few theoretical models were developed independently to explain the short lifetimes and diffuse spectral features in the experimental studies of weakly bound clusters. 10-13 Studying the vibrational predissociation of hydrogen bonded clusters and their dissociation dynamics can provide insight into the strengths of the couplings between the different vibrational modes and the partitioning of the excess energy. Due to the disparity between the frequencies of intramolecular and intermolecular modes of the hydrogen bonded clusters, the intramolecular vibrational redistribution is often incomplete, giving rise to nonstatistical product energy distributions. 14 Introduction Theoretical Studies 8 This is especially pronounced when the density of states of the clusters is small (spacings of energy levels are large). The product energy distributions of hydrogen bonded dimers that have been studied previously all exhibit nonstatistical behavior. 14-22 Detailed product energy distributions of hydrogen bonded trimers upon vibrational predissociation are scarce. The density of states of the water trimer is much larger than the water dimer, which may lead to more efficient energy transfer and thus more statistical distribution. Understanding the mechanisms of vibrational predissociation has proven to be a challenge to both experiment and theory. Various theoretical models have been developed to elucidate the experimental observations, and these are discussed briefly below. 1.3 Theoretical Studies Water clusters have been studied extensively by theory (see Chapter 4 – 6 for more references). 23-26 Emphasis has been placed on calculating the equilibrium structure, low-lying stationary points, binding energy (D e ), vibrational frequencies, tunneling motions and constructing the full-dimensional ab initio PES. Note that D e is different from D 0 in that D e describes the minimum of the PES. It does not include zero point energy and cannot be measured experimentally. The current theoretical methods (e.g. Diffusion Monte Carlo simulations on an ab initio full dimensional PES), in which the zero point energy leakage issue has been minimized, 27 are able to calculate D 0 accurately. 21,22 The components that contribute to hydrogen bond include electrostatic attraction, polarization and charge transfer. The single Introduction Theoretical Studies 9 hydrogen bond in the water dimer has been well studied and characterized, and it was shown that it is dominated by electrostatic interactions. For cooperative stabilization, theoretical studies that investigate many-body effects in water clusters attribute it to polarization and charge transfer. 9,28-30 The state-of-the-art ab initio calculations on a full-dimensional PES (called WHBB) performed by Wang and Bowman using Diffusion Monte Carlo simulations show that the cooperative interactions in the water trimer contribute roughly 500 cm -1 (6 kJ/mol) additional energy to stabilize the cyclic structure. 31 The components that contribute to the hydrogen bond cannot be accessed by experiment directly. Measuring the hydrogen bond strength however, can provide benchmark examination of theoretical models. Despite great advances in theory, it is at present impossible to calculate product energy distributions upon vibrational predissociation using quantum mechanical methods. Therefore, a hybrid of quantum and classical calculations (called quasi-classical trajectory calculation) has been developed to investigate the dissociation dynamics by propagating the vibrationally excited clusters on the PES over time. However, the challenge remains because the lifetime of the vibrationally excited state of the clusters is usually long due to inefficient coupling between the intramolecular and the intermolecular modes. The lifetimes are in the picosecond to nanosecond timescale. It has been observed experimentally that the product energy distributions upon vibrational predissociation of weakly bound dimers are nonstatistical. There Introduction Theoretical Studies 10 are a couple of commonly applied models that help in describing the experimental observations, mainly, the Ewing model 32-34 (energy and momentum gap law) and the angular momentum model proposed by McCaffery and coworkers. 35-37 The energy gap law was first developed by Beswick and Jortner 38,39 to predict the excited state lifetimes in vibrational predissociation of non-hydrogen bonded complexes. This model has however ignored the possibility that the dissociated fragments can be produced in high rotational states. George E. Ewing 32,34 extended this work and provided analytical expressions to determine the lifetime of the vibrational excited complexes based on the momentum gap law, which can be applied to hydrogen bonded complexes. Both models are similar in that vibrational predissociation relies on the coupling of the wavefunction of the excited vibrational mode to the dissociation coordinate. The momentum gap law proposed by Ewing predicts correctly the vibrational predissociation rate of a large number of complexes and explains why the preferred vibrational predissociation route often involves high vibrational excitation in fragments and small translational energy release. In general, the Ewing model 34 explains the propensity of populating the vibrational over the rotational over the translational degrees of freedom from the perspective of wavefunction overlap and efficiency in energy transfer. However, it deals only with rates, and does not account for the state-specificity in product energy distributions observed in the experiments. The complementary angular momentum model 35-37 is based on linear-to- angular momentum interconversion, which suggests that hard-shaped potentials Introduction Theoretical Studies 11 are involved in producing high rotational excitation in the fragments. The model identifies the principal geometries of the clusters upon dissociation and reproduces the rotational distributions well. This model, however, does not account for the state-specificity in the vibrational degrees of freedom. The water molecule is an asymmetric top. The projections of rotation on each of the principal axes are not equal, which gives rise to a very congested manifold of rotational levels. Therefore, it is not feasible to quantify the detailed rotational state distribution in the water products, because of insufficient experimental resolution. Thus, a model is developed to fit the experimental measurements in our water cluster studies, which will be discussed in Chapter 3. In addition, the statistical phase space theory (PST), in which all energetically allowed states are equally probable, has been applied for comparison. As the density of states of the product increases, the product energy distributions may be more statistical-like. To visualize the density of states, Figure 1.4 shows the rotational energy levels of HCl, H 2 O, D 2 O and (H 2 O) 2 for comparison. The density of states of HCl is the lowest, followed by H 2 O, then D 2 O and (H 2 O) 2 is the highest. One would expect the rotational energy distributions in the HCl fragment upon vibrational predissociation of HCl-H 2 O to be the least statistical. At the other extreme, we expect the rotational energy distribution of the (H 2 O) 2 fragment upon vibrational predissociation of (H 2 O) 3 to be statistical-like. Similarly, the density of states in the vibrational degree of freedom has the same trend with much higher density of states in (H 2 O) 2 due to the low frequency of the intermolecular modes (fundamentals, overtones, combination bands). Therefore, the product energy distributions upon In v ex st ca F ntroduction ibrational p xpected to tates of the an be found igure 1.4 R predissociat be more s product. Fu d in Chapter Rotational en tion of (H statistical-lik urther discu r 2. nergy levels 12 H 2 O) 3 prod ke due to m ussion of the s of HCl, H 2 O ucing H 2 O much highe e Ewing mo O, D 2 O and ( Th and (H 2 O) 2 er rovibrati odel and pha (H 2 O) 2 eoretical Stu 2 fragments ional densi ase space th udies s are ty of heory Introduction Experimental Studies 13 1.4 Experimental Studies The dissociation energy and product energy distributions of hydrogen bonded water clusters can be investigated utilizing velocity map imaging. In the experiments of small water clusters, most reports focus on structure and spectroscopy of water clusters in gas phase, matrix and He droplets environments (see Chapter 4 – 6 for more references). 6,40-42 In spectroscopic studies, gas phase rotational spectra provide information about the geometries; and vibrational frequency shifts reveal the fingerprints of hydrogen bonded geometries and hydrogen bond pairwise and nonpairwise interactions. The detailed high resolution spectroscopic studies of Saykally and coworkers mapped the vibration-rotation tunneling motions of water clusters and estimated the barriers between different conformers. 40,41 Pioneered by Miller and coworkers, the studies of hydrogen bonded dimers were extended from spectroscopic investigations to pair-correlated predissociation dynamics. 43 The pair-correlated velocity distributions of various small dimers, mainly hydrogen halides, CO 2 , HCN, acetylene dimers and mixed dimers, upon vibrational predissociation were determined. Additionally, hydrogen bond dissociation energies for the dimers were determined with spectroscopic accuracy. In their review article, 14 Miller and coworker report that the product energy distributions upon vibrational predissociation of the hydrogen bonded dimers are highly nonstatistical. Mode specificity has been interpreted as depending on how the two fragments are impulsively pushed apart during dissociation. 14 Introduction Experimental Studies 14 The pioneering studies of Miller were extended and improved by Reisler and coworkers to enable studies of vibrational predissociation dynamics of hydrogen bonded clusters of larger molecules. They exploited velocity map imaging, 15-22 which allowed them to determine D 0 with higher accuracy and pair-correlated velocity distributions with better resolution. Table 1.1 lists the hydrogen bonded dimers studied by Reisler and coworkers with the corresponding D 0 , vibrational mode used to induce vibrational predissociation and the observed fragment vibrational modes. Similar to other hydrogen bonded dimers, the product energy distributions are nonstatistical. There is a propensity to produce vibrationally excited fragments, which qualitatively agree with the Ewing model. The vibrational predissociation dynamics of HCl-H 2 O and water dimer are discussed further in Chapter 4 and 5, respectively. To investigate larger hydrogen bonded systems that consist of a hydrogen bond network, the experimental studies were extended to trimers, mainly(HF) 3 , (DF) 3 and (HCl) 3 , utilizing spectroscopic methods. 44-46 Michael and Lisy 44 investigated the vibrational predissociation of (HF) 3 and its deuterated analogues. The structure of (HF) 3 was found to be cyclic and the HF stretch fundamental lifetime was determined to be between 2.5 and 21 ps. Nesbitt and coworkers 45,46 further investigated the predissociation and intermolecular vibrational redistribution dynamics of (DF) 3 and (HCl) 3 and confirmed the six-member cyclic structure as the equilibrium geometry. A detailed spectroscopic analysis revealed that upon vibrational excitation, there was intramolecular vibrational Introduction Experimental Studies 15 redistribution-induced ring opening of the trimer. For (HCl) 3 , the energy is sufficient to break more than one hydrogen bonds, and thus ring opening is followed by predissociation to either (HCl) 2 + HCl or 3HCl. The excited state lifetime was found to be 40 ps and 1.3 ns for (DF) 3 and (HCl) 3 , respectively. This sequential bond breaking dynamics agree with our investigation of the vibrational predissociation dynamics of the water trimer. The vibrational frequency shifts in these clusters suggest the stabilization of the cyclic trimers by cooperative interactions. Table 1.1 A summary of hydrogen bonded dimers, excited vibrational modes for vibrational predissociation, D 0 and observed fragment vibrational modes obtained by using velocity map imaging. Dimer Excited mode D 0 (cm -1 ) Observed fragment vibrational mode References HCl-HCCH Asymmetric CH stretch 700 ± 10 HCl: 0v HCCH: 1ν 2 15,18 DCl-HCCH Asymmetric CH stretch 755 ± 10 DCl: 0v HCCH: 1ν 2 18 NH 3 -HCCH Asymmetric CH stretch 900 ± 10 HCCH: 2ν 2 , 1ν 4 + 1ν 5 , 1ν 4 NH 3 : 1ν 2 , 2ν 2 16 H 2 O-H 2 O Hydrogen bonded OH stretch 1105 ± 10 H 2 O: 0ν, 1ν 2 21,22 D 2 O-D 2 O Hydrogen bonded OD stretch 1244 ± 10 D 2 O: 0ν, 1ν 2 22 HCl-H 2 O HCl stretch 1334 ± 10 HCl: 0v H 2 O: 0ν 19,20 NH 3 -H 2 O Hydrogen bonded OH stretch 1538 ± 10 NH 3 : 0ν, 1ν 2 , 2ν 2 H 2 O: 0ν 17 The water trimer is the obvious prototype for a detailed examination of cooperative interactions and dissociation dynamics. The determination of D 0 and Introduction Experimental Studies 16 product energy distributions upon vibrational predissociation of the water trimer is discussed in Chapter 6. The studies of water clusters covered in this Dissertation provide accurate determination of D 0 , quantify cooperative interactions and attempt to enhance our understanding of vibrational predissociation dynamics. The knowledge obtained from these studies would help our understanding of larger and more complicated systems. A close collaboration with theory aids in the development of both theoretical models and experimental modifications. Chapter 7 presents possible future experiments that can help to further understand complicated hydrogen bonded molecular systems. Introduction References 17 Chapter 1 References (1) Latimer, W. M.; Rodebush, W. H. J. Am. Chem. Soc. 1920, 42, 1419-1433. (2) Pauling, L. Proc. Natl. Acad. Sci. U.S.A. 1928, 14, 359-362. (3) Pauling, L. The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry; Cornell University Press: New York, 1939. (4) Bernal, J. D.; Fowler, R. H. J. Chem. Phys. 1933, 1, 515-548. (5) Scheiner, S. Hydrogen Bonding: A Theoretical Perspective; Oxford University Press: New York, 1997. (6) Keutsch, F. N.; Saykally, R. J. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 10533- 10540. (7) Arunan, E.; Desiraju, G. R.; Klein, R. A.; Sadlej, J.; Scheiner, S.; Alkorta, I.; Clary, D. C.; Crabtree, R. H.; Dannenberg, J. J. Pure Appl. Chem. 2011, 83, 1637-1641. (8) Desiraju, G. R.; Steiner, T. The weak hydrogen bond in structural chemistry and biology; Oxford University Press: Oxford, 1999. (9) Glendening, E. D. J. Phys. Chem. A 2005, 109, 11936-11940. (10) Coulson, C. A.; Robertson, G. N. Proc. R. Soc. Lond. A 1974, 337, 167-197. (11) Coulson, C. A.; Robertson, G. N. Proc. R. Soc. Lond. A 1975, 342, 289-315. (12) Robertson, G. N. Philos. Trans. R. Soc. Lond. A 1977, 286, 25-53. (13) Ewing, G. Chem. Phys. 1978, 29, 253-270. (14) Oudejans, L.; Miller, R. Annu. Rev. Phys. Chem. 2001, 52, 607-637. Introduction References 18 (15) Li, G.; Parr, J.; Fedorov, I.; Reisler, H. Phys. Chem. Chem. Phys. 2006, 8, 2915- 2924. (16) Parr, J. A.; Li, G.; Fedorov, I.; McCaffery, A. J.; Reisler, H. J. Phys. Chem. A 2007, 111, 7589-7598. (17) Mollner, A. K.; Casterline, B. E.; Ch'ng, L. C.; Reisler, H. J. Phys. Chem. A 2009, 113, 10174-10183. (18) Pritchard, M.; Parr, J.; Li, G.; Reisler, H.; McCaffery, A. J. Phys. Chem. Chem. Phys. 2007, 9, 6241-6252. (19) Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2010, 114, 9774-9781. (20) Rocher-Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2011, 115, 6903-6909. (21) Rocher-Casterline, B. E.; Ch'ng, L. C.; Mollner, A. K.; Reisler, H. J. Chem. Phys. 2011, 134, 211101. (22) Ch’ng, L. C.; Samanta, A. K.; Czakó, G.; Bowman, J. M.; Reisler, H. J. Am. Chem. Soc. 2012, 134, 15430-15435. (23) Shields, R. M.; Temelso, B.; Archer, K. A.; Morrell, T. E.; Shields, G. C. J. Phys. Chem. A 2010, 114, 11725-11737. (24) Temelso, B.; Archer, K. A.; Shields, G. C. J. Phys. Chem. A 2011, 115, 12034- 12046. (25) Cobar, E. A.; Horn, P. R.; Bergman, R. G.; Head-Gordon, M. Phys. Chem. Chem. Phys. 2012, 14, 15328-15339. Introduction References 19 (26) Shank, A.; Wang, Y.; Kaledin, A.; Braams, B. J.; Bowman, J. M. J. Chem. Phys. 2009, 130, 144314. (27) Czakó, G.; Kaledin, A. L.; Bowman, J. M. J. Chem. Phys. 2010, 132, 164103. (28) Mo, O.; Yanez, M.; Elguero, J. J. Chem. Phys. 1992, 97, 6628-6638. (29) González, L.; Mó, O.; Yáñez, M.; Elguero, J. J. Mol. Struc. (Theochem) 1996, 371, 1-10. (30) Chen, W.; Gordon, M. S. J. Phys. Chem. 1996, 100, 14316-14328. (31) Wang, Y.; Bowman, J. M. J. Chem. Phys. 2011, 135, 131101. (32) Ewing, G. E. J. Chem. Phys. 1980, 72, 2096-2107. (33) Ewing, G. E. J. Phys. Chem. 1986, 90, 1790-1799. (34) Ewing, G. E. J. Phys. Chem. 1987, 91, 4662-4671. (35) McCaffery, A. J. Phys. Chem. Chem. Phys. 2004, 6, 1637-1657. (36) McCaffery, A. J.; Pritchard, M.; Reisler, H. J. Phys. Chem. A 2009, 114, 2983- 2990. (37) Sampson, R. K.; Bellm, S. M.; McCaffery, A. J.; Lawrance, W. D. J. Chem. Phys. 2005, 122, 074311. (38) Beswick, J. A.; Jortner, J. J. Chem. Phys. 1981, 74, 6725-6733. (39) Beswick, J. A.; Jortner, J. Chem. Phys. Lett. 1977, 49, 13-18. (40) Keutsch, F. N.; Cruzan, J. D.; Saykally, R. J. Chem. Rev. 2003, 103, 2533-2578. (41) Saykally, R. J.; Wales, D. J. Science 2012, 336, 814-815. (42) Buck, U.; Huisken, F. Chem. Rev. 2000, 100, 3863-3890. (43) Miller, R. E. Science 1988, 240, 447-453. (44) Michael, D. W.; Lisy, J. M. J. Chem. Phys. 1986, 85, 2528-2537. Introduction References 20 (45) Suhm, M. A.; Farrell, J. J. T.; Ashworth, S. H.; Nesbitt, D. J. J. Chem. Phys. 1993, 98, 5985-5989. (46) Farnik, M.; Nesbitt, D. J. J. Chem. Phys. 2004, 121, 12386-12395. Theoretical Models Introduction 21 Chapter 2: Theoretical Models The hydrogen bonding in the clusters described in this Dissertation is much weaker than covalent bonding, and the dissociation dynamics are similar to van der Waals complexes. Few theoretical models have been developed to explain the vibrational predissociation dynamics and product energy distributions of these systems. Three models have been applied to our studies: (1) The Ewing model (based on momentum and energy gap laws), (2) statistical phase space theory and (3) quasiclassical trajectory calculations. According to the Ewing model, upon vibrational predissociation of weakly bound complexes, the excess energy has a propensity to populate vibration over rotation over translation. On the other hand, the statistical phase space theory describes product energy distributions of all energetically and momentum allowed states as equally probable. The energy distributions calculated by Bowman and coworkers using quasiclassical trajectory calculations are described in Chapter 5 and 6. 1,2 Theoretical Models The Ewing Model 22 2.1 The Ewing Model Vibrational predissociation of hydrogen bonded clusters occurs when the energy of the excited intramolecular mode transfers to the intermolecular modes that couple to the dissociation coordinate. Therefore, the product energy distribution is sensitive to the couplings among modes. The disparity between the frequencies of the intramolecular and intermolecular vibrational modes causes energy transfer in the clusters to be inefficient. This leads to long dissociation lifetimes of the clusters, which are usually in the picoseconds to nanoseconds timescale. In the article— “Selection Rules for Vibrational Energy Transfer: Vibrational Predissociation of van der Waals Molecules”, 3 Ewing extended the energy gap law 4,5 and proposed that a “relaxation channel of a vibrationally excited molecule is efficient only when the total change in effective quantum numbers for the process is small.” The relaxation process favors maximum energy disposal with the least change of quantum numbers. Therefore, in general, there is a propensity to populate vibration over rotation over translation. As mentioned in Chapter 1, vibrational predissociation of the clusters occurs through vibrational intermolecular interactions. Ewing studied coupling to different product channels (vibration, rotation and translation) and proposed propensity rules. Specifically, vibrational relaxation can proceed by at least four channels: 1) The energy from the excited mode is all transferred to the dissociation coordinate and the fragments fly away with all the energy deposited as translational energy. Theoretical Models The Ewing Model 23 This is the denoted as vibrational-translational (V-T) channel. 2) The fragments contain rotational energies as they fly apart, and this is the vibration-rotation (V-R) channel. If the fragments also contain translational energy, the relaxation occurs through the vibration-translation, rotation (V-T, R) channel. 3) The vibrational excitation relaxes to fragments’ vibrations, and it is the (V-V) channel. 4) The vibrational excitation relaxes through intramolecular vibrational redistribution (IVR), in which the excited mode flows throughout the cluster by exciting isoenergetic internal modes without predissociation. Ewing proposed that the rate of vibrational predissociation through channels 1 – 3 can be described by the empirical expression: () () 113 13 10 10 rv t T n nn n ee           Eq. 2.1 where the change of total effective quantum number (Δn T ), is the sum of the change in translational (Δn t ), rotational (Δn r ) and vibrational (Δn v ) quantum numbers. The factor 10 13 s -1 gives the typical collision frequency of the monomers through the hydrogen bond that holds them together. The exponential term, () T n e   , describes the probability that the initial discrete state of the vibrationally excited dimer and the final state of the monomer fragments will mix during the half-collision. Therefore, the exponential term is a measure of the reluctance of the dimer to change quantum numbers during vibrational predissociation. This general selection rule shows that energy relaxation is most efficient (highest predissociation rate) with the smallest change in total effective quantum number, Δn T . Theoretical Models The Ewing Model 24 Ewing 3 used HF-HF dimer as an example to compare the efficiency of energy transfer through the V-T and V-T, R channels. Figure 2.1 shows the potential energy curves for the ground and vibrationally excited states along the hydrogen bond coordinate, energy terms and translational wave function for the V-T channel of the HF-HF dimer. The translational wave function is interpreted as proportional to the number of nodes of the plane wave describing the motion of the two monomer fragments. The number of nodes in the translational wave function is approximately q t /2 and thus Δn t ≈ | 2 - ν t | Eq. 2.2 The quantum number change in the V-T channel, Δn t , is the difference between the effective quantum number of nodes of the translational wave function, q t /2, of the monomer fragments and the number of nodes in the dimer vibrational wave function, ν t . As shown in Figure 2.1, the poor Frank-Condon type wave function overlap gives rise to inefficient energy transfer in the V-T channel, which is consistent with the exponential dependence in Eq 2.1. The Δn t term is relatively large due to the large number of nodes in the translational wave function and ν t has no node, which gives Δn v = 1. The total change of effective quantum numbers is large for the HF-HF dimer predissociation through the V-T channel and therefore energy transfer is not efficient. For comparison, Halberstadt et al. 6 performed close coupling calculations for the HF-HF dimer predissociation through the V-T, R channel. The potential energy Theoretical Models The Ewing Model 25 curves for the ground, vibrationally excited and rotationally excited states are constructed and shown in Figure 2.2 together with the vibrational and translational wave functions. Figure 2.1 Potential energy curve along the hydrogen bond coordinate, energy terms and translational wave functions for vibrational predissociation of the HF-HF dimer. Translational and vibrational wave functions are shown. * denotes vibrationally excited and r is the hydrogen bond length. 3 Theoretical Models The Ewing Model 26 This example is similar to Figure 2.1 with an additional potential energy curve constructed by adding rotational excitation to one of the HF fragments, HF(J = 10) + HF(J = 0). The effective potential is shallower than the near rigid HF-HF dimer and the effective separation is greater, because the rotating HF molecules sweep out spheres defined by the outermost boundaries of their van der Waals radii. Since most energy is deposited in the rotation of the HF fragment, the energy left for translation is low and the translational wave function in this case has much fewer nodes. As illustrated in Figure 2.2 the translational wave function effectively overlaps with the vibrational wave function. Thus, vibrational predissociation through this V-T, R channel is much more favorable than in the V-T channel. Figure 2.2 Potential energy curves along the hydrogen bond coordinate for ground, vibrationally excited and HF(J = 10) + HF(J = 0) states. Translational and vibrational wave functions are shown. * denotes vibrationally excited. 3 Theoretical Models The Ewing Model 27 For the V-V channel, since the change in vibrational levels can dispose the largest amount of energy with the smallest change in the number of quanta, the V-V channels are usually efficient in vibrational predissociation. The V-T and V-R channels, however, depend on the reduced mass of the cluster and the moment of inertia of the fragments. For the hydrogen chloride-water dimer and water dimer, the moments of inertia of the fragments are small. Therefore, if the V-V channel is energetically accessible, it is the most favorable channel and the V-R channel is expected to be more favorable than the V-T channel. As discussed previously, vibrational predissociation can occur after IVR and the final product energy distributions would then be dependent on the isoenergetic internal modes of the dimer. These IVR processes can increase the rate of vibrational predissociation because the change in effective quantum number can be reduced significantly. For lager molecules, the density of states of the cluster internal modes is higher, which gives rise to a greater chance of IVR. In this case, the Ewing model is no longer suitable. The statistical model (see Section 2.2) is expected to become more successful in predicting the product energy distributions upon vibrational predissociation of larger clusters, such as the water trimer. On the other hand, in certain cases the dimers can predissociate after IVR as well. Since the density of states of many polyatomic dimers is higher and the structures of these dimers are floppy, it is unclear a priori whether the vibrational predissociation of these dimers would exhibit statistical- like behavior. Theoretical Models The Ewing Model 28 In 1980, based on the selection rules discussed above, Ewing predicted that the “excitation of the stretching mode (~3700 cm -1 ) within the water dimer H 2 O*(100) ∙∙∙H 2 O(000) should predissociate rapidly to H 2 O*(010) + H 2 O(000) since the energy to the bending mode (~1600 cm -1 ) leaves just enough (~2100 cm -1 ) [energy] to break the hydrogen bond (~2000 cm -1 ).” 7 This prediction will be investigated and discussed in Chapter 5. Theoretical Models Phase Space Theory 29 2.2 Phase Space Theory The phase space theory (PST) for product energy distributions in chemical reactivity was developed by Light, Pechukas and Lin, 8-10 and applied widely in unimolecular reactions. It is a model that assumes that all allowed states are equally populated. The approach conserves angular momentum and energy, but does not take account of centrifugal barriers associated to the angular momentum of the fragments, which can be added as a constraint. It can describe product state distributions in a unimolecular reaction with a loose transition state. Further constraints have been added to PST to better describe specific systems. PST applies conservation of energy and angular momentum and assumes that all allowed states are equally populated. The conservation of energy gives h ν IR + E rot (cluster) = D 0 + E vib,rot (mon) + E vib,rot (cofrag) + E T Eq. 2.7 where hν IR is the IR photon energy used for excitation of the hydrogen bonded stretch of the dimer, E rot (dimer) is the dimer rotational energy, D 0 is the dissociation energy of the dimer, and E vib,rot (mon) and E vib,rot (cofrag) are the rovibrational energies of the detected monomer fragment and the cofragment, respectively. E T is the center-of-mass translational energy. Detailed energy partitioning will be discussed in Chapter 3. Conservation of angular momentum demands L = J(cluster) + j(mon) + j(cofrag) Eq. 2.8 Theoretical Models Phase Space Theory 30 where J(cluster), j(mon) and j(cofrag) are the angular momentum vectors of the parent molecule (dimer or trimer), monomer fragment and cofragment (either monomer or dimer), respectively, and L is the orbital angular momentum vector. The conservation of angular momentum is depicted in triangular vector forms as shown in Figure 2.3. Eq. 2.9 can be simplified by defining the sum of two vectors to be ω, such as j(mon) + j(cofrag) = ω Eq. 2.9 ω + J(cluster) = L Eq. 2.10 Since vector additions are commutative, the vectors in Eq. 2.9 can be added in any order and any two vectors can be defined as ω. Although the phase space constructed from vectors of different order is different, the integrated distributions are the same. The number of allowed L for each J(cluster), j(mon) and j(cofrag) can be calculated by integrating or summing over the phase space within the boundary of ω (Figure 2.4), max max min min () |( ) | || 1 Jcluster Jcluster Nd           Eq. 2.11 Theoretical Models Phase Space Theory 31 Figure 2.3 The vector relationship given in Eq. 2.9 and 2.10. The vectors in blue are obtained from experimental measurement and conservation of energy. The vectors relationship can be simplified by defining any two vectors to ω to form the first triangular relationship and similarly for the rest of the vectors. The allowed L is then calculated from conservation of angular momentum. The application of PST is justified when there is complete energy randomization prior to dissociation. The water dimer has higher density of vibrational states than does the hydrogen chloride-water dimer. Additionally, vibrational predissociation of the water dimer yields water monomer fragments, whose rotational levels are denser compared to the hydrogen chloride fragment. If IVR is more efficient than direct coupling from an intramolecular vibration to the dissociation coordinate and energy transfer to fragment rotation is more efficient, the product energy distributions in water dimer predissociation may be more statistical than predicted by Ewing. Both the Ewing and the PST models are considered in our studies in cases when the product energy distributions approach the statistical limit. Restrictions due to total orbital angular momentum and due to Theoretical Models Phase Space Theory 32 centrifugal barriers were found to be negligible and therefore are not discussed here. Figure 2.4 Phase space diagram representing the vector relationship shown in Figure 2.3 with respect to J(cluster), L and ω. The black lines mark the boundary of all allowed L states and the red dashed lines (and blue shade) show the allowed L states for a specific J(mon), J(cofrag) combination. Integrating the area shown in blue gives N for the specific J(cluster), j(mon) and j(cofrag) combination. As mentioned in Chapter 1.5, vibrational predissociation of hydrogen halide trimers involves IVR-induced sequential bond breaking. Due to the much higher density of states in the water trimer, a high degree of IVR is expected upon excitation of the hydrogen bonded OH stretch. Coupling to the intermolecular modes will eventually break two out of the three hydrogen bonds producing one water dimer and one monomer. The combination of the high probability of IVR and a high density of states in the dimer fragment suggests statistical-like distributions. Although the moment of inertia of the dimer fragment is large, quasiclassical Theoretical Models Phase Space Theory 33 trajectory calculations predict no truncation of high rotational quantum numbers. Therefore, no additional restriction is added to the trimer PST calculations. Simulations using PST for pair-correlated energy distributions and rotational distributions are presented in Chapter 3.8 and 3.9 for dissociation of dimers and the water trimer, respectively. Theoretical Models References 34 Chapter 2 References (1) Czakó, G.; Wang, Y.; Bowman, J. M. J. Chem. Phys. 2011, 135, 151102. (2) Ch’ng, L. C.; Samanta, A. K.; Czakó, G.; Bowman, J. M.; Reisler, H. J. Am. Chem. Soc. 2012, 134, 15430-15435. (3) Ewing, G. E. J. Phys. Chem. 1987, 91, 4662-4671. (4) Beswick, J. A.; Jortner, J. Chem. Phys. Lett. 1977, 49, 13-18. (5) Beswick, J. A.; Jortner, J. J. Chem. Phys. 1981, 74, 6725-6733. (6) Halberstadt, N.; Brechignac, P.; Beswick, J. A.; Shapiro, M. J. Chem. Phys. 1986, 84, 170-175. (7) Ewing, G. E. J. Chem. Phys. 1980, 72, 2096-2107. (8) Pechukas, P.; Light, J. C. J. Chem. Phys. 1965, 42, 3281-3291. (9) Pechukas, P.; Light, J. C.; Rankin, C. J. Chem. Phys. 1966, 44, 794-805. (10) Light, J. C.; Lin, J. J. Chem. Phys. 1965, 43, 3209-3219. Experimental Techniques Introduction 35 Chapter 3: Experimental Techniques Small water clusters and mixed clusters have been a fundamental, but challenging topic of study. One of the best methods to study small water clusters is by creating those clusters in the collision-free regions of molecular beams in a high vacuum chamber. This method provides well-defined initial conditions of the molecules. Figure 3.1 shows a simplified experimental scheme described in this Dissertation, in which the experiments were conducted in a vacuum chamber by generating water clusters in a skimmed supersonic molecular beam, photoexciting water clusters of selected size (using infrared absorption), ionizing the dissociation products (using ultraviolet absorption) in selected quantum states, and detecting the mass-selected fragments. Figure 3.1 General experimental scheme for predissociation studies of water clusters. The data collected from the position-sensitive detector utilizing velocity map imaging reflect the quantum state and momentum of the detected fragment upon predissociation. Experimental modifications and optimizations have to be carefully done in order to maximize the production of selected water clusters and the detection efficiency of the fragments. These include optimizing the molecular beam Experimental Techniques Experimental Arrangement 36 conditions for cluster production and laser conditions for the best signal-to-noise ratio. 3.1 Experimental Arrangement The experimental arrangement and the details of the supersonic molecular beams properties and vacuum systems were described previously. 1-6 The vacuum system used in the water clusters studies consisted of three differentially pumped chambers: the source, interaction and detection chambers (see Figure 3.2). The source chamber was pumped by a Leybold TMP1000C (1100 L/s N 2 ) turbomolecular pump backed by a Welch 1397 mechanical pump. The interaction chamber was evacuated by a Leybold TMP 361 (345 L/s N 2 ) turbomolecular pump backed by an Alcatel 2021I direct drive pump. The detection chamber was pumped by a Leybold TMP 1000C (1100 L/s N 2 ) turbomolecular pump backed by an Edwards E2M18 mechanical pump. The pressures in the source and the detection chambers were monitored by an iridium filament glass ion gauge (3/4" I-075-N) with a Granville-Philips vacuum gauge controller (350501-0-T1). The pressures were mid to high 10 -8 Torr when the chambers were evacuated. The operating pressures of the source and detection chambers when a pulsed nozzle was running at 10 Hz were ~1 x 10 -5 and 2 - 4 x 10 -7 Torr, respectively. A pneumatic valve and a stainless steel mesh flex trap were installed after each turbomolecular pump and before the mechanical pumps. The cryopumping system consisting of a “cold-finger” and a liquid nitrogen reservoir was installed at the interaction chamber (see Section 3.5.1). Experimental Techniques Experimental Arrangement 37 A home-built piezoelectric pulsed nozzle with a 0.5 mm orifice utilizing Physik Instrumente disk translator (P-286.23) was used to generate the supersonic molecular beam. The beam consisted of the species of interest seeded in a carrier gas. The nozzle, which operated at 10 Hz, was driven by a negative 300-500 V square pulse of ~200 μs duration. The nozzle was modified to include a heating option (see Section 3.5.4). The molecular beam was generated by sending water vapor seeded in a carrier gas (He) through the pulsed nozzle and expanding the mixture into the source chamber. The molecular beam was collimated by two skimmers (1.29 and 0.78 mm diameter; Beam Dynamics, Inc.) separated by 4 cm. The center of the molecular beam was then expanded into the interaction chamber where the exciting and ionizing laser beams intersect with the molecular beam (see Figure 3.2). Figure 3.2 Schematic diagram of the experimental apparatus: 1. piezo-electric nozzle; 2. skimmers; 3. electrostatic lens assembly; 4. μ-metal shielding; 5. MCP/phosphor screen assembly; 6. cryopumping system (see full description in ref 2). Experimental Techniques Experimental Arrangement 38 Figure 3.3 Schematic diagram of the electrostatic lens system chamber, field free drift tube, and the detector assembly. The interaction chamber consisted of four-electrode lens system, where the photodissociation and ionization of the molecular species took place (Figure 3.3). The interaction of the molecular species with the laser beams took place at approximately 5 cm away from the orifice of the second skimmer. The electrostatic lens designed by Ashfold and coworkers 7 was adapted for our experimental setup in 2002. The ions produced in the interaction region were focused and accelerated by the electric fields generated by the ion optics to the linear time-of-flight (TOF) spectrometer (60 cm drift tube) in the detection chamber. After passing through the drift tube, the ions arrived at a position sensitive detector—40 mm diameter dual- channel microchannel plate (MCP) coupled to a phosphor screen assembly (Burle Electro optics, Inc. APD 3040 FM with P-47 phosphor with fiber-optic window). The detector was replaced in 2012 by a Beam Observation System (Beam Imaging Solutions, Inc. Model BOS-40-6, 6.00” conflat flange mount with dual-channel 40 mm Experimental Techniques Experimental Arrangement 39 diameter and 60:1 aspect ratio MCP, P-43 phosphor screen). In order to eliminate stray fields in the interaction and TOF regions, both the ion optics and TOF drift tube were shielded by a μ-metal alloy tube (nickel-iron-copper-molybdenum AD Vance Magnetic, Inc., AD-MU-80). The apparatus could be operated in two different modes: TOF and imaging. In the TOF mode, the current collected by the MCP was amplified 100x (Phillips Scientific; DC-100 MHz bipolar amplifer, model 6931, 50 Ω input impedance) and monitored by an oscilloscope (Tektronix, TDS 3054, 500 MHz bandwidth). The data were transferred to a PC using LabView programs (National Instruments). In the imaging mode, a charged-coupled device (CCD) camera (LaVision, Imager 3, 13 bit, 1280 x 1024 pixel array) recorded images from the phosphor screen and exported the data to a PC for analysis using the DaVis software package (LaVision) that included event counting. The recording window (pixel array) and camera exposure time were adjusted for optimal events per image and minimum total data acquisition time. The typical voltages applied to the electrostatic lens system, MCP detector, and phosphor screen in different modes are shown in Table 3.1. The optimal voltage ratio for the electrostatic lens in our apparatus was found to be V Repeller : V Extractor : V Lens = 2.49 : 2 : 1. 2 Due to the low translational energy (100 – 2500 cm -1 ) of the ions of interest, the Newton spheres formed upon dissociation of the water clusters were small relative to the size of the detector. A lower set of voltages (V Extractor = 1000 V) Experimental Techniques Experimental Arrangement 40 was applied to the electrostatic lens system to obtain a larger Newton Sphere and thus better image resolution. For the study of water clusters, infrared (IR) radiation was used to excite a selected vibrational mode of a specific cluster and ultraviolet (UV) radiation was used to ionize the predissociation fragments state-selectively in both the TOF and imaging modes. The IR radiation was generated by an OPO/OPA system (LaserVision, up to 22 mJ/pulse; 0.4 cm -1 linewidth) pumped by the fundamental (1064 nm) of a seeded Nd:YAG laser (Continuum Precision II, 500 mJ/pulse, 10 Hz). UV radiation in the range of 238 – 280 nm was generated by frequency-doubling (Inrad Autotracker III) the output of a tunable dye laser (Continuum ND6000, Coumarin 480 and Coumarin 500 dye solution) pumped by the third harmonic (355 nm) of a Nd:YAG laser (Continuum Surelite III, 150-200 mJ/pulse, 10 Hz). The timings of the lasers were adjusted by delay generators (Standford, DG535) controlled through a GPIB interface (National Instruments). Figure 3.4 shows the schematic diagram of the lasers arrangement. Table 3.1 Typical voltages (in V) applied to the electrostatic lens system, MCP detector and phosphor screen in different modes of data collection. Mode Repeller Extractor Lens MCP Phosphor Screen Plate 1 Plate 2 TOF +1245 +1000 +500 > -1900 > -100 0 Ion Imaging +1245 +1000 +500 0 > +1900 +5000 Electron Imaging -4980 -4000 -2000 0 > +1900 +5000 Experimental Techniques Experimental Arrangement 41 Figure 3.4 Schematic diagram of the lasers arrangement. In the TOF mode, four types of data were collected: Fragment yield IR (action) spectra, resonance-enhanced multiphoton ionization (REMPI) spectra, nozzle-UV laser time delay scan and IR-UV laser time delay scan. The IR-UV laser time delay scan was determined by scanning the IR laser firing time relative to the UV laser firing. Maximum signal was observed when the IR laser fired ~70 ns before the UV laser (see Section 3.5.4). The IR action spectra and REMPI spectra were collected by alternating “IR on” and “IR off” conditions at each frequency. In “IR on”, the IR laser fired ~70 ns before the UV laser, whereas in “IR off”, the IR laser fired 1 μs after the UV laser. Nozzle-UV laser time delay scans were determined by alternating “IR on” and “IR off” at each time step (see Section 3.5.4). The timings at which maximum enhancement was achieved (IR on signal - IR off signal) were used. The IR laser conditions (focusing, power) were optimized to ensure single-photon absorption Experimental Techniques Infrared Action Spectra and Energetics 42 (see Section 3.5.4). The UV laser conditions were optimized for the best signal-to- noise ratio (see Section 3.5.3). The delay times of the lasers’ firings were carefully optimized to excite the clusters in the part of the molecular beam pulse where their highest relative abundance was found. A box purged by dry air was installed to prevent IR absorption of atmospheric water (see Section 3.5.2). 3.2 Infrared Action Spectra and Energetics The combination of vibrational predissociation, REMPI spectroscopy (see Section 3.3) and velocity map imaging (see Section 3.4) allows an accurate determination of clusters dissociation energies (D 0 ) and product energy distributions. The vibrational predissociation of the HCl-H 2 O dimer was achieved by exciting the HCl stretch at 2723 cm -1 . As this energy exceeded D 0 (1334 ± 10 cm -1 ) of the H-bond, it caused the bond to rapture. The excess energy (1389 cm -1 ) was insufficient to populate the vibrations of the HCl and H 2 O fragments, but could populate the rotational and translational degrees of freedom. The fragments were mass selected and detected via REMPI. By scanning the IR frequency in the region of the HCl stretch dimer and detecting the HCl fragment, fragment-yield IR spectra were obtained. The spectra were simulated using the PGOPHER 8 program with an a-type transition, published rotational constants 9-11 (Table 3.2) and a rotational temperature of 5 K. Figure 3.5 shows the HCl-H 2 O fragment yield IR enhancement (IR on – IR off) spectrum Experimental Techniques Infrared Action Spectra and Energetics 43 recorded by detecting the HCl fragment in the J" = 10 level. As stick spectrum is added for comparison and the transitions (J ʹ KaKc ← J" KaKc = 0 0,0 ← 1 0,1 and 1 0,1 ← 2 0,2 ) used for REMPI and imaging are boxed in green (2723 ± 1 cm -1 ). The internal energy of the dimer was calculated from the J" KaKc of the transitions. Table 3.2 Molecular constants (in cm -1 ) of the HCl stretch of the HCl-H 2 O dimer. 9-11 Constant/ Band Ground State HCl Stretch Band origin [ ν 0 ] 0 2723.35 A 11.034 - B 0.1311 - C 0.1298 - Figure 3.5 Fragment yield IR enhancement spectrum of HCl-H 2 O obtained by monitoring HCl fragments in J" = 10. The black curve shows the IR enhancement signal. The blue lines represent the simulated stick spectrum of an a-type band with a rotational temperature of 5 K, obtained by using published spectroscopic constants. 9-11 Green lines mark transitions that were used for estimation of the dimer internal energy. Experimental Techniques Infrared Action Spectra and Energetics 44 Similarly, the vibrational predissociation of the water dimer was achieved by exciting the H-bonded OH and OD stretch fundamentals of (H 2 O) 2 and (D 2 O) 2 at 3602 and 2634 cm -1 , respectively. The D 0 values determined experimentally are 1105 and 1244 ± 10 cm -1 for (H 2 O) 2 and (D 2 O) 2 , respectively. The corresponding excess energies of 2497 and 1390 cm -1 can populate the vibrational, rotational and translational degrees of freedom. Upon excitation of the H-bonded stretch of the dimers, the excess energy is only sufficient to populate one quantum bending vibration of one of the fragments (see Table 3.3 for relevant vibrational energies). Two channels are open: (1) (010) + (000) (2) (000) + (000), where (000) and (010) are the ground and first bending vibrational states of the monomer fragments, respectively (Figure 3.6). The water monomers can then be detected in the (000) or (010) states by REMPI. Details of REMPI of the water fragments are discussed in Section 3.3. The experimental scheme of the vibrational predissociation of the water dimers is presented in Figure 3.7. Table 3.3 Experimental vibrational energies (in cm -1 ) of H 2 O and D 2 O. 12 Vibrations H 2 OD 2 O Symmetric Stretch 3656.65 2671.46 Bend 1594.59 1178.33 Asymmetric Stretch 3755.79 2788.05 Experimental Techniques Infrared Action Spectra and Energetics 45 Figure 3.6 Dissociation channels of the water dimers, (H 2 O) 2 and (D 2 O) 2 via excitation of the H-bonded OH stretch. Two channels are open for the fragments: (i) (010) + (000) (ii) (000) + (000). The water monomers can be detected either in the (000) or (010) states. Figure 3.7 Experimental scheme for the vibrational predissociation of the water dimers. An IR photon (h ν IR ) excites the H-bonded stretch of the dimer to initiate dissociation. Water monomer fragments in the (010) and (000) states are detected by REMPI using UV photons. E Excess corresponds to the excess energy available for rovibrational excitation of both fragments and to c.m. translation. Experimental Techniques Infrared Action Spectra and Energetics 46 (H 2 O) 2 and (D 2 O) 2 IR spectra were simulated with a-type transitions, published rotational constants 13 and a rotational temperature of 15 K. Table 3.4 lists the constants used in the (D 2 O) 2 IR spectrum simulation shown in Figure 3.8. Table 3.4 Molecular constants (in cm -1 ) of the (D 2 O) 2 H-bonded O-D stretch. 13,14 Constant/ Band Ground State Bonded O-D Stretch Band origin [ ν 0 ] 0 2632.33 A 4.190 4.089 K a = 0 (B + C)/2´ [ ] 0.18108 0.18202 K a = 1 (B + C)/2´ [ ] 0.1811 0.18177 (B - C)´ [ΔD] 0.0036 0.0036 Due to unresolved rotational transitions, rotational temperatures cannot be directly extracted from the IR spectra. The temperature of 15 K was obtained from previous studies and estimated from the temperature of monomers in the He seeded molecular beam (see Section 3.5.4). The spectrum in Figure 3.8 exhibits saturation broadening due to the tight focusing conditions necessary to maximize the signals from the fragments. It is also important to note that this is an action spectrum; in order to observe enhancement, there must be absorption of IR photons, and this absorption must lead to the production of the detected fragment in the monitored Experimental Techniques Infrared Action Spectra and Energetics 47 J" KaKc state. Thus, the transitions are not well resolved and the overall shape of the spectrum is slightly different from that of an IR absorption spectra. Figure 3.8 Fragment yield IR spectra of (D 2 O) 2 [monitoring a D 2 O (000) transition with a major contribution from J" KaKc = 13 1,12 ]. The red curves show the dimer spectrum obtained by monitoring the monomer fragment. The black curves show background signals from monomers in the molecular beam under the same conditions. The blue curves are the simulated spectra of an a-type band with a rotational temperature of 15 K using published rotational constants. 13 Green lines mark the transitions that were included in calculating the dimer internal energy. For the water trimer, vibrational predissociation of (H 2 O) 3 was initiated by exciting the H-bonded OH stretch at 3536 cm -1 . The calculated and measured values D 0 are 2726 ± 30 and 2650 ± 150 cm -1 , 15 respectively. The excess energy of ~900 cm -1 is insufficient to populate any vibrational state of the monomer fragment (Table 3.3). Thus, the H 2 O fragment can be detected only in the ground vibrational state by REMPI. None of the intramolecular modes of the dimer fragments are energetically accessible, but all six Experimental Techniques Infrared Action Spectra and Energetics 48 intermolecular modes of the dimer fragment are energetically available (Table 3.5). Figure 3.9 shows the experimental scheme of the water trimer. Figure 3.9 Experimental scheme for vibrational predissociation of water trimer. An IR photon excites the H-bonded stretch of the trimer to initiate dissociation, which has a dissociation energy of D 0 . Water monomer fragment in the ground vibrational state are detected by REMPI using UV photons. All intermolecular modes (fundamental, overtones and combination bands) of the dimer are energetically accessible. Blue lines show the increase in vibrational density of states with increasing energy. Experimental Techniques Infrared Action Spectra and Energetics 49 Table 3.5 Calculated and experimental intermolecular vibrational energies (in cm -1 ) of (H 2 O) 2 . Vibrations (H 2 O) 2 Calculated 16 Ne matrix 17,18 Hydrogen bond torsion 91 116 Acceptor twist 105 150 Acceptor wag 110 122 O-O stretch 133 173 In-plane bend 305 309 Out-of plane bend 533 522 Figure 3.10 shows the fragment yield IR spectrum of (H 2 O) 3 recorded at 3512 – 3562 cm -1 by monitoring H 2 O fragments via the 1 B 1 (000) [J' KaKc = 2 0,2 ] ← 1 A 1 (000) [J" KaKc = 3 2,1 ] transition. The spectrum shows distinct IR enhancement in the range of 3527 – 3551 cm -1 , which is in agreement with previously published spectra. 19,20 The enhancement beyond 3551 cm -1 peaking at 3559 cm -1 has been assigned previously as the (H 2 O) 6 band. 20 The signal-to-noise ratio of the water trimer IR action spectrum is significantly lower than for the water dimer, which is due to the lower IR radiation fluence used in the experiments to minimize multiphoton excitation. The E rot (cluster) is estimated from the rotational temperature of the H 2 O monomer REMPI spectra to be 14 K (see Section 3.3) using <E rot > = K B T Eq. 3.1 E w (0 e F fr cu b u 3 st se se a Experimenta where E rot is 0.695 cm -1 K stimated to igure 3.10 ragment C  1 urve shows ottom (blac nder the sa 3.3 Reso of W REMP tepwise res everal adva election rul re forbidde al Technique s the rotatio K -1 ) and T is be 10 ± 10 0. Fragment B 1 (000) [J' K s the trimer ck) curve s me conditio onance-e Water Fra PI is a sen sonant exci antages ov es for multi en in the s es onal energy s the rotatio cm -1 . t yield IR s KaKc = 2 0,2 ] ← r spectrum shows back ons. enhance agments nsitive and tation of a ver single p iphoton tran ingle photo 50 y of the mo onal temper pectrum of ← X  1 A 1 (000 obtained b kground sig ed Multip state-selec molecule v photon spe nsitions allo on transitio onomer, K B rature, the a f (H 2 O) 3 ob 0) [J" KaKc = 3 2 by monitori gnal from H photon Io ctive ioniza via an inter ectroscopy. ows the obs ons. In addi is the Boltz average rota btained by m 2,1 ] transitio ing the H 2 O H 2 O in the m onization ation techn rmediate st Mainly, th servation of ition, it is REMPI of W zmann con ational ener monitoring on. The top O fragment. molecular b n (REMP nique that tate. REMPI he differenc f transitions highly sens Water stant rgy is H 2 O (red) . The beam I) uses I has ce in s that sitive Experimental Techniques REMPI of Water 51 because the probability of ionization is enhanced by the resonance with the intermediate state. In addition, REMPI can be mass selective if used in combination with TOF detection. It allows recording of the REMPI spectrum of the desired molecules without interference from the parent species or the other molecules. In the HCl-H 2 O studies, the HCl and H 2 O fragments were detected via REMPI. The HCl REMPI spectra have been reported in detail previously. 6,21 Therefore, only REMPI of the water fragments is discussed here. In our studies, 2 + 1 REMPI of H 2 O and D 2 O [ 1 B 1 (000) ← 1 A 1 (000 or 010)] combined with TOF mass spectrometry was used for spectroscopic investigations. The water monomer fragments absorb two UV photons to reach the -state and one additional photon to the ionization continuum (Figure 3.11). Figure 3.11 2 + 1 REMPI process via the 1 B 1 ← 1 A 1 transition. The REMPI spectra of the water molecules are complicated due to the fast predissociation (short lifetime) of the electronically excited states and the spectral congestion of an asymmetric top molecule (C 2v ). Ashfold and coworkers 22 and Yang Experimental Techniques REMPI of Water 52 et al. 23 studied the REMPI spectra of water and identified several predissociation mechanisms for the transitions via the 1 B 1 state. One is a heterogeneous mechanism induced by rotation of the water molecules around the a-axis (b 1 symmetry). The water molecules predissociate via a state of A 1 symmetry (B 1 × B 1 = A 1 ), the nearby 1 A 1 state. The second mechanism is a homogeneous predissociation via a state of the same symmetry, the 1 B 1 . The overall model for the lifetime broadened linewidths in the -state was proposed to be of the form: ω = ω 0 + ω a < J a ' 2 > Eq. 3.2 where ω 0 and ω a are the homogeneous and the heterogeneous components, respectively. < J a ' 2 > is the average of the square of the operator for the projection of J' onto the a-axis. The linewidth of each transition is proportional to the K a quantum number of the -state. Therefore, it is more difficult to observe transitions with high K a '. In this Dissertation, K a ' ≤ 3 and 5 were observed for H 2 O and D 2 O, respectively. Although the projection quantum numbers (K a , K c ) are not good quantum numbers for asymmetric tops, they are useful for unambiguous labeling. Simulations of the H 2 O and D 2 O REMPI spectra were accomplished by using the PGOPHER 8 computer packages. The H 2 O and D 2 O 1 B 1 (000) ← 1 A 1 (000) REMPI spectra have been published and the simulations are available online. 23 The H 2 O and D 2 O 1 B 1 (000) ← 1 A 1 (010) REMPI spectra were simulated by using the published rotational constants 24,25 and simulated by PGOPHER. The rotational Experimental Techniques REMPI of Water 53 temperatures of the REMPI spectra were calculated by using the contour fitting method of PGOPHER. As mentioned in the previous section, H 2 O and D 2 O fragments can be detected in the 1 A 1 (000) and 1 A 1 (010) states by REMPI via the 1 B 1 state. For (H 2 O) 2 , the excess energy is 2497 cm -1 , which can populate H 2 O (000) J" ≤ 15. The H 2 O (010) state, which has an excess energy of ~900 cm -1 , can populate J" ≤ 8. For (D 2 O) 2 , the excess energy of 1390 cm -1 can populate the D 2 O (000) and (010) states up to J" ≤ 16 and 5, respectively. Different complications were encountered when detecting H 2 O and D 2 O using REMPI. The 1 B 1 excited state of H 2 O is more predissociative, which prevents us from detecting certain high rotational levels and makes the detection scheme more dependent on the excitation conditions. For this reason, the H 2 O REMPI spectra have lower signal-to-noise ratio compared to that of D 2 O, which is less predissociative. On the other hand, the D 2 O spectra are more congested due to smaller spacings between rotational levels. This limits our ability to select single transition for imaging. Relevant rotational constants and predissociation parameters are listed in Table 3.6. 23 A similar method is used for the detection of the H 2 O fragments produced from the vibrational predissociation of (H 2 O) 3 . In this case, the excess energy of ~900 cm -1 can populate the H 2 O fragment in the ground vibrational state and J" ≤ 8. A REMPI cell was built with a heating element to study the REMPI spectra of water at various temperatures. The design of the cell and the H 2 O spectrum are presented in Appendix A. Experimental Techniques REMPI of Water 54 Table 3.6 Spectroscopic constants for H 2 O and D 2 O. 23-25 Constant/ Parameter (in cm -1 )H 2 OD 2 O 1 A 1 (000) State A 27.8310(24) 15.347(10) B 14.5271(19) 7.2543(45) C 9.2763(16) 4.8308(32) Δ K x 10 3 27.368(50) 7.361(42) Δ JK x 10 3 -5.201(42) -2.84(13) Δ J x 10 3 1.252(15) 0 δ K x 10 3 1.348(49) 0 δ J x 10 3 0.5126(56) -0.0720(44) 1 A 1 (010) State Origin 1594.643 1178.365 A 31.0683 16.6362 B 14.7023 7.3390 C 9.1328 4.7940 Δ K x 10 3 49.6746 12.8373 Δ JK x 10 3 -6.1850 -1.3192 Δ J x 10 3 1.4043 0.2865 δ K x 10 3 3.1454 -0.02014 δ J x 10 3 0.5884 -0.1292 1 B 1 (000) State Origin 80625.068(96) 80751.681(51) A 25.385(53) 14.6983(85) B 12.529(11) 6.3378(36) C 8.5274(44) 4.4197(32) δ J x 10 5 — -6.84(84) ω 0 1.5(0.18) 1.00(0.08) ω a 0.9(0.22) 0.40(0.07) Experimental Techniques Velocity Map Imaging 55 3.4 Velocity Map Imaging Velocity map imaging is a powerful method for studying momentum distributions of free particles, scattering and dissociation products. This method can be combined with the highly sensitive and state-selective REMPI detection (Section 3.3) to study state-resolved photochemical reaction dynamics. The ion imaging method was developed by Chandler and Houston in 1987 for studying photochemical reactions. 26 The resolution of this imaging technique was greatly improved by Eppink and Parker in 1997, who replaced the conventional grid electrodes with an electrostatic ion lens with open electrodes. 27 The electric field arrangement allow ion particles with the same initial velocity vector that originate at different initial distances from the ion lens axis to arrive at the same point on the detector. Therefore, the effect of the finite size of interaction volume of the laser and molecular beam cross section is eliminated. This technique is commonly called velocity map imaging and is widely used today. Velocity distributions measured by velocity map imaging provide much information about the dissociation process, including speed and angular distributions of the products, product branching ratios and recoil anisotropy parameters (β), orientation and alignment and pair-correlated energy distributions of cofragments. Using conservation of energy and momentum, this method allows determination of dissociation energies with spectroscopic accuracy. Moreover, it can also give insight into isomerization pathways and fragmentation mechanisms. Velocity map imaging can also be used to detect photoelectrons. It is a useful Experimental Techniques Velocity Map Imaging 56 method to study cation vibrational structure and obtain information about the nature of intermediate excited states, including conical intersection, and resonances of rovibronic states. Nonadiabatic transitions and/or isomerization can affect photoelectron images, reflecting underlying dynamics. 28,29 In the velocity map imaging mode, laser radiation photodissociates molecules in the molecular beam and the fragments are ionized by the same or another laser radiation utilizing REMPI. The fragment ions are accelerated by the electric fields generated by the ion optics into the TOF tube toward the position sensitive detector—a MCP coupled to a phosphor screen. Figure 3.12 shows a general scheme of velocity map imaging in a coordinate system where the x and y axes are parallel to the detector plane and z is perpendicular to it. The molecular beam is along the z axis and crossed by the dissociation and ionization laser beams. Two ions at different initial spatial position (red dots) due to the overlap of the beams but have the same velocity vector, , are accelerated and mapped on to the same spot (green dot) on the detector by the ion optics. The event (x-y position of the green dot) is recorded by a CCD camera using event counting. The distance and angle of each ion spot from the center of the image are and , respectively. The two-dimensional projection of the Newton spheres on the detector is formed from ion fragments with different velocities () and ang les (). The distance of the spot from the center of the image, radius () in pixel, is proportional to . A schematic diagram of the photofragment imaging approach to measuring projections of the Newton sphere is shown in Figure 3.13. Experimental Techniques Velocity Map Imaging 57 Figure 3.12 General scheme of velocity map imaging. Two ions (red dots) formed at a different initial space with a same velocity vector, v, are accelerated and mapped to a same spot (green dot) on the detector by a specially designed ion optics system field, E. Conservation of energy and momentum relates the ion velocities of the detected fragments to their cofragments. For example, in Figure 3.13, the parent molecules formed in a molecular beam are dissociated by laser radiation. Fragments in selected quantum state are ionized by UV laser radiation and the cofragments can be in the allowed quantum states, v i , j i ; v j , j j ; v k , j k . Conservation of energy and momentum dictate that the corresponding excess energy available for translation decreases when the internal energy of the cofragment decreases. The Newton sphere is smaller when the cofragment is in a quantum state with high internal energy. The images were reconstructed to give the three-dimensional velocity distributions using centroiding and the basis set expansion (BASEX) Abel transform Experimental Techniques Velocity Map Imaging 58 method. 30 The speed distribution P(v) is obtained from the velocity distribution I(v, θ) (count) by integration over all angles. The speed is proportional to the radius of the image and inversely proportional to the square root of the mass (m) of the charged particle (detected fragment). Figure 3.13 Schematic diagram of the photofragment imaging approach to measuring the projections of the Newton sphere. (a) Photodissociation of molecules in a molecular beam gives rise to the Newton sphere. (b) Conversion of molecules making up the Newton spheres into ions by laser ionization. (c) Projection of the ion spheres onto a two-dimensional detector. (d) Mathematical transformation of the two-dimensional image back to the three dimensional data using BASEX reconstruction method. The data is then converted to speed distributions. The center-of-mass (c. m.) translational energy of the charged particle does not depend on and is proportional to the square of : = 2 Eq. 3.3 where α is the magnification factor. α is directly proportional to the voltages applied to the electrostatic lens. It is also independent of the mass, m. In order to calibrate Experimental Techniques Velocity Map Imaging 59 the imaging system, α is determined by imaging molecules with well-known translational energy release. The center-of-mass translational energy distribution of the charged particles can be plotted using Eq 3.3 with the corresponding Jacobian as: = = () 2 Eq. 3.4 The center-of-mass translational energy distribution of the two products can be plotted using = − Eq. 3.5 where M is the mass of the parent molecule. The speed can be calculated from the experimental radius using the following relation between v and r: = 2 Eq. 3.6 Using the Jacobian = 2 , the speed distribution P(v) in velocity units can be obtained from the speed distribution in pixels: = =() 2 Eq. 3.7 Experimental Techniques Technical Challenges in Studying Water Clusters 60 3.5 Technical Challenges in Studying Water Clusters The major technical challenges for studying water clusters arise from: (1) Water background in the vacuum chamber, (2) IR absorption of atmospheric water before the laser beam entering the vacuum chamber, (3) low detection efficiency of the water fragments, and (4) difficulty in optimization of sample conditions. The issue of background water in the vacuum chamber can be minimized by cryopumping the interaction chamber during data acquisition and baking the chambers periodically (see Section 3.5.1). The issue of IR absorption of atmospheric water was resolved by installing a dry box along the laser beam path (see Section 3.5.2). The detection of water fragments by REMPI is challenging due to the predissociative nature of the electronically excited states of the water molecules. The detection efficiency was improved by optimizing laser focusing conditions (see Section 3.5.3). The water dimer and trimer productions were carefully optimized to maximize the cluster size of interest and minimize the formation of higher clusters (see Section 3.5.4). 3.5.1 Minimizing Background Water in the Vacuum Chamber The interaction chamber was modified to include two cryopumping systems cooled by liquid nitrogen traps in order to reduce background water in the vacuum chamber. The system consists of a “cold-finger” connected to the outside of the chamber through a 1/4" inch stainless steel tubing. The initial design of the “cold- finger” was intended for use with cold air and consisted of a large stainless steel Experimental Techniques Technical Challenges in Studying Water Clusters 61 sheet attached to a looped stainless steel tubing. However, pumping cold air through the “cold-finger” was found to be inefficient in reducing background water. The system was then modified to pump liquid nitrogen and the design is shown in Figure 3.14. A Styrofoam liquid nitrogen reservoir was installed. Copper sheets were added to the “cold-fingers”, and installed diagonally across the chamber to increase the overall cooling surface area. The first cryopump reduces the background water signal by a factor of 5 in about 20 minutes. The second cryopump reduces the background further by a factor of 2. Figure 3.14 The “cold-finger” used for condensation of background water in the vacuum chamber. Figure 3.15 shows comparisons of the background water REMPI scan without cryopumping, with one cryopump and with both cryopumps. A clear increase in background water signal was observed when the cryopumping system operated longer than 8 hours. It was due to (1) saturation of water ice on the cold surface and (2) solidification of atmospheric water in the cryopumps that caused Experimental Techniques Technical Challenges in Studying Water Clusters 62 clogging. Dry air is pumped through the system after each experiment to remove water. Additionally, the chamber was baked for 2 - 4 days every 1 - 3 weeks in order to remove background water and hydrocarbons in the vacuum chamber. The chambers were insulated using fiberglass sheeting and baked by heating tapes. The temperature of each chamber was kept at 80 - 100 o C, monitored separately by a thermocouple controller (Auber Instruments, SYL-2342). Before baking the nozzle was removed and the chamber was evacuated. After baking, the system was passivated with HCl or H 2 O. Figure 3.15 Comparison of background water signal without cryopumping, with one and with two cyopumps. 3.5.2 IR Absorption of Atmospheric Water The IR frequency range of interest in this experiment coincides with the IR absorption of the atmospheric water. This caused a drop in the IR laser power after E th b ex a at to N F ab fr F ab Experimenta he laser bea ox was ins xperiments ir dryer (P tmospheric o 9 mJ/puls Note that sea igure 3.16 In the bsorption o requency by or the (D 2 O bsorption u al Technique am passed t stalled arou s. The dry ai Parker Bals c water incr se) in ~45 m aling the dry Power of IR e (H 2 O) 2 an of atmosph y sending th O) 2 experim using a phot es through the und the la ir was gener ston 64-02) reased from minutes wh y air box is R radiation nd (H 2 O) 3 ex eric water he laser bea ents, the OP toacoustic c Technica 63 e air before aser path a rated by sen ). The IR l m its lowest hen the box crucial for p over time w xperiments was used f am through PO/OPA las ell. 6 al Challenge the vacuum and purged nding ~46 p laser powe value to th x was purge proper purg when the bo described for calibrat air and mo ser was calib es in Studyin m chamber. d with dry psi air throu r at the fr he maximum ed by dry a ging. x is purged in this Diss tion of the onitoring the brated by s ng Water Clu An acrylic air during ugh a memb requency of m (~ 2 mJ/p ir (Figure 3 by dry air. sertation, th OPO/OPA e power cha canning the usters glass g the brane f the pulse 3.16). he IR laser ange. e HCl Experimental Techniques Technical Challenges in Studying Water Clusters 64 3.5.3 Optimization of Water Fragment Detection Efficiency The electronically excited states of water are predissociative and therefore the signal-to-noise ratio of the water REMPI spectrum is very low. In order to overcome predissociation and obtain reasonable signal-to-noise ratio of the water REMPI spectrum, a high UV laser beam fluence is needed. A 20 cm f. l. focal lens was used for the majority of the experiments for focusing the UV laser beam. However, the fluence generated by using the 20 cm f. l. focusing lens with the maximum UV laser power (~1 mJ/pulse into the chamber) is insufficient for detecting the internally excited water fragments. Therefore, an expanding lens (-100 cm f. l.) was used before the focusing lens for tighter focusing. The distance of the expanding lens (negative lens) away from the focusing lens (positive lens) determines the laser fluence. The farther the expanding lens is away from the focusing lens, the tighter the focusing and thus higher fluence is achieved. However, tight focusing can cause space charge issues that reduce the resolution of the images. Another complication of detecting water comes from the spectral congestion. Although high fluence is needed to overcome predissociation, it can cause power broadening and thus overlap of multiple nearby transitions. Therefore, the position of the expanding lens was carefully optimized to maximize signal-to-noise ratio and minimize space charge and power broadening effects. In detecting H 2 O from HCl-H 2 O vibrational predissociation, the focusing conditions were optimized individually for each spectrum and image. The best condition was obtained with ~0.4 mJ/pulse UV power and the -100 cm f. l. Experimental Techniques Technical Challenges in Studying Water Clusters 65 expanding lens placed 60-90 cm before the 20 cm f. l. focusing lens. These were the best conditions for the majority of the spectra and images, except the J KaKc = 4 1,3 ← 4 1,4 transition. The peak was clearly resolved under high UV power and therefore the maximum UV laser power (1.0 mJ/pulse) was used for imaging using the H 2 O J" KaKc = 4 1,4 level. In the (H 2 O) 2 , (D 2 O) 2 and (H 2 O) 3 experiments described in this Dissertation, due to very low signal-to-noise ratio, the expanding lens was placed 137 cm before the focusing lens for higher UV fluence. 3.5.4 Optimization of Molecular Beam Conditions, Laser Conditions, and Laser Timings The optimization of the molecular beam conditions was needed for maximizing the formation of the cluster size of interest. The optimization of laser fluence and timings was necessary to maximize the excitation of the species of interest and the detection of its photofragments. The molecular beam cooling conditions were adjusted by optimizing the carrier gas mixture (helium, neon, argon), backing pressure, nozzle temperature and nozzle voltage. The optimization of IR-UV laser and nozzle-UV laser timings were obtained by scanning the time delay controlled by the delay generators to find the timing where the maximum photofragment signals produced from the species of interest were observed. Firstly, conditions were set to optimize the detection of the monomer via REMPI. In this study, the H 2 O and D 2 O were detected by 2 + 1 REMPI via the 1 B 1 (000) ← 1 A 1 (000) band. The molecular beam temperature and the UV laser Experimental Techniques Technical Challenges in Studying Water Clusters 66 frequency calibration can be determined by fitting the REMPI spectra to simulations using known rotational constants. As shown in Figure 3.17 a, the H 2 O molecules were cooled in the molecular beam to 14 K (rotational temperature). The time profile of the nozzle pulse carrying the monomer is observed by scanning the nozzle-UV laser time delay while monitoring the highest populated REMPI transition (low J" rotationally cold peak) of the monomer. Figure 3.18 a shows the nozzle-UV laser time delay scan monitored by the H 2 O monomer in the molecular beam. In addition, the intensity of the background water in the vacuum chamber can be investigated by scanning the UV frequency over the range of REMPI without turning on the nozzle. The background water exhibits ambient rotational temperature (Figure 3.18 b). Figure 3.17 2 + 1 H 2 O REMPI spectra of the a) molecular beam and b) background in the vacuum chamber (nozzle off) obtained by scanning over the the 1 B 1 (000) ← 1 A 1 (000) band. Black and red curves are the experimental measurements and PGOPHER simulations, 8 respectively. The rotational temperatures were obtained from the PGOPHER contour fitting. Experimental Techniques Technical Challenges in Studying Water Clusters 67 Attempts were made to detect enhancement of the REMPI signal with the addition of the IR laser after the REMPI detection scheme was established for the monomer. The frequency of the IR laser was tuned to a vibrational mode of the cluster of interest to induce vibrational predissociation. The excess energy was estimated (see Section 3.2). The energetically forbidden rotational levels were excluded in the PGOPHER simulation and the rotational temperature was estimated. The IR laser was set to ~70 ns before the UV laser to allow the clusters to dissociate before ionization. The nozzle-UV laser time delay scan with alternating “IR on” and “IR off” of the fragment ions showed enhancement (IR on – IR off) produced from the vibrational predissociation of clusters. Figure 3.18 b shows an example of the nozzle-UV time delay scan from the vibrational predissociation of (H 2 O) 3 and detecting the H 2 O monomer at the 2 0,2 ← 3 2,1 REMPI transition. The delay time that produced the largest enhancement was selected. Figure 3.18 Nozzle-UV laser time delay scans obtained by monitoring H 2 O J' KaKc ← J" KaKc = a) 2 2,0 ← 1 0,1 and b) 2 0,2 ← 3 2,1 (black curve), and the same level produced in the vibrational predissociation of (H 2 O) 3 (red curve). The maximum enhancement is at 392 μs. Experimental Techniques Technical Challenges in Studying Water Clusters 68 If no enhancement was observed, other REMPI transitions or other IR frequencies were used. When enhancement was seen, the IR-UV laser timing was optimized. Figure 3.19 shows an example of a scan of the delay between the IR and the UV laser firing times. The IR-UV delay timing was rather insensitive to the types of clusters. Therefore, the IR laser was set to fire 70 ns before the UV laser for all the experiments described in this Dissertation. Figure 3.19 IR-UV time delay scan by monitoring D 2 O (major contribution from J" KaKc = 13 1,12 ) upon vibrational predissociation of (D 2 O) 2 . The nozzle-UV time delay was usually the first condition optimized because of the short time required to scan the beam pulse duration. After enhancement was found in the scan, the optimum time delay was set for REMPI spectra acquisition. Then, UV laser conditions were optimized (see Section 3.5.3). Finally, fragment yield IR spectra were collected (see below). High IR fluence caused saturation effects and Experimental Techniques Technical Challenges in Studying Water Clusters 69 multiphoton absorption. A typical IR spectrum has a full-width at half-maximum (FWHM) of ~5 cm -1 . Multiphoton absorption can be observed both in the IR enhancement spectra and the photofragment images. For multiphoton absorption, the IR spectra exhibit frequency independent enhancements, and the images show excessive population at high velocities, which exceed the estimated maximum E T . A vacuum distillation method was used to prepare water clusters. Unsuccessful attempts were made to create water dimers in the supersonic expansion by bubbling helium carrier gas through the room temperature liquid. 19 The overall concentration of water in the sample was limited by the vapor pressure of H 2 O and D 2 O at room temperature (24 Torr at 25 o C). Therefore, the nozzle was modified to include a heating option to generate higher H 2 O concentrations. Heating tapes covering the nozzle and thermocouple were connected through an 8-pin electrical feedthrough to a variable transformer and a thermocouple controller, respectively. Heating the sample before the supersonic expansion gave inconsistent results. The best result was achieved at ~ 2% H 2 O in helium at a stagnation pressure of 1.5 atm at room temperature. In contrast, D 2 O did not show clustering issues at high backing pressure. Approximately 1.6% D 2 O in helium at a stagnation pressure of 2 atm at room temperature was used. Unsuccessful attempts were made to optimize (D 2 O) 3 production by using neon and argon as the seeding gases. There was a tendency to form higher clusters. In addition, high H 2 O concentrations and backing pressures tend to produce larger clusters as well. A similar observation was reported by Saykally and coworkers. 19 Experimental Techniques Technical Challenges in Studying Water Clusters 70 The optimization of the (H 2 O) 3 conditions was very challenging due to low signal-to- noise ratios. Therefore, the majority of the optimizations were accomplished in the imaging mode. Best results were achieved at ~1% H 2 O in helium at a stagnation pressure of 1.4 atm at room temperature. For (H 2 O) 2 , the combination of sample conditions and IR fluence turned out to be the most critical. Low IR fluence (20 cm f.l.; 2 mJ/pulse) was used for the excitation of the (H 2 O) 2 H-bonded OH stretch and monitoring H 2 O fragments in the ground vibrational state without contributions from higher clusters. When monitoring H 2 O fragments in the bending excited state, no effects due to larger clusters and multiphoton absorption were observed at high IR fluence (20 cm f.l.; 12 mJ/pulse). For the production of (D 2 O) 2 , the dimer formation was rather insensitive to the backing pressure of the sample. In addition increasing the IR fluence did not lead to an increase in the signal from larger clusters at the H-bonded OH stretch frequency. Therefore, high backing pressures and high IR fluences (20 cm f.l.; ~5 mJ/pulse) were used for these experiments. Low IR fluence (20 cm f.l.; 1 mJ/pulse) was used to prevent multiphoton absorption when scanning the fragment yield IR spectra. For (H 2 O) 3 , IR fluence was a sensitive optimization factor. Multiphoton absorptions and contributions from higher clusters were observed when a focusing lens was used. It may be due to the nearby hexamer band at the blue side of the (H 2 O) 3 H-bonded OH stretch band. 20 The best (H 2 O) 3 results were obtained with low IR fluence (no focusing lens; ~5 mJ/pulse). Experimental Techniques Image Fitting and Analysis 71 3.6 Image Fitting and Analysis In the studies of H-bonded clusters, the speed distributions of fragments produced by vibrational predissociation were obtained from reconstructed images collected in the ion imaging mode. Fitting was accomplished by assigning a Gaussian-shaped curve to each rotational levels of each cofragment vibrational state. The positions of these Gaussians were determined by conservation of energy, h ν IR + E rot (cluster) = D 0 + E vib,rot (mon) + E vib,rot (cofrag) + E T Eq. 3.8 where E rot (cluster) is the internal energy of the cluster estimated from fitting the IR spectra (Section 3.2), hν IR is the IR photon energy used to induce vibrational predissociation, E T is the measured center-of-mass translational energy (Section 3.4); and E vib,rot (mon) and E vib,rot (cofrag) are the rovibrational energies of the monitored fragment and the cofragment, respectively. The E vib,rot (mon) was defined by REMPI (Section 3.3) and E vib,rot (cofrag) was obtained from all energetically allowed rovibrational states of the cofragment. The position and intensity of each cofragment state are shown as a stick spectrum convoluted with the Gaussian profile (Eq. 3.9) to account for the experimental resolution. The Gaussian profile is given by − (− ) 2 2 2 Eq. 3.9 where x is the x-axis (in pixel), x i is the position calculated from Eq. 3.8 and converted to pixel, and σ is the width of the Gaussians. The FWHM of the Gaussians are obtained from fitting the images and by the conversion, Experimental Techniques Image Fitting and Analysis 72 2√2 2 ≈ 2.3548 Eq. 3.10 The positions of the Gaussians were shifted together by adjusting D 0 until both the observed structures and the maximum speed were well matched in all the images. The widths of the Gaussians were determined from experiments of vibrational predissociation of HCl-H 2 O in which the H 2 O fragments were monitored. 31 For the vibrational predissociation of HCl-H 2 O, the HCl and H 2 O fragments were detected independently and the same D 0 was obtained. Figure 3.20 shows the relative speed distribution in HCl-H 2 O predissociation obtained by detecting the H 2 O fragment at J" KaKc = 4 1,4 and the simulation. Figure 3.20 Speed distribution of a reconstructed HCl-H 2 O image obtained by detecting H 2 O J" Ka,Kc = 4 1,4 fragment. Blue, black and red curves correspond to the reconstructed image, Gaussians and the sum of all Gaussians, respectively. The numbers correspond to the J" levels of the HCl cofragment. When the H 2 O fragment was detected, a well-resolved rotational distribution of the HCl cofragment was obtained due to the large spacings of the HCl rotational energy Experimental Techniques Image Fitting and Analysis 73 levels. This experiment is ideal for calibration of the imaging setup and determination of imaging resolution. The width of the Gaussian was determined from fitting the structure in the image. A FWHM of ~8 pixels (or 42.4 m/s) was obtained. Since each rotational level, especially those at high J"s is well-resolved, the intensity of the Gaussians were adjusted individually. However, the rotational levels of the water molecules are very congested. Therefore, the intensities of the Gaussians cannot be adjusted unambiguously to fit the image when water (monomer or dimer) fragments are the cofragments. Thus, a fitting model was needed. As shown in Figure 3.21, it is evident that the vibrational predissociation of HCl-H 2 O gives populations that decrease as the translational energy release increases. This result agrees with the Ewing propensity rule. 32,33 Speed distributions of multiple images were fit using polynomial functions. Although the fits were good, the best fit parameters were different for the images recorded by detecting fragments in different rovibrational transitions. When an exponentially decaying function as a function of increasing translational energy release was used, the general profiles of the images fit fairly well. In addition, only one fitting parameter was used. The fitting function is defined as = − Eq. 3.11 where C is a fitting parameter and E T is the total center-of-mass translational energy. Whenever possible, the Gaussians were adjusted to account for state-to-state fluctuations after simulations were generated by using Eq. 3.11. Experimental Techniques Image Fitting and Analysis 74 For the cases of H-bonded dimers and trimers, the reconstructed images were fit in pixel space and converted to speed distributions using Eq. 3.7. It is beneficial to fit the images in pixel space instead of the energy space to improve the visibility of the structures of the images. Figure 3.21 shows the comparison of fitting the images in a) pixel and b) energy space. For simplicity, the images and simulations shown in the rest of this section are in units of pixels. Images recorded by detecting fragments in different rovibrational states (thus different , ( ) that result in different E T ) were fit simultaneously. D 0 was adjusted to shift the simulations horizontally until both the maximum speed and the structures were well matched. The final value of D 0 was derived from weighted averages of all the best fits for the images. Figure 3.22 shows an example of fitting multiple images, and using different D 0 values. Note that ( ) was not included for the fits shown in this section. Experimental Techniques Image Fitting and Analysis 75 Figure 3.21 Speed distributions of reconstructed images produced in vibrational predissociation of (H 2 O) 2 by detecting H 2 O fragments in the H 2 O (010), J" KaKc = 3 2,1 state plotted in (a) pixel and (b) energy (α pixel 2 ) space. Blue and red curves correspond to the reconstructed image and the total simulation, respectively. Gaussians in black correspond to energetically allowed rotational levels of the H 2 O (000) cofragment. E Experimenta al Technique es 76 Image Fitt ting and Ana Figure 3.22 A matrix of speed distributions derived from reconstructed images of the H 2 O (010) fragment with different J" KaKc produced in the vibrational predissociation of (H 2 O) 2 plotted in pixels (velocity in m/s = 5.19 x pixels). The positions of Gaussians used in the simulation were determined by using the known H 2 O rotational energies and the fit parameter D 0 . Each alysis column corresponds to (H 2 O) mon (010) J" KaKc shown at the top and each row shows the change of the D 0 parameter. The range of D 0 was estimated from fitting all images simultaneously and the final value of D 0 was calculated from the weighted average of all images. Each image was fit individually within the range to obtain the best D 0 with an estimated uncertainty. Experimental Techniques Image Fitting and Analysis 77 Although not unique, each Gaussian height can be adjusted to better fit the images when only one set of Gaussians is possible for the cofragment. Figure 3.23 shows an example of such fitting, which reproduces very well the observed speed distribution. Figure 3.23 Speed distribution of a reconstructed image produced in vibrational predissociation of (H 2 O) 2 by detecting fragments in the H 2 O (010), J" Ka,Kc = 3 2,1 level (blue curve). Each Gaussian height was adjusted to obtain the best fit. Total simulation is shown in red. Multiple sets of Gaussians have to be used when: (1) the selected REMPI peak consists of an overlap of several rotational transitions, or (2) more than one vibrational state of the cofragment are allowed. Images of type (1) provide information on the relative contribution of rotational transitions of the detected fragment. Figure 3.24 shows examples of D 2 O (000) images produced in the vibrational predissociation of (D 2 O) 2 . The selected REMPI enhancement peak used for imaging includes overlapping of transitions due to spectral congestion. As shown Experimental Techniques Image Fitting and Analysis 78 in Figure 3.24, although low J" transitions have to be considered to account for the high speed components (long tail), it is the high J" transitions that contribute predominantly to the structures of the images. Images of type (2) reveal information regarding the rovibrational populations of the cofragments. Figure 3.25 shows examples of fitting images obtained from the vibrational predissociation of (H 2 O) 2 by detecting the H 2 O (000) fragment. In this instance, the H 2 O cofragment is energetically allowed in both the (000) and (010) states. The images cannot be fit either by (000) or (010) states alone in the cofragment (first and second rows) is clear from the second row of the images that the (010) state dominates the structures at low E T . However, to account for high E T features and some structures at low E T , cofragments in the (000) state have to be included. The ratio of the two sets of Gaussians was adjusted for best fit. These images reveal that upon vibrational predissociation of (H 2 O) 2 , two channels are open: (1) (000) + (000) and (2) (000) + (010). Both channels were indeed observed and their ratio was estimated from the simulations. Note that in the case of the dimer, it is important to account for the rotational constants difference caused by the anharmonic oscillator, i.e, the spacings of the rotational levels of H 2 O (000) and H 2 O (010) are different. For water cofragments, the rotational population distributions as a function of K a " and K c " quantum numbers were examined. In general, there is no strong preference for rotation over a specific principal axis of the water molecules. E F fr (D re co g le th o to co Experimenta igure 3.24 ragments w D 2 O) 2 . The b espectively. ofragment w reen curves In fitt evels of the he PGOPHE f rotational o very high onstants wo al Technique Speed distr with the indic blue and red . The purple when the de s are the tot ting H 2 O im (H 2 O) 2 cofr ER 8 program l constants rovibration ould be indi es ributions de cated J" KaKc d curves are e and green etected frag tal simulatio ages from ( ragment we m with know for the inte nal density o istinguishab 79 erived from produced in e the experi Gaussians c gment is in t on of each s (H 2 O) 3 → H 2 ere obtained wn rotation ermolecular of states, eff ble with our reconstruc n the vibrat imental data correspond the indicate et of Gaussi 2 O + (H 2 O) 2 d by genera nal constant r modes of ( fects of anha r experimen Image Fitt ted images tional predis a and total s d to rotation d levels. Th ians. dissociatio ating its ene ts. 14,34 Expe (H 2 O) 2 are i armonicity ntal resoluti ting and Ana of D 2 O (000 ssociation o simulation, nal levels of e purple an n, the rotat ergy levels u erimental va incomplete. in the rotat ion. alysis 0) of the nd ional using alues . Due ional E Experimenta al Technique es 80 Image Fitt ting and Ana Figure 3.25 A matrix of speed distributions derived from reconstructed images of H 2 O (010) fragment with different J" KaKc produced in the vibrational predissociation of (H 2 O) 2 . Each column corresponds to the (H 2 O) mon (000) J" KaKc level shown at the top and all the images were fit with D 0 of 1100 cm -1 . The first and second rows correspond to fitting the cofragment with only alysis the (000) and (010) states, respectively. The third row combines the cofragments in the (000) and (010) states with a ratio of 1:2. Experimental Techniques Dimer Simulations using PST 81 Due to very high rovibrational density of states of the (H 2 O) 2 cofragment and the lack of unique structures in the images, simulations of (H 2 O) 3 images using Eq. 3.11 and various rovibrational populations gave equally good fits. Simulations were done by assuming that the (H 2 O) 2 cofragment was in the (1) ground vibrational state, (2) ground and fundamental intermolecular modes (all vibrational modes equally populated), and (3) ground and fundamental intermolecular modes, with vibrational modes scaled by , where C is a fitting parameter. 3.7 Simulations of Fragment Energy Distributions using Phase Space Theory 3.7.1 Dissociation of Dimers The description of phase space theory (PST) is presented in Chapter 2, and simulations of rotational distributions, REMPI spectra and velocity distributions using PST are discussed here. PST applies conservation of energy (Eq. 3.8) and angular momentum: = + +() Eq. 3.12 where , and are the angular momentum vectors of the parent molecule (water dimer or trimer), monomer fragment and cofragment (either monomer or dimer), respectively, and L is the orbital angular momentum vector. No constraints due to centrifugal barriers and impact parameters are included in the calculations. J(cluster) and j(mon) are obtained from the IR and REMPI spectra, respectively. j(cofrag) includes all energetically allowed rotational levels of the cofragment. The calculation of all possible orbital angular momenta (L) Experimental Techniques Dimer Simulations using PST 82 in a three-dimensional space using Eq. 3.12 can be simplified by placing the vectors in a two-dimensional space and defining the vector ω: = +() Eq. 3.13 where from angular momentum vector addition we get: , = | − | , | −() | + 1, … , + −1, +() Eq. 3.14 =+ Eq. 3.15 The energetically allowed pairs of j(mon) and j(cofrag) are calculated first and ω is obtained from the allowed angular momentum combinations (Eq. 3.14) for each pair. According to PST the probability of producing a given pair of j(mon) and j(cofrag) is proportional to the numbers of L states. N is obtained by counting all the allowed L states in Eq 3.15 by using the same method, as described by Eq. 3.14: (), = |() − |, |() − | + 1,…,() + − 1,() + Eq. 3.16 For simplicity, a phase space diagram of L as a function of ω can be constructed with boundaries of = | ( ) − ( )| and = ( ) +() Eq. 3.17 N can then be easily calculated by integrating the phase space within the boundary of a given ω (pairs of j(mon) and j(cofrag)) Experimental Techniques Dimer Simulations using PST 83 max max min min () |( ) | || 1 Jcluster Jcluster Nd           Eq. 3.18 Examples of simulations for the vibrational predissociation of (D 2 O) 2 are shown below. J(dimer) states of (D 2 O) 2 in the range 3 - 5 are most likely to be excited, and conservation of energy (Eq. 3.8) demands that j(mon) ≤ 5 (or j kakc ≤ 5 1,4 ) and j(cofrag) ≤ 5 (or j kakc ≤ 4 3,1 ) for D 2 O fragments. The rotational energies are slightly different for j(mon) and j(cofrag) due to the anharmonicity of the bending excited state of the monomer. Note that water is an asymmetric top and thus different rotational levels with the same j are observed due to the projection of j on the a- and c-axes. Only the j quantum numbers are considered in the PST calculations. Figure 3.26 shows examples of phase space diagrams. The black lines show phase space diagram constructed with respect to different J(dimer). N is counted by integrating the phase space diagram of L vs. ω within ω min and ω max . The states excluded are forbidden by conservation of angular momentum. Figure 3.26 Phase space diagrams of L vs ω. a) For J(dimer) = 3, j(mon) = 2 and j(cofrag) = 3, the summation range is ω min = 1 to ω max = 5 and N = 29. b) For J(dimer) = 5, j(mon) = 4 and j(cofrag) = 2, the summation range is ω min = 2 to ω max = 6 and N = 43. Experimental Techniques Dimer Simulations using PST 84 Figure 3.27 shows an example of D 2 O (010) J" KaKc = 1 1,0 velocity distribution simulated by phase space calculation. In this case, the pair-correlated distribution was calculated by summing the number of allowed L states for each energetically allowed j(cofrag) correlated with a specific j(mon) [e.g. J" KaKc (D 2 O) = 1 1,0 ]. Figure 3.27 Velocity distribution of reconstructed image produced in vibrational predissociation of (D 2 O) 2 and detecting the D 2 O fragments in the H 2 O (010), J" Ka,Kc = 1 1,0 state (red curve). The Gaussians (black curves) are generated from conservation of energy and angular momentum using PST. The integration of all Gaussians gives blue curve for comparison to the experimental image. Experimental Techniques Trimer Simulations using PST 85 3.7.2 Dissociation of the Water Trimer For (H 2 O) 3 → H2O + (H 2 O) 2 , the excess energy E Excess ~900 cm -1 (excite OH stretch at 3536 cm -1 , D 0 = 2640 ± 140 cm -1 before internal energy correction, E excess = 896 cm -1 ) allows the fundamental, overtones and combination bands of all six intermolecular modes of the (H 2 O) 2 fragment to be populated. Simulations using PST are accomplished in the following sequence of steps (details will be discussed later): 1. Calculate the available energy (E avail , which is also the maximum c.m. translational energy, E T,max ) for (H 2 O) 2 rovibrational and c.m. translational energy distributions (i.e., for detecting H 2 O (000) J" KaKc = 3 2,1 , E avail = 3536 – 2640 – 212 = 684 cm -1 ). 2. Calculate the vibrational density of states up to E avail using the Beyer- Swinehart algorithm. 3. For each D 0 value and each vibrational energy scaled by the number of states at the specific energy, examine the pair-correlated rotational distribution of the (H 2 O) 2 cofragment by counting the allowed number of orbital angular momentum states L. Vary D 0 in the range 2000 ≤ D 0 ≤ 3000 (or any reasonable range and step size) Vary 0 ≤ ν ≤ E avail Vary 0 ≤ j(cofrag) ≤ j(cofrag) max Calculate N for each pair of j(mon) and j(cofrag) Multiply N by the number of vibrational states at the energy ν. Experimental Techniques Trimer Simulations using PST 86 4. To determine the vibrational energy distribution in (H 2 O) 2 , integrate all N for each ν. For the (H 2 O) 2 rotational distributions or c.m. translational energy distributions, populations result in the same E rot or E T are gathered and integrated. Note that rotational levels are quantized and energy distributions are not continuous. Therefore, the population distributions can be converted directly to speed space, convoluted with Gaussian profiles and compared to the measured speed distributions. However, because of the classical nature of the trajectory calculations, approximation has to be made in order to compare PST to the quasiclassical trajectory (QCT) calculations (see Section 3.7.2.2). All QCT calculations used for comparison in this Section are obtained from hard constraint on the zero point energy of the fragments (see Chapter 6 for details). 3.7.2.1 Angular Momentum Constraints on Rotational Populations Due to the low rotational temperature (14 K) molecular beam, the large rotational density in states of the (H 2 O) 2 fragments and the low j(mon) selected for imaging, varying different J(cluster) [rotational quantum number of (H 2 O) 3 ] in the PST calculations does not lead to a change in the overall distributions. Therefore, for simplicity, J(cluster) = 0 is used. Instead of constructing a phase space diagram (L vs. ω) and integrating L over ω min and ω max , the angular momentum quantum numbers of the fragments are examined and the number of L states is counted directly. Explicitly, all the allowed Experimental Techniques Trimer Simulations using PST 87 j(cofrag)’s are calculated and compared to j(mon), and the population of a specific pair of j(mon) and j(cofrag) is defined as 2j + 1, where j is the smallest value of the pair. For example, for j(mon) = 3 and j(cofrag) = 5, the allowed L states are | j(mon) - j(cofrag)|, | j(mon) - j(cofrag) +1|, …, | j(mon) + j(cofrag) - 1|, | j(mon) + j(cofrag)|, which gives L = 2, 3, 4, 5, 6, 7, 8 and N = 7. In this case, N = 2 j(mon) + 1 = 7. For j(mon) = 3 and j(cofrag) = 1, L = 2, 3, 4 and N = 2 j(cofrag) + 1 = 3. The number of orientation that the orbital angular momentum vector can assume is limited by the smallest value of the rotational quantum number of the fragments. No additional restriction is added to the total orbital angular momentum for PST calculations. Because of the high vibrational density of states at high energies, the populations with low translational energy are dominated by states with high vibrational and low rotational energies (instead of high rotational and low vibrational energies in the (H 2 O) 2 cofragment). Therefore, limiting the maximum allowed J"(cofrag) does not change the energy distributions significantly. 3.7.2.2 Treatment of Rotational Quantum Numbers of an Asymmetric Rotor Water molecules are an asymmetric top molecule, thus the quantum number J KaKc , is conveniently used to describe the rotational levels. In the PST calculations, only the J quantum number is considered for all combinations of K a and K c quantum numbers. For instance, for J = 2, there are a total of five (2J + 1) levels— 2 0,2 , 2 1,2 , 2 1,1 , 2 2,1 , 2 2,0 . All energetically allowed levels are included in the simulations and j(mon) = 2 is used for counting N. For comparison with the QCT calculations, because the Experimental Techniques Trimer Simulations using PST 88 QCT calculations only treat J quantum numbers, all the J KaKc (mon) levels calculated by PST for each J are summed for direct comparison. For example, when comparing the energy distributions calculated by PST and QCT for J(mon) = 2 – 4, energy distributions calculated by PST for J KaKc (mon) for J’s in the range 2 – 4 are summed. There are a total of 21 levels for J(mon) = 2 – 4 (J = 2, 3, 4 have 5, 7, 9 levels, respectively). The pair-correlated vibrational, rotational and c.m. translational energy distributions for all 21 J KaKc (mon) levels are calculated using PST and summed together to derive the energy distributions that correspond to the QCT calculations. 3.7.2.3 Comparison of Speed Distributions Simulated by PST and Quasiclassical Trajectory Calculations As mentioned previously, the pair-correlated vibrational and rotational distributions of the (H 2 O) 2 cofragments and the c.m. translational energy distributions can be obtained from PST calculations. To compare with the measured speed distributions, the pair-correlated c.m. translational energy distributions are converted to speed space and convoluted with Gaussian profiles. Best fit D 0 is obtained by fitting the overall profile of the images. Figure 3.28 shows an example of a measured speed distribution obtained by monitoring J" KaKc = 2 2,1 and its comparison to a PST simulation using D 0 = 2640 cm -1 . E F p cu m e co fr le Experimenta igure 3.28 redissociati urve). The r To co measured sp nergy) usin omparison ragment in evels. al Technique 8 Speed dis ion of (H 2 O red curve sh ompare the peed distri ng Eq. 3.6 of the mea the J" KaKc = es stribution o O) 3 measur hows the sim e measured butions are and the asured velo = 3 2,1 level a 89 of reconstru red by dete mulation ob d speed di e converted Jacobian fa ocity distrib and the QC T ucted imag ecting H 2 O btained by P istributions d to the en actor Eq. 3 bution obta CT calculatio Trimer Simul ge produced (000), J" Ka, PST calculat to QCT c nergy spac 3.7. Figure ined by de ons where lations using d in vibrat ,Kc = 2 2,1 (b ion. calculations, ce (translat 3.29 show tecting the J(mon) = 2 g PST ional black , the ional ws a H 2 O 2 – 4 E F im H d 3 ca ca d ro a b A ca Experimenta igure 3.29 mage produ H 2 O (000), J" istribution 3.7.2.4 As m alculations alculations, irectly. In t ounded to pproximati in size can A bin size s alculations al Technique Center-of-m uced in vibra " Ka,Kc = 3 2,1 ( calculated b Compar Calculat mentioned are continu where ener this case, d a given int on is valid a be used for similar to when comp es mass transla ational pred black curve by QCT for J rison of PS tions previously, uous (not qu rgy is quant data binnin terval and t as long as t r fast simula the QCT c paring the Q 90 ational ener dissociation e). The red c J mon = 2 – 4. ST and Qu , the ener uantized). T tized, canno g method i the populat the bin size ations, as it alculations QCT to the P T rgy distribu n of (H 2 O) 3 a curve shows uasiclassic rgy distrib Therefore, t ot be compa is applied, tions are in is sufficien requires m (6 – 10 c ST calculati Trimer Simul ution of reco and measure s the transla cal Traject utions obt the direct ou ared to the Q in which th ntegrated ac ntly small. In much less co cm -1 ) is us ions (Figure lations using onstructed ed by detec ational ener tory tained by utput of the QCT calcula he energies ccordingly. n addition, l mputation ed for the e 3.30). g PST ting rgy QCT e PST tions s are This large time. PST Experimental Techniques Trimer Simulations using PST 91 As shown in Figure 3.30 b and c, that the PST calculations give a similar results to the QCT calculations when the density of states of the specific degrees of freedom is high (e.g. translation and rotation). However, there is a discrepancy for the vibrational distribution (Figure 3.30 a), because the energy distributions from the QCT calculations have not been quantized (Gaussian binning is the common technique used in QCT calculations, in which more weight is given to the populations that are closer to the allowed vibrational state). Experimental Techniques Trimer Simulations using PST 92 Figure 3.30 Comparison of a) (H 2 O) 2 vibrational, b) (H 2 O) 2 rotational and c) c.m. translational energy distributions, where H 2 O fragments are in J" = 2 – 4, obtained from QCT calculations and PST calculations. Experimental Technique References 93 Chapter 3 References (1) Zyrianov, M. Photoinitiated Decomposition of HNCO, University of Southern California, 1998. (2) Dribinski, V. Photoelectron and Ion Imaging Studies of the Mixed Valence/Ryberg Excited States of the Chloromethyl Radical, CH 2 Cl and the Nitric Oxide Dimer (NO) 2 , University of Southern California, 2004. (3) Potter, A. B. Ion Imaging Studies of the Spectroscopy and Photodissociation Dynamics of Chloromethyl Radical and Nitric Oxide Dimer, University of Southern California, 2005. (4) Parr, J. A. Imaging the State-Specific Vibrational Predissociation of Hydrogen- Bonded Complexes, University of Southern California, 2007. (5) Federov, I. Photoelectron and Ion Imaging Investigations of Spectroscopy, Photoionization, and Photodissociation Dynamics of Diazomethane and Diazirine, University of Southern California, 2009. (6) Rocher, B. E. Velocity Map Imaging of the State-Specific Vibrational Predissociation of Water-Containing Hydrogen-Bonded Complexes, University of Southern California, 2011. (7) Wrede, E.; Laubach, S.; Schulenburg, S.; Brown, A.; Wouters, E. R.; Orr-Ewing, A. J.; Ashfold, M. N. R. J. Chem. Phys. 2001, 114, 2629-2646. (8) PGOPHER 2010, a Program for Simulating Rotational Structure, Western, C. M., University of Bristol, http://pgopher.chm.bris.ac.uk. (9) Kisiel, Z.; Pietrewicz, B. A.; Fowler, P. W.; Legon, A. C.; Steiner, E. J. Phys. Chem. A 2000, 104, 6970-6978. Experimental Technique References 94 (10) Huneycutt, A. J.; Stickland, R. J.; Hellberg, F.; Saykally, R. J. J. Chem. Phys. 2003, 118, 1221-1229. (11) Odde, S.; Mhin, B. J.; Lee, S.; Lee, H. M.; Kim, K. S. J. Chem. Phys. 2004, 120, 9524-9535. (12) Shimanouchi, T. Tables of Molecular Vibrational Frequencies Consolidated Volume I; National Bureau of Standards, 1972. (13) Paul, J. B.; Provencal, R. A.; Chapo, C.; Petterson, A.; Saykally, R. J. J. Chem. Phys. 1998, 109, 10201-10206. (14) Fraser, G. T. Int. Rev. Phys. Chem. 1991, 10, 189-206. (15) Wang, Y.; Bowman, J. M. J. Chem. Phys. 2011, 135, 131101-131103. (16) Kalescky, R.; Zou, W.; Kraka, E.; Cremer, D. Chem. Phys. Lett. 2012, 554, 243- 247. (17) Ceponkus, J.; Uvdal, P.; Nelander, B. J. Chem. Phys. 2008, 129, 194306. (18) Ceponkus, J.; Uvdal, P.; Nelander, B. J. Phys. Chem. A 2008, 112, 3921-3926. (19) Paul, J. B.; Collier, C. P.; Saykally, R. J.; Scherer, J. J.; O'Keefe, A. J. Phys. Chem. A 1997, 101, 5211-5214. (20) Moudens, A.; Georges, R.; Goubet, M.; Makarewicz, J.; Lokshtanov, S. E.; Vigasin, A. A. J. Chem. Phys. 2009, 131, 204312-204311. (21) Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2010, 114, 9774-9781. (22) Ashfold, M. N. R.; Bayley, J. M.; Dixon, R. N. Chem. Phys. 1984, 84, 35-50. (23) Yang, C.-H.; Sarma, G.; ter Meulen, J. J.; Parker, D. H.; Buck, U.; Wiesenfeld, L. J. Phys. Chem. A 2010, 114, 9886-9892. Experimental Technique References 95 (24) Rothman, L. S.; Gordon, I. E.; Barbe, A.; Benner, D. C.; Bernath, P. F.; Birk, M.; Boudon, V.; Brown, L. R.; Campargue, A.; Champion, J. P.; Chance, K.; Coudert, L. H.; Dana, V.; Devi, V. M.; Fally, S.; Flaud, J. M.; Gamache, R. R.; Goldman, A.; Jacquemart, D.; Kleiner, I.; Lacome, N.; Lafferty, W. J.; Mandin, J. Y.; Massie, S. T.; Mikhailenko, S. N.; Miller, C. E.; Moazzen-Ahmadi, N.; Naumenko, O. V.; Nikitin, A. V.; Orphal, J.; Perevalov, V. I.; Perrin, A.; Predoi- Cross, A.; Rinsland, C. P.; Rotger, M.; Šime čková, M.; Smith, M. A. H.; Sung, K.; Tashkun, S. A.; Tennyson, J.; Toth, R. A.; Vandaele, A. C.; Vander Auwera, J. J. Quant. Spectrosc. Radiat. Transfer 2009, 110, 533-572. (25) Brunken, S.; Muller, H. S. P.; Endres, C.; Lewen, F.; Giesen, T.; Drouin, B.; Pearson, J. C.; Mader, H. Phys. Chem. Chem. Phys. 2007, 9, 2103-2112. (26) Chandler, D. W.; Houston, P. L. J. Chem. Phys. 1987, 87, 1445-1447. (27) Eppink, A. T. J. B.; Parker, D. H. Rev. Sci. Instrum. 1997, 68, 3477-3484. (28) Whitaker, B. J. Imaging in Molecular Dynamics. Technology and Applications; Cambridge University Press, 2003. (29) Suits, A. G.; Continetti, R. E. Imaging in Chemical Dynamics; American Chemical Society: Washington DC, 2001. (30) Dribinski, V.; Ossadtchi, A.; Mandelshtam, V. A.; Reisler, H. Rev. Sci. Instrum. 2002, 73, 2634-2642. (31) Rocher-Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2011, 115, 6903-6909. (32) Ewing, G. E. J. Chem. Phys. 1980, 72, 2096-2107. (33) Ewing, G. E. J. Phys. Chem. 1987, 91, 4662-4671. Experimental Technique References 96 (34) Zwart, E.; ter Meulen, J. J.; Leo Meerts, W.; Coudert, L. H. J. Mol. Spectrosc. 1991, 147, 27-39. Hydrogen Chloride – Water Dimer Introduction 97 Chapter 4: Hydrogen Chloride – Water Dimer In this chapter, the vibrational predissociation dynamics and accurate dissociation energy of HCl-H 2 O are reported. Utilizing velocity map imaging, vibrational predissociation of the HCl stretch of HCl-H 2 O has been investigated and compared to phase space statistical theory. Two separate experiments were conducted by detecting the HCl and H 2 O fragments, which are discussed in Part 1 and Part 2 of this chapter, respectively. Due to the large spacing of HCl rotational transitions and high detection efficiency, this system serves as a calibration for our experimental setup later on. In addition, this study helps us to develop the detection techniques of the internally excited H 2 O, which is very challenging experimentally. The techniques for detection of the internally excited H 2 O described in Part 2 of this chapter and Chapter 3 is crucial for the following experiments discussed in Chapter 5 and 6. Part of the work described in this chapter has been published previously. 1-3 Figure 4.1. Vibrational predissociation of HCl-H 2 O dimer was investigated by photoexciting the HCl stretch. The HCl and H 2 O fragments were detected in separate experiments and described in Part 1 and Part 2 of this chapter, respectively. Hydrogen Chloride – Water Dimer Part 1: Introduction 98 Part 1: Detection of HCl Fragments 4.1 Introduction A general introduction, experimental setup and data analysis of hydrogen- bonded clusters have been presented in the previous chapters. Only information relevant to the HCl-H 2 O dimer will be presented in this chapter. A fundamental understanding of hydrogen bonds, their nature, strength and dynamics, remains an important goal of physical chemistry research. Experimental results on binding energies, energy transfer pathways, and predissociation in polyatomic hydrogen- bonded dimers are needed for testing the accuracy of potential energy surfaces (PES) and extending our understanding of hydrogen bonding to larger systems. Previous studies of several hydrogen-bonded complexes have revealed nonstatistical predissociation behavior due to the disparity between the frequencies of the intramolecular and intermolecular vibrational modes. 4 The interaction of HCl with H 2 O (gaseous, liquid, and solid) has attracted attention for over a century as a model for the dissociation of strong acids in aqueous solutions. HCl-H 2 O is of particular interest because of the role interactions of HCl with ice in aerosols and in polar stratospheric clouds play in formation of the ozone hole. 5-9 As a result, HCl(H 2 O) x clusters of various sizes have been the focus of numerous experimental and theoretical studies, 10-31 with several focusing on the transition from molecular HCl hydrogen-bonded to water to dissociated H + and Cl - microsolvated by water. According to theory it takes four water molecules to dissociate HCl into solvated H + and Cl - . 10,11,27 Recent experiments report vibrational Hydrogen Chloride – Water Dimer Part 1: Introduction 99 signatures of several (HCl) x (H 2 O) y mixed clusters. 12,13,15,24-26 Detailed study of the simplest HCl-H 2 O complex, the dimer, provides a benchmark for our understanding of the energetics and dynamics of the bonding in these systems. The structure of HCl-H 2 O has been studied previously both experimentally and theoretically. 14-17 As shown in Figure 4.2, the minimum energy structure of the dimer has a nearly linear hydrogen bond (<OHCl ≈ 178º), with the HCl acting as hydrogen-bond donor to the oxygen of water. Structures with the H 2 O acting as the hydrogen-bond donor have not been observed experimentally nor are they predicted by theory to be relevant in the gas phase. 18 Alikhani and Silvi calculated two optimized structures, one with Cs (pyramidal) and one with C 2v (planar) symmetry. 14 The pyramidal (Cs) structure seen in Figure 4.2 is one of two equivalent calculated global minimum structures. The planar (C 2v ) structure was calculated to be an inversion transition state with the barrier to inversion through the plane calculated to be 85 cm -1 at the CCSD(T)/6-311++G(2d,2p) level of theory/basis set. 14 The barrier to rotation around the internal C 2 axis of the water subunit that switches the structure between two minima is estimated to be 14 cm -1 from microwave spectroscopy. 15,16 The experimentally determined equilibrium geometry has an out of plane bend angle of the H 2 O subunit ( θ 2 ) of 145.3°, whereas the calculated global minimum structure has a θ 2 of 133.7°. 15,16 The discrepancy arises from the fact that the experimentally determined value is an average over all observed angles. Hydrogen Chloride – Water Dimer Part 1: Introduction 100 Figure 4.2. Minimum energy geometry of the HCl-H 2 O dimer. 14  1 = 178.4 ;  2 = 133.7; R 1 = 1.287 Å; R 2 = 1.933 Å. In addition to its structure, information on the infrared (IR) spectroscopy and intermolecular modes of the dimer is essential for explaining energy flow pathways in vibrational predissociation (VP). The IR spectrum of HCl-H 2 O was first measured in low-temperature matrices. 19-22 The HCl stretch of the dimer was observed at 2545-2664 cm -1 , depending on the nature of the matrix. More recently, the dimer was identified in He droplets with the HCl stretch band center of H 2 O- H 35 Cl at 2714.5 cm -1 . 24 The first mid-IR spectra of gas-phase HCl-H 2 O clusters were observed by ragout-jet FTIR spectroscopy with 0.25-2.0 cm -1 resolution and a dimer rotational temperature of ∼10 K. 25,26 A sharp feature at 2723.5 cm -1 with distinct P- and R- branches was assigned to the HCl stretch of the HCl-H 2 O dimer. Although this feature was surrounded by unassigned low intensity features, it was isolated from all other intense bands. The IR spectrum of HCl-H 2 O was also measured in the gas phase with 0.04 cm -1 resolution and a rotational temperature of ∼12 K using cavity ringdown (CRD) spectroscopy in a slit jet expansion. 15 The origin band of the HCl stretch of the dimer assigned by Huneycutt et al. is at 2723 cm -1 , red-shifted 162 cm - Hydrogen Chloride – Water Dimer Part 1: Introduction 101 1 from the monomer HCl stretch, and isolated from contributions from larger clusters. 15 The large red shift indicates strong hydrogen bonding interaction. The IR spectrum of the HCl stretch of the dimer is not rotationally resolved. The upper state lifetimes of HCl-H 2 O and DCl-D 2 O following excitation of the H(D)Cl stretch are ∼29 and ∼38 ps, respectively. 15 These lifetimes were estimated from the broadening in the IR spectra of the H(D)Cl stretch of the dimers, which include both intramolecular vibrational redistribution (IVR) and predissociation rate contributions, thus constituting a lower limit on the predissociation lifetimes. Huneycutt et al. attribute predissociation as the predominant loss mechanism for the upper state lifetimes of HCl-H 2 O and DCl-D 2 O. 15 For comparison, the lifetimes of (H 2 O) 2 and (D 2 O) 2 following excitation of the bound OH(D) stretch were found to be 80 ps and 5 ns, respectively. 32 The 29 ps lifetime of HCl-H 2 O should allow the complex to live in the excited state for multiple vibrational periods prior to dissociation. In contrast to the HCl stretch vibration, the OH stretches of the HCl-H 2 O dimer are not as well separated from the OH stretches of the H 2 O monomer. In the FTIR spectra, a group of peaks attributed to the OH stretches of the dimer were within 42 cm -1 of ν 3 of the H 2 O monomer. 26 In argon matrix, the water stretch frequencies of the dimer (3721-3629 cm -1 ) are only slightly red-shifted from those in the monomer (3733-3638 cm -1 ). 21 Recent spectroscopic studies in He droplets, in which the amount of complexation can be controlled, attributed four bands to the OH stretch of HCl-H 2 O, all lying between 3732 and 3793 cm -1 . 13 The small shifts for Hydrogen Chloride – Water Dimer Part 1: Introduction 102 the free OH stretch of H 2 O suggest that it is only weakly coupled to the hydrogen bond coordinate. A complete set of fundamental vibrational frequencies for the HCl-H 2 O dimer was calculated at the MP2/TZP level of theory/basis set with the CC-VSCF method. 27 In this calculation, the dimer’s HCl stretch was at 2709 cm -1 , in good agreement with the experimentally observed value. 15 The calculated red shift from the HCl monomer stretch, 240 cm -1 , was larger than the experimentally observed shift of 163 cm -1 reflecting the tendency of MP2 calculations to overestimate the hydrogen bond strength. The five intermolecular modes were calculated to lie in the 324-673 cm -1 range but were not assigned to specific intermolecular motions. 27 In addition to a large red shift, the HCl stretch intensity of the dimer was calculated to be greater than the monomer HCl stretch intensity by more than a factor of 20: 28 km/mol in the monomer and 625 km/mol in the dimer. 27 Much less information is available on the IR absorption of larger clusters. The HCl stretches of the cyclic (HCl) 2 -H 2 O trimer were observed at 2753 cm -1 for the Cl · · · H–Cl stretch and 2500 cm -1 for the O · · · H–Cl stretch in the argon matrix. 21 The corresponding stretches found via ragout-jet FTIR spectroscopy were assigned to the bands at 2757 and 2580 cm -1 , respectively. 26 The HCl stretch of the cyclic HCl- (H 2 O) 2 trimer was observed at 2390 cm -1 in the argon matrix. 21 The corresponding stretch found via ragout-jet FTIR spectroscopy was assigned to the band at 2460 cm - 1 . 26 The HCl stretch of the HCl-(H 2 O) 3 complex at 2500 cm -1 was observed in the argon matrix. 21 The OH stretches for the (HCl) n (H 2 O) m , complexes with n, m = 0 – 3 Hydrogen Chloride – Water Dimer Part 1: Introduction 103 have been observed in matrices and He droplets to lie above 3600 cm -1 . 13,21 In addition, the HCl stretches for clusters of pure (HCl) n with n = 2 – 6 have been observed in the range 2760-2900 cm -1 . 33 It is important to note that the OH and HCl stretches of these larger clusters do not overlap with the dimer HCl stretch frequency at 2723 cm -1 . Despite the ongoing interest in the HCl-H 2 O dimer, there has been no experimental determination of the strength of the hydrogen bond. There exist, however, a number of ab initio calculations of the dissociation energy, D 0 , which are summarized in Table 4.1. 28-31 The most recent and sophisticated calculation at the CCSD/aug-cc-pVDZ+ level of theory/basis set yielded a D 0 of 3.40 kcal/mol (1189 cm -1 ). 29 The calculated values for D 0 of HCl-H 2 O indicate that the energy required to dissociate HCl-H 2 O is similar to the measured value for D 0 of NH 3 -H 2 O (1538 cm -1 ). 34 Table 4.1. Comparison of calculated dissociation energies, D 0 for the HCl-H 2 O dimer at different theoretical levels / basis sets. Values given in kcal/mol and (cm -1 ). D 0 Level/ Basis Set 3.1 (1100) 30 MP2/ DZP 4.06 (1406) 31 MP2/ TVZP 4.5 (1574) 28 B3LYP/ D95++(p,d) 4.45 (1556) 29 B3LYP/ 6-311++G** 3.40 (1189) 29 CCSD/ aug-cc-pVDZ+ Hydrogen Chloride – Water Dimer Part 1: Experimental Details 104 This chapter reports the state-to-state study of the VP dynamics of HCl-H 2 O. Complexes were formed in a pulsed molecular beam, and the dimer’s HCl stretch fundamental was excited by a pulsed IR laser to induce VP. Resonance-enhanced multiphoton ionization (REMPI) was used to detect the HCl fragments in specific rotational (J") states and velocity-map imaging (VMI) was exploited to obtain rotational energy distributions of H 2 O fragments pair-correlated with specific rotational states of HCl. The fragments’ rotational distributions were broad but nonstatistical. The dimer’s dissociation energy was determined to be D 0 = 1334 ± 10 cm -1 . 4.2 Experimental Details Vibrational predissociation of HCl-H 2 O formed in a pulsed supersonic molecular beam was studied following pulsed IR laser excitation. Rotationally excited HCl fragments were ionized by 2 + 1 REMPI and detected by time-of-flight (TOF) mass spectrometry and VMI. The experimental procedures were similar to those used in studies of NH 3 -H 2 O, 34 HCl-C 2 H 2 , 35 DCl-C 2 H 2 , 36 and NH 3 -C 2 H 2 . 37 The dimers were formed in a pulsed supersonic molecular beam by expanding a mixture of 0.5% H 2 O and 3% HCl (Matheson Trigas, 99.995%) in He (Gilmore, 99.999%) at a stagnation pressure of ∼1 atm through the 0.5 mm orifice of a pulsed valve (∼150 µs opening time) operating at 10 Hz. Samples were prepared by transferring H 2 O by vacuum distillation to an evacuated bulb followed by adding gaseous HCl. The backing pressure and concentrations were optimized to maximize signal from the dimer. The skimmed molecular beam was intersected at right angles by two counter Hydrogen Chloride – Water Dimer Part 1: Experimental Details 105 propagating laser beams in the interaction region. Focused IR laser radiation [∼1.5 mJ/pulse, lens focal length (f. l.)] 40 cm) was used to excite the HCl stretch of the dimer at 2723 cm -1 , and focused ultraviolet (UV) radiation (0.04-0.28 mJ/pulse, f.l. ) 20 cm; ∼0.4 cm -1 line width) was used to ionize state-selected HCl fragments. The IR radiation was generated by an OPO/OPA system (LaserVision, up to 10 mJ/pulse; ∼0.4 cm -1 line width) pumped by the fundamental of a seeded Nd:YAG laser (Continuum Powerlite 8000). The IR frequency was calibrated by measuring the well-known absorption spectrum of gaseous HCl. The UV radiation was generated by frequency-doubling (Inrad Autotracker III) the output of a dye laser (Continuum ND 6000, Coumarin 480) pumped by a Nd:YAG laser (Continuum Surelite-III) and frequency calibrated by the known REMPI spectrum of HCl. The f 3 ∆ 2 ( ν' = 0) ← X 1 Σ + ( ν'' = 0) transition was used for HCl photofragment imaging while the V 1 Σ + ( ν' = 11 and 12) ← X 1 Σ + ( ν'' = 0) transitions were used to determine relative populations of the HCl rotational states. It is not possible to use the f 3 ∆ 2 ← X 1 Σ + transition to determine relative populations because the rotational line strengths for this transition vary greatly between each rotational state. 38,39 In addition, no rotational states with J'' ≥ 8 were observed in this band. On the other hand, it is not possible to obtain clean images of the HCl photofragments via the V 1 Σ + ( ν' = 11 and 12) states because the HCl + formed by 2 + 1 REMPI via these excited states is dissociative. 40 The timing of the lasers was adjusted by a delay generator (Stanford, DG535) controlled through a GPIB interface (National Instruments). Spectra were collected by alternating “IR on” and “IR off” conditions at each frequency. In “IR on”, the IR laser was fired 70 ns before the UV laser, whereas in “IR off”, the IR laser was fired 2 Hydrogen Chloride – Water Dimer Part 1: Experimental Details 106 µs after the UV laser. Laser conditions (timing, focusing, power) were optimized to maximize signal from the dimer. The timing of the lasers’ firings was carefully optimized to excite dimers in the coldest part of the molecular beam pulse where their highest relative abundance was found. The UV spectra were modeled using the program PGOPHER 41 with rotational constants from Callaghan et al. 42 The VMI arrangement has been described in detail previously. 43,44 In brief, it consists of a four-electrode ion acceleration assembly, a 60 cm field-free drift tube, and a microchannel plate (MCP) detector (BURLE Electro-Optics Co.) coupled to a phosphor screen that is monitored by a CCD camera (LaVision, Imager). In this experiment, two modes were used to collect data: (i) TOF mass spectrometry for spectroscopic investigations and (ii) VMI mode for determining center-of-mass (c.m.) translational energy distributions. In VMI mode, the two-dimensional projections were collected using an event counting method (DaVis) and reconstructed to three- dimensional images using the BASEX method. 45 Speed distributions were obtained by summing over the angular distribution for each radius, and were converted to c.m. translational energy distributions using momentum conservation, the appropriate Jacobian (α E T -1/2 ), and calibration constants obtained by imaging NO products from the well known NO 2 photodissociation. 46 The translational energy distributions were analyzed to determine the internal energy distributions of the H 2 O cofragments as well as the dissociation threshold of HCl-H 2 O. Hydrogen Chloride – Water Dimer Part 1: Results and Analysis 107 4.3 Results and Analysis 4.3.1 Infrared Action Spectra IR spectra of the dimer in the range of the HCl stretch fundamental were obtained by monitoring HCl photofragments in selected rotational states by REMPI while scanning the IR laser frequency. A typical spectrum recorded at 2718-2728 cm -1 by monitoring HCl (J" = 10) is shown in Figure 4.3. Qualitatively similar spectra were obtained while monitoring HCl (J" = 7). The spectral curve depicts the enhancement of the HCl + signal following IR excitation and has the background HCl + signal with the IR laser off subtracted. It is important to note that these are “action” spectra; in order to observe a signal there must be absorption of IR photons and this absorption must lead to the production of HCl fragments in the specific J" state being monitored. A similar band was observed previously in gas phase absorption and assigned to the HCl stretch of HCl-H 2 O. 15 No contributions from other HCl- containing clusters were seen in the region of the dimer peak (2675-2950 cm -1 ). IR scans were taken with various combinations of gas concentrations, backing pressures, and laser powers to obtain an optimized dimer signal. The spectrum shown in Figure 4.3 was obtained without focusing the IR radiation in an attempt to minimize saturation. However, it is likely that there is still partial saturation at the powers used in this study, which results in some broadening. The action spectra did broaden further at higher laser powers than used in this study. H F sh p li te fr p et ro ex w o m it ro a Hydrogen Ch igure 4.3. H hows the av ulse energy nes are a st emperature rom Odde et Also i rofile using t al. 29 (A). T otational te xcited state was quite ins f the shape matched wit t consists o otational fin nd R-branc hloride – Wa HCl (J" = 10 verage of 7 s y (unfocused tick spectrum e of 5 K and t al. 29 ). included in g published The simulat emperature e constants sensitive to near the ce th a tempera of P- and R ne structure hes do not ater Dimer 0) fragment scans of the d), 1% H 2 O, m simulatio published r Figure 4.3 rotational tion (obtain of 5 K, and were identi the value o enter of the ature of 10 R-branch su e is observe vary with e 108 yield IR spe e peak assig 3% HCl, an on of an a-ty rotational co is a stick sp constants fr ned by Asyr d an origin a ical to the g of A, and a te band. The w K. The obse ub-bands. A ed. The rela experiment ectra of the ned to H 35 C nd 1 atm bac ype band wi onstants (B pectrum sim from Kisiel e rot 47 ) assum at 2723 cm ground state emperature wings of the erved IR ban As in the a ative intensi tal condition Part 1: Res dimer. The Cl-H 2 O taken cking pressu ith a rotatio and C from mulation of et al. 16 (B a mes an a-ty m -1 . It was as e constants e of 5 K gave e band, thou nd has a ∼4 absorption ities and po ns. All data ults and Ana black line n with 1.5 m ure. The gre onal m Kisiel et al the dimer b and C) and O ype transiti ssumed tha . The simula e the best m ugh, were b 4 cm -1 fwhm spectrum, 1 ositions of th reported b alysis mJ IR ey ., 16 A band Odde on, a at the ation match better m and 15 no he P- below Hydrogen Chloride – Water Dimer Part 1: Results and Analysis 109 were obtained with the IR frequency fixed on the P-branch peak at 2723 cm -1 , which encompasses mostly rotational states) J" = 1 and 2 of the dimer. 4.3.2 REMPI Spectroscopy of HCl Fragments REMPI spectra of HCl fragments in the region of the V 1 Σ + ( ν' = 11 and 12) ← X 1 Σ + ( ν'' = 0) bands from the VP of HCl-H 2 O excited at 2723 cm -1 are shown in Figure 4.4. The spectra show enhancement for states with HCl (J" = 4-7, 10, 11). The HCl (J" = 11) state is difficult to see in Figure 4.4a due to the presence of an unidentified background signal, but its enhancement is clear in Figure 4.4b. The enhancement in HCl (J" < 4) populations cannot be detected due to background REMPI signal from HCl monomers in the molecular beam, and it is not possible to observe HCl (J" = 8, 9) in the ( ν' = 11) ← ( ν'' = 0) band due to strong ion signals from unassigned contamination in that spectral region. The normalized relative populations of the HCl rotational states are shown in Figure 4.5. They were determined by measuring the enhancement peak area for each HCl (J") state observed by using the V 1 Σ + ← X 1 Σ + system. Areas were converted to relative populations using previously reported rotational line strengths. The line strengths are constant for J" = 0 – 8 of the ( ν' = 11) ← ( ν'' = 0) transition and the line strengths of J" = 10 and 11 measured via the ( ν' = 12) ← ( ν'' = 0) transition are weaker by a factor of 1.55 due to the vibrational Franck-Condon factor. 48 The populations for J" = 4 – 7 and 10 are similar with a noticeable drop in relative population at J" = 11. The fairly large error bars are a result of the need to subtract H si b F th re “I b Hydrogen Ch ignificant b eam. igure 4.4. H he HCl stret egion of the IR off” back ackground hloride – Wa background HCl photofr tch of HCl-H e V 1  + ( ν ′ = ground scan subtracted. ater Dimer signals as agment 2+1 H 2 O at 2723 11 and 12) n is shown. . 110 ssociated w 1 REMPI sur cm -1 and sc ) ← X 1  + ( ν b) Data sho with HCl mo rvey spectru canning the ′′ = 0) trans own are the Part 1: Res onomers in um obtaine UV laser th sitions of HC “IR on” wit ults and Ana n the mole d by excitin rough the Cl. a) Only th th the “IR of alysis cular ng he ff” H F sq p 4 fr th 4 v th v ra th n b fr Hydrogen Ch igure 4.5. R quares) and opulation. 4.3.3 Ion I Repre ragments ar he Q (4 – 7) .6 shows th elocity spac he center o elocity (m/ anged from hen conver ormalized r elow). To ragment, co hloride – Wa Relative pop d calculated maging R esentative r re shown in ) transitions he BASEX r ce (pixels). f the image /s) is equal m 140 pixels rted to c.m relative pop determine onservation ater Dimer pulations of d by PST (red Results and results obt n Figures 4 s of the f 3 ∆ reconstruct The size of e and is pro to 3.6 time (J" = 5) to . translatio pulations of the correl n of energy 111 f the HCl rot d triangles) d Analysis ained by V .6 and 4.7. ∆ 2 ← X 1 Σ + sy ion of the f each imag oportional to s the numb 115 pixels onal energy f the H 2 O ro lated rotati y was use tational stat , normalize s VMI by mo Images we ystem as de raw images ge in pixels o the speed ber of pixels (J" = 7). Th y distributio tational sta ional state ed. Given t Part 1: Res tes observed ed to HCl (J′′ nitoring HC re recorded scribed in s s for J" = 5 is the radia d of the HCl s. Observed he speed dis ons. Figure ates used to distributio the excitati ults and Ana d (black ′ = 7) Cl (J" = 5 d by monito section 2. Fi 5 – 7, plotte al distance l + fragment maximum stributions w 4.7 shows fit the data ons of the ion energy alysis – 7) oring igure ed in from . The radii were s the a (see H 2 O and Hydrogen Chloride – Water Dimer Part 1: Results and Analysis 112 measured D 0 (see below), hν - D 0 = 2723 - 1334 = 1389 cm -1 is obtained. Therefore, vibrational modes of neither monomer are energetically accessible and E vib (HCl) and E vib (H 2 O) are set to zero. Conservation of energy requires E int (HCl-H 2 O) + hν = D 0 + E T + E rot (HCl) + E rot (H 2 O) where E int (HCl-H 2 O) is the internal energy of the dimer prior to excitation, hν is the photon energy used for vibrational excitation of the dimer (2723 cm -1 ), D 0 is the dissociation energy of the dimer, E T is the c.m. translational energy, and E rot (HCl) and E rot (H 2 O) are the rotational energies of the HCl and H 2 O fragments, respectively. The internal energy of the dimer, E int (HCl-H 2 O), is estimated to be 1 ± 1 cm -1 from a T = 5 K Boltzmann distribution (see Section 4.4.1). State selective REMPI defines E rot (HCl) and E T is determined from the images. D 0 and E rot (H 2 O) are the remaining unknowns. Reconstructed images in velocity space (pixels) were used to determine the rotational state populations of pair-correlated water fragments. Fitting in velocity space instead of energy space improves the ability to resolve structures at low E T and identify the maximum observed E T . Fitting was accomplished by assigning a Gaussian-shaped curve to each rotational state of H 2 O 49 with a width characteristic of the experimental resolution (ca. six pixels). The positions of these Gaussians were then shifted together by adjusting D 0 until both the observed structure and maximum E T were best matched. The heights of the Gaussians were first described by a smooth function of E T and then adjusted to fit distinct structural features at low E T . All images had clearly observable structure and could be fit unambiguously with H a a F fr p d o in re a Hydrogen Ch consistent ssuming no igure 4.6. a ragments pr ixels (propo etermined b f the Gaussi ndicates the elative popu nd calculate hloride – Wa D 0 . From f o uncertainty a) The BASE roduced in t ortional to v by known H ians are det e maximum ulations of t ed from PST ater Dimer fits of seven y in other p EX-reconstr the vibratio velocity). Po H 2 O rotation termined by velocity cor the water ro T (red triang 113 n images, D parameters ructed imag onal prediss ositions of G nal energies y the experim rresponding otational sta gles). D 0 of 1334 (see below) e of state-se ociation of Gaussians us s and the fit mental reso g to D 0 = 13 ates used to Part 1: Res ± 8 cm -1 (2 ). elected HCl HCl-H 2 O plo sed in the si parameter olution. The 334 cm -1 . b) o fit the data ults and Ana 2σ) was der (J′′ = 5) otted in unit imulation w D 0 . The wid e arrow The norma a (black squ alysis rived ts of were dths alized uares) H F fr p d o in re a Hydrogen Ch igure 4.7. a ragments pr ixels (propo etermined b f the Gaussi ndicates the elative popu nd calculate hloride – Wa a) The BASE roduced in t ortional to v by known H ians are det e maximum ulations of t ed from PST ater Dimer EX-reconstr the vibratio velocity). Po H 2 O rotation termined by velocity cor the water ro T (red triang 114 ructed imag onal prediss ositions of G nal energies y the experim rresponding otational sta gles). e of state-se ociation of Gaussians us s and the fit mental reso g to D 0 = 13 ates used to Part 1: Res elected HCl HCl-H 2 O plo sed in the si parameter olution. The 334 cm -1 . b) o fit the data ults and Ana (J′′= 6) otted in unit imulation w D 0 . The wid e arrow The norma a (black squ alysis ts of were dths alized uares) Hydrogen Chloride – Water Dimer Part 1: Discussion 115 4.4 Discussion 4.4.1 Infrared Spectrum of HCl-H 2 O The position of the HCl-stretch band in the HCl-H 2 O dimer shown in Figure 4.3 is in good agreement with the previously reported spectra. 15,26 The relative intensities of the high-frequency and the low-frequency peaks in the action spectra and the overall width of the bands differ from the absorption spectrum observed by Huneycutt et al. 15 The differences can be explained by noting that only H 35 Cl fragments (mass to charge ratio of m/z = 36) are monitored while in the absorption measurements, spectra of both H 35 Cl and H 37 Cl isotopologues of the dimer are recorded. The low-frequency peak corresponds mainly to the H 37 Cl band 15 and thus would have less intensity in the experiments. The absorption spectrum reported by Huneycutt et al. has a fwhm of ∼6 cm -1 , composed of the two dimer bands of H 35 Cl and H 37 Cl that differ in band origins by 2.1 cm -1 . 15 The action spectra have widths of only ∼4 cm -1 because they do not include contributions from the lower-frequency H 37 Cl band. The intensity discrepancy near the band origin between the data and the simulation may be due to saturation effects from the relatively high laser power used in this work. In addition, because we observe action spectra instead of absorption spectra, the observed IR intensities correspond only to frequencies that are absorbed and lead to the production of specific HCl (J") fragments. Due to the agreement of the spectrum with previously reported spectra and the simulation, we are confident that we are exciting the P-branch of the H 35 Cl-H 2 O dimer. In addition, we are confident that the H 35 Cl fragments that we observe come from dissociation of Hydrogen Chloride – Water Dimer Part 1: Discussion 116 the H 35 Cl-H 2 O dimer because no contributions from other HCl-containing clusters were seen in the region of the dimer peak (2675-2950 cm -1 ). The simulation shows that at 2723 cm -1 we are exciting dimers mainly in J" = 1 and 2 at a temperature of T = 5 K. 4.4.2 Dissociation Energy of the HCl-H 2 O Several factors lend confidence to the accuracy of the D 0 value determined for the HCl-H 2 O dimer. The most important of these is the consistency of D 0 required to fit images obtained by monitoring several different rotational states of HCl. All images for which we could resolve some rotational structure for the water cofragment were fit with D 0 within a range of 11 cm -1 . The D 0 value derived from each image is narrowly constrained by the structure in the velocity distribution. The finite width of the observed peaks places a lower limit on the fitting uncertainty at (2 cm -1 , but depending on the signal-to-noise ratio this uncertainty can be as high as 10 cm -1 . The calibration constant used to convert images from pixels to translational energy has an uncertainty of ∼5%. However, an error in these calibration constants would impact the ability to simultaneously fit peaks at different E T and is probably reflected in the fit uncertainties. From the calibrations, the uncertainty in the IR frequency is estimated to be on the order of 1 cm -1 . The uncertainty in the internal energy of the dimer, E int (HCl-H 2 O), is estimated to be 1 cm -1 . Taking a weighted average of all the data and combining random and systematic uncertainties, we arrive at a value of D 0 = 1334 ± 10 cm -1 .The HCl REMPI spectra also support the value for D 0 ; the maximum J" observed, HCl (J" = 11, E rot = 1369 cm -1 ), is consistent Hydrogen Chloride – Water Dimer Part 1: Discussion 117 with the D 0 value of 1334 cm -1 . The significant drop in relative population between HCl (J" = 10) and HCl (J" = 11) indicates that the energy available for translation and rotation of the H 2 O fragment after dissociation is small: E avail = hν – D 0 – E rot (HCl) = 19 cm -1 . Surprisingly, despite the great interest in HCl-H 2 O, there has been no previous experimental determination of the strength of the hydrogen bond. Therefore the measured D 0 can now be used as a benchmark to test the accuracy of ab initio calculations (see Table 4.1). The most recent high-level electronic structure calculations by Odde et al. 29 give D 0 = 3.40 kcal/mol (1189 cm -1 ) at the CCSD/aug-cc- pVDZ+ level of theory/basis set. This value underestimates the measured D 0 by 11%, which is consistent with previous comparisons of calculated and measured values of D 0 . 34 In the case of the NH 3 -H 2 O dimer, for example, similar calculations of D 0 were 6% lower than the measured D 0 . 34,50,51 The calculated frequency for the HCl stretch of the HCl-H 2 O dimer from Odde et al. (2702 cm -1 ) 29 is very close to the experimentally observed value (2723 cm -1 ). 15 4.4.3 Fragments’ Rotational State Populations The imaging data provide information on the rotational states in the water cofragment pair-correlated with specific HCl (J") states. For the HCl-H 2 O dimer, only a modest number of rotational states of HCl (J" ≤ 11) are energetically allowed whereas a large number of H 2 O J" KaKc levels can be populated (69 for J" = 5). Although this large density of water levels prevents us from unambiguously assigning exact populations to individual J" KaKc states, we can safely conclude that Hydrogen Chloride – Water Dimer Part 1: Discussion 118 the entire range of energetically allowed rotational water levels is populated. Had some K a K c levels been excluded, much more structure would have been observed in the images. The highest allowed J" for the water fragment is 11 for any level (9 4,5 for the highest energy level), but this number is reduced for images correlated with higher HCl (J"). For example, for HCl (J" = 7) the highest allowed J" is 8 (7 2,5 ). Levels of H 2 O with the highest internal energies are the most resolved in the velocity spectra. Assuming a fairly smooth variation of rotational populations with energy, we find a gradual increase in H 2 O rotational state population with increasing internal energy of the H 2 O fragment. This is in accord with the momentum gap law that predicts a preference for rotational excitation over translational energy release, as long as the angular momentum (AM) “load” is not too large. 36,37,52-56 Although the H 2 O rotational state populations show a smooth increase with internal energy at low internal energies, at the highest rotational energies a good fit to the experimental data can only be achieved by including significant state-to-state variations in the rotational populations. Such fluctuations are not unusual in cases when the density of final states is low. They have been observed, for example, in the photodissociation of molecules such as H 2 O, NO 2 , and H 2 CO when pair-correlated distributions were measured or when the initial state was well-defined. 57-62 The largest contribution to the uncertainties in the water rotational populations shown in Figure 4.7 arises from the large number of water levels that have similar energies. When states have almost identical energies, we are unable to Hydrogen Chloride – Water Dimer Part 1: Discussion 119 distinguish exactly which states contribute significantly to the shape of the image and which do not. 4.4.4 Comparison of Rotational Distributions with Phase Space Theory (PST) Rotational state distributions were computed for all energetically allowed rotational states of each cofragment following dissociation of the dimer from the J" = 1 and 2 levels according to energy conservation (hν - D 0 = E avail =1389 cm -1 ). The calculations also take into account angular momentum conservation 63-67 which dictates that J(dimer) = j(HCl) + j(H2O) + L where J(dimer), j(HCl), and j(H 2 O) are the angular momentum vectors of the HCl- H 2 O dimer, HCl fragment, and H 2 O fragment, respectively, and L is the orbital angular momentum vector. The equation can be simplified by placing the vectors in two-dimensional space and defining the vector, ω = j(HCl) + j(H 2 O) and J(Dimer) = L + ω Explicitly, for each energetically allowed J" KaKc state of the H 2 O cofragment, all allowed orbital angular momenta are calculated. For each J" KaKc state, the allowed orbital angular momenta are counted to compute the probability of creation of that state. No constraints due to centrifugal barriers are included in the calculation. Table 4.2 lists the energetically allowed pairs of j(HCl) and j(H 2 O) and the number of ω states. Hydrogen Chloride – Water Dimer Part 1: Discussion 120 Table 4.2. Energetically allowed pairs of j(HCl) and j(H 2 O) and number of ω states for each j(HCl). j(HCl) j(H 2 O) j ka,kc a # of ω states 0 0, 1, 2, …,11 0 0,0 , 1 0,1 , 1 1,1 , …, 9 4,5 88 1 0, 1, 2, …,11 0 0,0 , 1 0,1 , 1 1,1 , …, 9 4,5 88 2 0, 1, 2, …,10 0 0,0 , 1 0,1 , 1 1,1 , …, 10 2,9 84 3 0, 1, 2, …,10 0 0,0 , 1 0,1 , 1 1,1 , …, 8 5,3 81 4 0, 1, 2, …,10 0 0,0 , 1 0,1 , 1 1,1 , …, 8 4,4 75 5 0, 1, 2, …,9 0 0,0 , 1 0,1 , 1 1,1 , …, 7 5,2 69 6 0, 1, 2, …,9 0 0,0 , 1 0,1 , 1 1,1 , …, 7 4,3 62 7 0, 1, 2, …,8 0 0,0 , 1 0,1 , 1 1,1 , …, 7 2,5 52 8 0, 1, 2, …,7 0 0,0 , 1 0,1 , 1 1,1 , …, 5 4,1 41 9 0, 1, 2, …,6 0 0,0 , 1 0,1 , 1 1,1 , …, 6 1,6 30 10 0, 1, 2, …,4 0 0,0 , 1 0,1 , 1 1,1 , …, 4 1,4 16 11 0 0 0,0 1 a j kakc is sorted by energy. All 687 ω states were then used to generate the possible L values. According to PST the probability of producing a given pair of j(HCl) and j(H 2 O) is proportional to the number of L states (N). N for each J(Dimer) can be counted by summing the total number of states in the phase space diagram of L vs. ω all the L states in the range ω min to ω max . States forbidden by conservation of angular momentum are excluded from the summation. Figure 4.8 shows examples of such diagrams used to determine N for each combination of J(Dimer), j(HCl), and j(H 2 O). To determine the probability of forming a specific HCl J" state, all H 2 O cofragment level probabilities corresponding to that state are summed. The rotational state distributions in H 2 O fragments correlated with J" = 5-7 obtained from the data and from PST calculations are shown in Figure 4.7. The calculated relative HCl rotational state populations are shown in Figure 4.5 in comparison to H th a F j( = 4 w a ro w so ca o re p Hydrogen Ch he experim ccording to igure 4.8. P (H 2 O) = 8, th 2, j(HCl) = 3. The e with HCl J" = re more hig otational en with increas omewhat be an be said a bserved lev easonable t redicted by hloride – Wa entally obs a 5 K Boltz Phase space he summati 6, and j(H 2 experimenta = 5-7 show ghly popula nergy (high sing E rot (HC etter with P about the H vels, in con o suggest th y PST. ater Dimer erved value mann distri e diagrams o on range is 2 O) = 3, the al rotationa that H 2 O c ated than pr h E T ) are les Cl) the H 2 O PST predicti HCl rotation njunction w hat higher H 121 es. In all th ibution givi of L vs ω. a) ω min = 5 to summation al state distr cofragments redicted by ss populate O rotationa ions, though nal state dis with the H 2 HCl rotation e calculatio ng a level ra For J(Dime ω max = 11 a n range is ω ributions of s with high PST. Accor ed than pre al state dis h this may b tributions d 2 O rotation nal states ar P ons, J(dimer atio 1:2 = 0. er) = 1, j(HC and N = 21. ω min = 3, ω ma f H 2 O fragm rotational rdingly, frag dicted by P stributions be fortuitou due to the s al state dis e also more Part 1: Discu r) was weig .367:0.633. Cl) = 3, and b) For J(Dim x = 9 and N ments corre energy (low gments with PST. In addi seem to a us. Although small numb stributions e populated ssion ghted mer) N = lated w E T ) h low ition, agree h less ber of it is than Hydrogen Chloride – Water Dimer Part 1: Discussion 122 4.4.5 Comparison with Rotational Energy Distributions in Other Dimers Several models are commonly used to describe rotational energy distributions in small dimers. Although not directly predicting populations, the propensity rules defined by Ewing, 54-56 which are based on the momentum gap law, predict that the largest reaction rate would correspond to processes that minimize translational energy release and the number of quanta transferred. This model predicts that for small diatomic molecules with large rotational constants, fragment rotational energy would be favored over fragment translation. The model, however, does not discuss the mechanism for generation of rotational excitation nor does it take into account angular momentum constraints. The angular momentum (AM) model proposed by McCaffery and co-workers 52,53 recognizes that, similar to inelastic collisions, high rotational excitation in the weakly bound complex must involve the repulsive (hard-shaped) part of the potential surface and angular momentum must be conserved. In addition, the restricted range of geometries can limit the impact parameters accessible to the complex. The AM model has been successful in fitting the rotational distributions of a large number of small dimers, and first steps toward a predictive model have been taken. 68 It emphasizes the need to restrict the “AM load” in the dissociation; i.e., there is only a limited amount of angular momentum that can be generated in a given process even when hard- shaped potentials are involved. When the subunits have large rotational constants, rotational levels up to the maximum allowed by energy are often observed, in Hydrogen Chloride – Water Dimer Part 1: Discussion 123 agreement with the momentum gap law. Product state distributions are usually nonstatistical, though in some cases they can appear statistical-like. 4,35 The results are compared to the dimers that include HCl or H 2 O subunits. The only other dimers of H 2 O for which product state distributions are available are OH- H 2 O 69 and NH 3 -H 2 O. 34 The geometries of OH-H 2 O and HCl-H 2 O are very similar with the H 2 O fragment acting as the hydrogen acceptor. The bound OH radical stretch of the OH-H 2 O dimer (3490 cm -1 ) is red shifted by 78 cm -1 from the monomer, about half the shift of the HCl stretch of the HCl-H 2 O (162 cm -1 ). The experimental upper limit for D 0 of the OH-H 2 O dimer determined by Soloveichik et al. is 5.14 kcal/mol (1797 cm -1 ), whereas the calculated value is 3.6 kcal/mol (1260 cm -1 ) at the CCSD(T) level of theory extrapolated to the complete basis set limit. 69 While the D 0 values of OH-H 2 O and HCl-H 2 O are of the same magnitude, the available energy in the former is much higher due to the higher frequency of the OH radical stretch. As a result, the water bend is accessible and Soloveichik et al. observed OH product state distributions correlated to H 2 O fragments with and without bend excitation. 69 Pair- correlated H 2 O fragment state distributions were not observed. The highest observed OH rotational state is J" = 9 (E rot (OH) = 1695 cm -1 ). This demonstrates that this level of fragment angular momentum is accessible for this geometry. In the near-linear NH 3 -H 2 O dimer the H 2 O fragment acts as the hydrogen donor and the bound OH stretch is red-shifted by 171 cm -1 from the monomer. The greater shift in the NH 3 -H 2 O dimer is consistent with the larger D 0 , (1538 cm -1 ). The observed rotational excitation in NH 3 is smaller than in HCl because accessible Hydrogen Chloride – Water Dimer Part 1: Discussion 124 vibrational channels involving the NH 3 fragment umbrella mode absorb much of the available energy. Nevertheless, those H 2 O fragments that are pair-correlated with ground-state NH 3 are populated up to the maximum allowed by energy (J" = 11), demonstrating again that this level of rotational excitation constitutes an acceptable AM load for the dimer. In the case of HCl-H 2 O, no fragment vibrational excitation is possible and the available energy is distributed only as rotation and translation. Similarly to NH 3 -H 2 O, the pair-correlated H 2 O rotational states in HCl-H 2 O span the entire range allowed by energy, with increasing population of those level combinations that minimize E T . It appears that the floppiness of both complexes allows access to a range of impact parameters that can produce all the energetically allowed rotational states and that the rotational constants of H 2 O are large enough to accommodate the available energy without an excessive AM load. Also, whereas in both dimers it is the repulsive (hardshaped) part of the intermolecular PES that generates the observed high rotational excitation needed to minimize E T , exit channel interactions involving the long-range, attractive part of the potential likely contribute to the smooth population of the lower rotational states whose energy spacings are small. Comparisons with previous work on mixed dimers containing HCl or HF subunits show that HX fragments can achieve a fairly high degree of rotational excitation when acting as proton donors (Lewis acids). 4 We have observed high rotational excitation in HCl fragments generated by VP of the HCl-C 2 H 2 dimer following excitation of the HCl stretch vibration, which is shifted by 79 cm -1 from the Hydrogen Chloride – Water Dimer Part 1: Discussion 125 monomer. 35 The HCl-C 2 H 2 geometry, however, is “T-shaped” with the hydrogen bond forming between the hydrogen of the HCl and the center of the distribution of π electrons of C 2 H 2 . 35 Although the available energy in the VP of HCl-C 2 H 2 is larger (2100 cm -1 compared to ∼1400 cm -1 in HCl-H 2 O), the excitation of bending levels in C 2 H 2 leads to a maximum observed level of J" = 8 in the HCl fragments, slightly lower than the excitation observed in the present work. Perhaps more relevant are results of VP of dimers where HX forms a traditional hydrogen bond. For example, in VP of the HCl dimer 4,70 as well as the DF- HF and HF-HCN dimers, 71-73 the donor HX fragment reaches levels of excitation similar to those observed in the present work, and rotational excitation extends up to the available energy. Apparently, the bent geometries involved in dissociation of these complexes allow access to impact parameters that sample repulsive regions of the PES that generate a high level of rotational excitation. Even though the rotational distributions of both fragments can be broad and encompass all the rotational states allowed by the available energy, they are not statistical, as shown by the comparisons with PST calculations. This is most apparent in the pair-correlated H 2 O rotational energy distributions where the number of accessible levels is greater and less averaging is involved than in the global HCl (J") distributions. The propensity toward larger than statistical populations of high rotational levels is clear in all the correlated distributions, despite some fluctuations in the populations of high rotational states. This agrees in general with the momentum gap law and the Ewing propensity rules, even though Hydrogen Chloride – Water Dimer Part 1: Summary 126 some rotational energy redistribution might take place through exit-channel interactions. 4.5 Summary The state-to-state VP of the hydrogen-bonded HCl-H 2 O dimer was studied following excitation of the bound HCl stretch. VMI and REMPI were used to determine the product energy distributions. Following vibrational excitation of the bound HCl stretch fundamental, HCl fragments were detected by 2 + 1 REMPI via the f 3 ∆ 2 ( ν' = 0) ← X 1 Σ + ( ν'' = 0) and V 1 Σ + ( ν' = 11 and 12) ← X 1 Σ + ( ν'' = 0) transitions. REMPI spectra show that the highest rotational state populated reaches the maximum allowed by conservation of energy. The fragments’ c.m. translational energy distributions were determined from images of selected rotational states of HCl and were converted to rotational state distributions of the H 2 O cofragment. All the distributions could be fit well when using a dimer dissociation energy of D 0 of 1334 ± 10 cm -1 . The rotational distributions in the H 2 O cofragment pair-correlated with specific rotational states of HCl were broad and encompass all the J" KaKc levels allowed by energy conservation. A detailed analysis of pair-correlated state distributions was complicated by the large number of H 2 O rotational states available, but the data show that the H 2 O rotational populations increase with decreasing translational energy. Hydrogen Chloride – Water Dimer Part 2: Introduction 127 Part 2: Detection of H 2 O Fragments 4.6 Introduction One of the experimental techniques that provide state-specific information on VP is photofragment VMI. 1,43,74 A limitation of the present method is that it requires that at least one photofragment be detected by REMPI. This complicates, for example, the VP studies of pure H 2 O clusters because REMPI has not been used previously to detect H 2 O photofragments state-specifically. HCl-(H 2 O) x complexes have generated much interest because theory predicts that it takes only 4-5 water molecules for HCl to behave as an acid. 10,11,27 The state- to-state VP dynamics of the HCl-H 2 O dimer have been examined before using similar techniques by detecting the HCl fragment via REMPI following excitation of the dimer’s HCl stretch fundamental and described in Part 1. In the previous study, H 2 O state distributions pair-correlated with individual HCl rotational states were derived from images obtained by detecting selected HCl (J") levels. In this part, the results of the experiments in which H 2 O is detected by REMPI as a photofragment of VP are presented. Directly detecting H 2 O fragments in VP of the HCl-H 2 O dimer provides the added benefit of observing HCl rotational distributions pair-correlated with specific water states, which is complementary to the previous study. From the perspective of developing a REMPI scheme for water products, detection of the H 2 O fragments provides an opportunity to examine H 2 O in states with higher rotational excitation, and the HCl-H 2 O dimer serves as a good test case Hydrogen Chloride – Water Dimer Part 2: Introduction 128 for evaluating the feasibility of using the H 2 O 2 + 1 REMPI scheme. At the energy used to excite the HCl stretch fundamental of the dimer, vibrational excitation of HCl or H 2 O is energetically inaccessible, and the large rotational constant of the diatomic HCl fragment limits the number of its accessible rotational states to J" ≤ 11. This allows the pair-correlated rotational states of the HCl fragment to be determined unambiguously from H 2 O images. The Rydberg states of H 2 O have been studied extensively via multiphoton spectroscopy at room temperature and in molecular beams. The 1 B 1 ← 1 A 1 transition has been investigated previously by 3 + 1 REMPI detection, 75,76 and more recently 2 + 1 REMPI spectroscopy was used to investigate several Rydberg states. 77-80 Both schemes have been successfully implemented for detection of H 2 O in molecular beams, 76-78 and in scattering experiments. 81,82 One known complication of H 2 O detection via REMPI is the predissociation of high rotational levels of the -state. Both heterogeneous and homogeneous predissociation have been observed, with predissociation being the dominant lifetime broadening factor. 75,76,79,80,83 The heterogeneous predissociation lifetime has a strong dependence on the component of the rotation along the a-axis, and it takes place most likely via the 1 A 1 state. The homogeneous predissociation mechanism is independent of rotational level, and dissociation is via the 1 B 1 state. 75 The most recent study by Yang et al. reports a significantly narrower linewidth (≥ 1.3 cm -1 , attributed to homogeneous predissociation) than in previous studies indicating a longer lifetime of the -state. 80 Hydrogen Chloride – Water Dimer Part 2: Introduction 129 In the study of Yang et al., 80 only lower energy rotational states (J" = 0-3) of the ground electronic state of water were detected. In this work, H 2 O states with higher rotational excitation (J" = 11) are expected to be populated. Yang et al. also provide rotational parameters that can be used in a standard simulation program (PGOPHER) 41 to simulate the H 2 O REMPI spectrum. The simulation used by Yang et al. included a linewidth model that accounted for lifetime broadening due to predissociation of the excited state. 80 Referring to the state-to-state VP of the HCl-H 2 O dimer, the structure of the dimer has been studied previously both experimentally and theoretically and discussed in Part 1. 14-17 Complexes were formed in a pulsed molecular beam, and the dimer’s HCl stretch fundamental was excited by a pulsed IR laser to induce predissociation. Individual H 2 O (J" KaKc ) rotational states were selected by 2 + 1 REMPI and VMI was used to measure the pair-correlated HCl distributions for selected H 2 O states. While the congested and predissociative H 2 O REMPI spectrum limits the states that can be used for imaging, we demonstrate that it is possible to measure some pair-correlated HCl distributions by VMI. These distributions are consistent with the previously measured dissociation energy of D 0 = 1334 ± 10 cm -1 and show a clear preference for the formation of high rotational states of the HCl cofragment that minimize translational energy release. Hydrogen Chloride – Water Dimer Part 2: Experimental Details 130 4.7 Experimental Details Experimental setup and IR radiation conditions have been discussed in Part 1. Only the UV radiation conditions, which allow the detection of H 2 O fragments are discussed here. Focused ultraviolet (UV) radiation (0.2 - 1.1 mJ/pulse, f. l. = 20 cm; ∼ 0.4 cm- 1 linewidth) was used to ionize H 2 O fragments state-selectively. For imaging, the UV beam was expanded by using an additional lens (f.l. = -100 cm) placed 86 cm before the focusing (f.l. = 20 cm) lens. The addition of the negative focal length lens expanded the laser beam prior to focusing to provide tighter focusing and a higher photon density to increase the ionization efficiency of the H 2 O fragment. Attempts were made to focus even more tightly, but a signal likely due to multiphoton absorption and/or weak overlapping transitions became observable, interfering with single state selection. As an alternative, utilizing a tunable picosecond laser would increase the pumping rate and maximize the efficiency of H 2 O detection by competing more effectively with dissociation. UV radiation at 247-250 nm was generated by frequency doubling (Inrad Autotracker III) the output of a dye laser (Continuum ND 6000, Coumarin 500) pumped by a Nd:YAG laser (Continuum SureliteIII) and frequency calibrated by the known REMPI spectrum of HCl. The 1 B 1 (000) ← 1 A 1 (000) transition was used for H 2 O photofragment detection. The UV spectra were modeled using the program PGOPHER 41 with rotational constants from Yang et al. as discussed below. 80 Background signals due to room temperature H 2 O monomers were reduced by Hydrogen Chloride – Water Dimer Part 2: Experimental Details 131 modifying the chamber design to include a cryopumping system cooled by several liquid nitrogen traps. Laser conditions (timing, focusing, power) were optimized to maximize signal from the dimer while ensuring that no contributions from other H 2 O-containing clusters were observed. The timing of the lasers’ firings was carefully optimized to excite dimers in the coldest part of the molecular beam pulse where their highest relative abundance was found. Calibration constants are obtained by imaging O products from the well- known O 2 photodissociation. 84 The translational energy distributions were analyzed to determine the internal energy distributions of the HCl cofragments as well as the dissociation threshold of HCl-H 2 O. The H 2 O (J" KaKc ) fragments that can be detected state selectively by the 2 + 1 REMPI are limited by the lifetimes of the excited states, the selection rules, and spectral overlap of the transitions. A PGOPHER simulation that also takes into account lifetime broadening effects due to predissociation of the excited state was used previously by Yang et al. 80,82 The predissociation rate scales with <J a 2 >, the average of the square of the operator for the projection of J' onto the a-axis. It should be noted that K a ' is in fact not a good quantum number for asymmetric tops, therefore <J a 2 > is used in ref 77 instead of <K a 2 >. Here we follow the commonly used J" KaKc notation for clarity. The simulation only includes the 1 B 1 (000) ← 1 A 1 (000) origin band and it fits the spectral line positions well. Hydrogen Chloride – Water Dimer Part 2: Results and Discussion 132 4.8 Results and Discussion 4.8.1 Infrared Action Spectra IR action spectra of the dimer in the frequency region of the HCl stretch fundamental were obtained by monitoring H 2 O photofragments by REMPI while scanning the IR laser frequency. A typical spectrum recorded at 2716 – 2732 cm -1 by monitoring a group of overlapping states dominated by H 2 O (J" KaKc = 3 2,1 ) is shown in Figure 4.9 and compared with Figure 4.3 (IR spectrum of the dimer taken by monitoring HCl photofragments). The spectral curve depicts the enhancement of the H 2 O + signal following IR excitation. The background H 2 O + signal taken with the IR laser off is also shown. It is important to note that these are action spectra; in order to observe enhancement, there must be absorption of IR photons, and this absorption must lead to the production of H 2 O fragments in the monitored J" KaKc state. No contributions from other H 2 O-containing clusters were seen in the region of the dimer peak (2709 – 2738 cm -1 ). The spectrum shown in Figure 4.9 exhibits saturation broadening due to the tight focusing conditions necessary to maximize the signals from the H 2 O fragments. The position of the HCl-stretch band in the HCl-H 2 O dimer shown in Figure 4.9 is in good agreement with the previously reported spectra. 1,15,25,26 The high- frequency and low-frequency peaks in the action spectra obtained by monitoring the H 2 O fragments are less well resolved than spectra recorded previously by monitoring HCl fragments. This is likely due to the higher IR laser power and tighter Hydrogen Chloride – Water Dimer Part 2: Results and Discussion 133 focusing conditions required to detect H 2 O fragments. Because we compare action spectra, we note that the observed IR intensities are proportional to both the absorption cross section at the excitation frequencies and the fractional yield of the monitored HCl (J") or H 2 O (J" KaKc ) fragment states. The lower signal-to-noise ratio in the H 2 O (J" KaKc ) spectrum relative to HCl (J") is a result of the lower REMPI efficiency and greater number of fragment quantum states of H 2 O. The similarity of the two spectra and the absence of absorption bands from larger clusters near the dimer band confirm that the H 2 O (J" KaKc ) signals observed by monitoring H 2 O derive from VP of the HCl-H 2 O dimer. Figure 4.9. Fragment yield IR spectra of the dimer. The red (top) lie shows the spectrum assigned to HCl-H 2 O taken while monitoring the H 2 O photofragment with 1.0 mJ IR pulse energy (f.l. = 50 cm), in a mixture of 0.5% H 2 O, 3% HCl, and 2 atm backing pressure. The black (middle) line shows the background signal from H 2 O monomers in the molecular beam under the same conditions. The blue (bottom) line shows the IR enhancement spectrum taken while monitoring the HCl photofragment (Figure 4.3) with 1.5 mJ IR pulse energy (unfocused), 1% H 2 O, 3% HCl, and 1 atm backing pressure. 2716 2720 2724 2728 Intensity (arb.) IR Energy (cm -1 ) Hydrogen Chloride – Water Dimer Part 2: Results and Discussion 134 4.8.2 REMPI Spectroscopy of Water Fragments A representative REMPI spectrum of H 2 O fragments in the region of the 1 B 1 (000) ← 1 A 1 (000) transition obtained following 2723 cm -1 excitation of HCl-H 2 O is shown in Figure 4.10. The spectrum shows enhancement (relative to the IR off signal) for several states that can be used for imaging. A simulation with a rotational temperature of 250 K is also shown for comparison of line positions. The simulation uses the published rotational constants and the PGOPHER 41 program from Yang et al. 80 State-selection of H 2 O (J" KaKc ) levels was complicated by the fast predissociation in the -state for many states as well as spectral congestion and overlap. Background signals from ambient H 2 O monomers were reduced by a factor of 5 by using several liquid nitrogen cooled traps. The background REMPI spectrum was fit well with T = 300 K. The most intense enhancements originated from overlapping transitions dominated by H 2 O (J" KaKc = 3 2,1 ) and H 2 O (J" KaKc = 2 2,1 ) as seen in Figure 4.10. The only transitions in this study that were identified as isolated from other transitions and showed significant enhancement following VP were those with H 2 O (J" KaKc = 4 2,3 ) and H 2 O (J" KaKc = 4 1,4 ). H F e a tr = 2 n th in 4 fo re a th th U Hydrogen Ch igure 4.10. nhancemen nd scanning ransition of 250 K. The 0,2 ← 2 2,1 , an ormalized t he data corr ntensity wa 4.8.3 Ion I Repre or H 2 O (J" K econstructio ngular distr he radial di he H2O + fra UV power an hloride – Wa . The black nt spectrum g the UV las f H 2 O. The re e labeled tra nd (d) 4 1,3 ← to the other responds to s too large t maging R esentative v KaKc = 4 2,3 ) on of the r ributions of stance from agment. The nd focusing ater Dimer (top) line co obtained b er through ed (bottom) ansitions are ← 4 1,4 . Note: r peaks beca o the region to measure Results and velocity spe and Figur raw images f the images m the center e speed (m/ conditions 135 orresponds y exciting th the region o ) line corres e dominated the intensit ause it had t of low-J tra enhanceme d Analysis ectra obtain re 4.10b fo s plotted in s were isotr r of the ima /s) is equal were optim Pa to the H 2 O he HCl stret of the C 1 B 1 sponds to th d by (a) 2 0,2 ty of the pea to be record ansitions for ent. s ned by VMI or H 2 O (J" K n velocity ropic. The s age and is p to 5.3 times mized for th art 2: Result photofragm tch of HCl-H (000) ← X 1 he simulated ← 4 2,3 , (b) 2 ak labeled ( ded separate r which the are shown KaKc = 4 1,4 ), space (m/s ize of the im roportional s the numb he best sign ts and Discu ment 2+1 RE H 2 O at 2723 1 A 1 (000) d spectrum 2 0,2 ← 3 2,1 , ( (d) is not ely. The gap background in Figure 4 , as the BA s). All obse mage in pix l to the spe er of pixels al-to-noise ssion EMPI cm -1 at T (c) p in d 4.11a ASEX erved els is ed of . The ratio Hydrogen Chloride – Water Dimer Part 2: Results and Discussion 136 for each image. Higher UV fluence, obtained either by increasing the UV power or placing the negative lens further from the focusing lens to provide tighter focusing, resulted in unresolved peaks due to power broadening and/or background contributions. For the J" KaKc = 4 2,3 and 3 2,1 images, a lower UV fluence (0.4 mJ/pulse, f.l. = -100 cm lens placed 86 cm before f.l. = 20 cm lens) was used to minimize contributions from neighboring transitions. A higher UV fluence (0.9 mJ/pulse) was used for the J" KaKc = 4 1,4 image, as this transition is well isolated and no background contributions were observed even at high fluences. Reconstructed images in velocity space were used to determine the rotational state populations of pair-correlated HCl fragments. Fitting in velocity space instead of energy space improves the ability to resolve structures at low E T and identify the maximum observed E T . Fitting method is similar to those discussed in Part 1. A Gaussian width of fwhm ∼ 8 pixels was used. Rotational states of HCl are assigned by fitting the structure in the images to the known rotational energies of HCl. This procedure establishes that the highest allowed rotational states of HCl are populated preferentially for each imaged H 2 O (J" KaKc ) fragment. One disadvantage of obtaining images by detecting H 2 O fragments by REMPI is the difficulty of finding isolated transitions. When the H 2 O transition is not overlapped with other transitions, the structure in the image corresponding to HCl rotational states can be assigned unambiguously, and an accurate value of D 0 can be determined. As in previous case, all images with clearly observable structure could be fit accurately with a unique value of D 0 . By contrast, most of the transitions in the REMPI spectrum of water are overlapped. When a rotational state with low K a ' overlaps transitions with rotational states with high K a ', the transitions with high Hydrogen Chloride – Water Dimer Part 2: Results and Discussion 137 K a ' can usually be neglected in the image fitting because they are broadened much more by fast predissociation and contribute less to the peak height in the REMPI spectrum. The H 2 O distributions shown in Figure 4.11 were fit with the D 0 value obtained in Part 1 For these H 2 O states, most of the individual HCl rotational states are clearly resolved, and the fits are unambiguous. When images were recorded by monitoring overlapped transitions of H 2 O, some rotational structure could still be resolved for the HCl cofragment, and images were consistently fit with D 0 = 1334 cm -1 , even though a unique pair-correlated HCl distribution could not be determined. An example is shown in Figure 4.12. Several features in the image could not be fit without including the H 2 O 2 0,2 ← 3 2,1 transition in the simulation. Although the image could be better fit by including, for example, the nearby 5 0,5 ← 6 0,6 , 5 1,5 ← 6 1,6 , and/or 4 2,3 ← 5 2,4 transitions, the fitting was not unique, and we could not conclusively determine which one(s) contribute(s) to the image. In addition, it is possible that other broad transitions, whose peaks are farther away, also contribute to the image. Because all of the contributing H 2 O states could not be determined for this image, the heights of the Gaussians pair-correlated with H 2 O (J" KaKc = 3 2,1 ), were described by a smooth function of E T and not adjusted to fit the heights of distinct structural features in the image. Although the relative populations of the HCl states could not be unambiguously determined from the image, D 0 could be estimated even when monitoring an overlapped transition of H 2 O. H F o V  T fr m w b Hydrogen Ch igure 4.11. f state-selec VP of HCl-H 2  pixels). The The Gaussian ragment. Th mJ UV pulse were collecte efore the se hloride – Wa . The black cted H 2 O fra 2 O plotted a e red (trian ns are label he images w energy and ed with two econd (f.l. = ater Dimer (solid) line agments a) s a velocity gles) line co ed with the were collecte d b) 230,000 o focusing le 20 cm). 138 correspond (J  KaKc = 4 2,3 distribution orresponds correspond ed over app 0 shots with enses, with o Pa ds to the BA 3 ) and b) (J  n in units of to the total ding rotatio roximately h 0.9 mJ UV one (f.l. = -1 art 2: Result SEX-recons  KaKc = 4 1,4 ) p f m/s (veloc l simulated f onal level of a) 400,000 pulse energ 100 cm) pla ts and Discu structed ima produced in city in m/s = fit of the im the HCl co- shots with gy. All image ced 86 cm ssion age n the = 5.3 mage. 0.4 es H F o u J  o li co a H m = 4 ro st al p sp co Hydrogen Ch igure 4.12. f H 2 O fragm nits of m/s  KaKc = 2 0,2 ← ther overlap ne position orrespondin re describe HCl (J  = 10) mJ UV pulse -100 cm) p 4.8.4 Frag The i otational st tates. Only llowed, wh opulated. T pecific rota onservation hloride – Wa . The black ments produ (velocity in ← J  KaKc = 3 2,1 pped transi s assuming ng rotationa d by a smoo . The image energy. All placed 86 cm ments’ Tr imaging dat tates of the a modest n hereas a la The rotation ational state n. For examp ater Dimer (solid) line uced in the V n m/s = 5.3  1 transition itions. The r H 2 O (J  KaKc al level of th oth function e was collect images wer m before the ranslation ta provide e HCl cofra number of r arger numb nal distribut es of H 2 O e ple, in the c 139 correspond VP of HCl-H 2  pixels). Th though like red (triangle = 3 2,1 ). The he HCl co-fr n of E T and a ted over app re collected e second (f.l nal and Ro informatio gment pair otational st ber of H 2 O tions of the encompass .m. E T distri Pa ds to the BA 2 O plotted a he image is ely has contr es) line corr Gaussians a agment. Th are normaliz proximately d with two fo l. = 20 cm). otational E on on the r r-correlated tates of HCl O (J" KaKc ) le e HCl cofrag all of the J ibution for J art 2: Result SEX-recons as a velocity dominated ributions fr responds to are labeled e heights of zed to the p y 610,000 s ocusing lens Energy Po relative pop d with spec l (J" ≤ 11) a evels can b gment pair- " levels allo J" KaKc = 4 2,3 ts and Discu structed ima y distributio by the H 2 O rom several o a simulatio with the f the Gaussi peak height hots with 0 ses, with on opulations pulations o cific H 2 O (J are energeti be energeti -correlated owed by en shown in Fi ssion age on in on of ans of .4 ne (f.l. s f the " KaKc ) ically ically with nergy igure Hydrogen Chloride – Water Dimer Part 2: Results and Discussion 140 4.13a, where hν = 2723 cm -1 , and E rot (H 2 O) = 300 cm -1 , the energy available for c. m. translation or rotation of the HCl fragment is ∼1090 cm -1 . Thus, only HCl (J" ≤ 9) states can be populated. The observed pair-correlated HCl rotational states are consistent with this prediction, and the maximum translational energy is consistent with D 0 value obtained in Part 1. We can compare the observed pair-correlated distributions with the prediction of statistical theories. Previously we were unable to determine whether the HCl rotational state distribution was statistical because the populations of several rotational levels could not be determined due to experimental difficulties. The observed HCl populations appeared evenly distributed among all accessible rotational states. On the other hand, we showed that the high water rotational states pair-correlated with each HCl (J") state were favored relative to the statistical predictions (PST). Due to conservation of energy, these states must be paired with low rotational levels of HCl. This in effect causes a more even distribution of HCl rotational state populations when all H 2 O rotational states are taken into account. By imaging a single rotational state of H 2 O, we are able to compare the pair- correlated HCl rotational state distribution for each H 2 O rotational state with statistical calculations. Figure 4.13 demonstrates that the rotational energy distributions of HCl fragments pair-correlated with a specific H 2 O (J" KaKc ) state are nonstatistical, with HCl fragments that have the highest allowed rotational energy (low E T ) more highly H p e F im st re G T b si Hydrogen Ch opulated th nergy (high igure 4.13. mages show tate-selecte ed (triangle Gaussians ar The blue (sq y PST. The a imulation p hloride – Wa han predict h E T ) are less . Translatio w in in Figur ed H 2 O fragm es) lines cor re labeled w uares) lines areas under lots. ater Dimer ted by PST. s populated nal energy d re 4.11. The ments a) (J  respond to with the corr s correspon r the PST pl 141 . 63,67 Accord d than predi distribution e black (soli  KaKc = 4 2,3 ) a the total sim responding nd to transla ots are norm Pa dingly, frag icted by PST ns derived fr id) lines cor and b) (J  KaK mulated fits rotational l ational ener malized to t art 2: Result gments with T. from the rec rrespond to Kc = 4 1,4 ) of H s of the imag level of the H gy distribut the areas un ts and Discu h low rotat constructed the images HCl-H 2 O. Th ges. The HCl co-fragm tions calcula nder the ssion ional s of he ment. ate Hydrogen Chloride – Water Dimer Part 2: Results and Discussion 142 The results on rotational excitation agree well with the propensity rules described by Ewing, 54-56 which combine the momentum (or energy) gap law with the requirement that the number of quanta transferred in the VP be minimized. This model explains why the preferred VP route often involves small translational energy (E T ) release, i.e., high rotational excitation when no excited vibrational levels are available. The complementary angular momentum (AM) model proposed by McCaffery and co-workers 52,53 is based on linear-to-angular momentum interconversion. It has been used recently to describe rotational distributions in the VP of weakly bound dimers. Realizing that there is insufficient anisotropy in the long-range part of the PES to explain the observed high fragment rotational excitation, the involvement of the repulsive, hard-shaped part of the PES is invoked. The AM model identifies the principal geometries and impact parameters from which dissociation occurs and reproduces well the fragments’ rotational distributions. The results suggest that the extent of rotational excitation is constrained by the hard-shaped potential, dimer geometry, and angular momentum conservation. Using these considerations, it was possible to predict some fragment HX rotational excitation in a series of acetylene-HX dimers (X = F, Cl, O) excited to the HX or asymmetric CH stretch vibration. 68 The nonstatistical nature of most of the observed rotational distributions in HX-containing complexes suggests that interactions with the repulsive part of the potential are more important than initial coupling of the OH stretch to all the available intermolecular modes followed by statistical predissociation. Hydrogen Chloride – Water Dimer Part 2: Summary and Conclusions 143 4.9 Summary and Conclusions The state-to-state VP of the hydrogen-bonded HCl-H 2 O dimer was studied following excitation of the bound HCl stretch via detection of the H 2 O photofragment. VMI and REMPI were used to determine the product energy distributions. Following vibrational excitation of the bound HCl stretch fundamental, H 2 O fragments were detected by 2 + 1 REMPI via the 1 B 1 (000) ← 1 A 1 (000) transition. The fragments’ c.m. translational energy distributions were determined from images of selected rotational states of H 2 O and were converted to rotational state distributions of the HCl cofragment. All the distributions could be fit well when using the previously published dissociation energy of D 0 = 1334 cm -1 . The rotational energy distributions of the HCl cofragment pair-correlated with specific rotational states of H 2 O encompassed all of the J" levels allowed by energy conservation. A detailed analysis of pair-correlated state distributions was complicated by the H 2 O REMPI spectrum, but the results show that the HCl rotational populations are nonstatistical with preference to rotational states that minimize translational energy release, in agreement with the conclusions reached from images of HCl (J") fragments. In addition, the HCl-H 2 O dimer study proves the feasibility of using the H 2 O 2 + 1 REMPI scheme to detect H 2 O fragments, even when water is a minor species of the sample. Compared to detection of NH 3 and HCl fragments, 1,34 H 2 O detection suffers from severe band overlap in the 1 B 1 (000) ← 1 A 1 (000) transition, which makes selection of isolated H 2 O states difficult. Additionally, the upper state is predissociative, reducing the REMPI efficiency, and only transitions with upper Hydrogen Chloride – Water Dimer Part 2: Summary and Conclusions 144 states having low values for K a ' can be detected. While the signal is reduced relative to monitoring the HCl and NH 3 fragments, the achieved signal-to-noise ratio in the images is sufficient to determine both D 0 and the pair-correlated state distributions. In the future, it may be advantageous to look for REMPI systems other than the 1 B 1 (000) ← 1 A 1 (000) transition for H 2 O detection, and to use a picosecond laser to compete effectively with predissociation. The successful detection and imaging of the H 2 O fragment provides a basis for looking at larger, more complicated H 2 O- containing complexes, including the H 2 O-H 2 O dimer (Chapter 5) and (H 2 O) 3 trimer (Chapter 6). Hydrogen Chloride – Water Dimer References 145 Chapter 4 References (1) Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2010, 114, 9774. (2) Rocher-Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2011, 115, 6903. (3) Rocher, B. E. Velocity Map Imaging of the State-Specific Vibrational Predissociation of Water-Containing Hydrogen-Bonded Complexes, University of Southern California, 2011. (4) Oudejans, L.; Miller, R. E. Annu. Rev. Phys. Chem. 2001, 52, 607. (5) Solomon, S.; Garcia, R. R.; Rowland, F. S.; Wuebbles, D. J. Nature 1986, 321, 755. (6) Molina, M. J.; Tso, T.-L.; Molina, L. T.; Wang, F. C.-Y. Science 1987, 238, 1253. (7) Tolbert, M. A.; Rossi, M. J.; Malhotra, R.; Golden, D. M. Science 1987, 238, 1258. (8) Peter, T. Annu. Rev. Phys. Chem. 1997, 48, 785. (9) Finlayson-Pitts, B. J.; Pitts, J. N. Chemistry of the Upper and Lower Atmosphere: Theory, Experiments and Applications; Academic Press: San Diego, CA, and London, 2000. (10) Lee, C.; Sosa, C.; Planas, M.; Novoa, J. J. J. Chem. Phys. 1996, 104, 7081. (11) Milet, A.; Struniewicz, C.; Moszynski, R.; Wormer, P. E. S. J. Chem. Phys. 2001, 115, 349. (12) Gutberlet, A.; Schwaab, G.; Birer, Ö.; Masia, M.; Kaczmarek, A.; Forbert, H.; Havenith, M.; Marx, D. Science 2009, 324, 1545. Hydrogen Chloride – Water Dimer References 146 (13) Skvortsov, D.; Lee, S. J.; Choi, M. Y.; Vilesov, A. F. J. Phys. Chem. A 2009, 113, 7360. (14) Alikhani, M. E.; Silvi, B. Phys. Chem. Chem. Phys. 2003, 5, 2494. (15) Huneycutt, A. J.; Stickland, R. J.; Hellberg, F.; Saykally, R. J. J. Chem. Phys. 2003, 118, 1221. (16) Kisiel, Z.; Pietrewicz, B. A.; Fowler, P. W.; Legon, A. C.; Steiner, E. J. Phys. Chem. A 2000, 104, 6970. (17) Legon, A. C.; Willoughby, L. C. Chem. Phys. Lett. 1983, 95, 449. (18) Bernal-Uruchurtu§, M. I.; Kerenskaya, G.; Janda, K. C. Int. Rev. Phys. Chem. 2009, 28, 223. (19) Schriver, A.; Silvi, B.; Maillard, D.; Perchard, J. P. J. Phys. Chem. 1977, 81, 2095. (20) Ault, B. S.; Pimentel, G. C. J. Phys. Chem. 1973, 77, 57. (21) Amirand, C.; Maillard, D. J. Mol. Struct. 1988, 176, 181. (22) Ayers, G. P.; Pullin, A. D. E. Spectrochimica Acta Part A: Molecular Spectroscopy 1976, 32, 1641. (23) Bacskay, G. B. Mol. Phys. 1992, 77, 61 (24) Ortlieb, M.; Birer, O.; Letzner, M.; Schwaab, G. W.; Havenith, M. J. Phys. Chem. A 2007, 111, 12192. (25) Weimann, M.; Fárník, M.; Suhm, M. A. Phys. Chem. Chem. Phys. 2002, 4, 3933. (26) Farnik, M.; Weimann, M.; Suhm, M. A. J. Chem. Phys. 2003, 118, 10120. (27) Chaban, G. M.; Gerber, R. B.; Janda, K. C. J. Phys. Chem. A 2001, 105, 8323. (28) Re, S.; Osamura, Y.; Suzuki, Y.; Schaefer Iii, H. F. J. Chem. Phys. 1998, 109, 973. Hydrogen Chloride – Water Dimer References 147 (29) Odde, S.; Mhin, B. J.; Lee, S.; Lee, H. M.; Kim, K. S. J. Chem. Phys. 2004, 120, 9524. (30) Packer, M. J.; Clary, D. C. J. Phys. Chem. 1995, 99, 14323. (31) Cabaleiro-Lago, E. M.; Hermida-Ramon, J. M.; Rodriguez-Otero, J. J. Chem. Phys. 2002, 117, 3160. (32) Huang, Z. S.; Miller, R. E. J. Chem. Phys. 1989, 91, 6613. (33) Skvortsov, D.; Choi, M. Y.; Vilesov, A. F. J. Phys. Chem. A 2007, 111, 12711. (34) Mollner, A. K.; Casterline, B. E.; Ch'ng, L. C.; Reisler, H. J. Phys. Chem. A 2009, 113, 10174. (35) Li, G.; Parr, J.; Fedorov, I.; Reisler, H. Phys. Chem. Chem. Phys. 2006, 8, 2915. (36) Pritchard, M.; Parr, J.; Li, G.; Reisler, H.; McCaffery, A. J. Phys. Chem. Chem. Phys. 2007, 9, 6241. (37) Parr, J. A.; Li, G.; Fedorov, I.; McCaffery, A. J.; Reisler, H. J. Phys. Chem. A 2007, 111, 7589. (38) Kandel, S. A.; Rakitzis, T. P.; Lev-On, T.; Zare, R. N. J. Chem. Phys. 1996, 105, 7550. (39) Rudić, S.; Ascenzi, D.; Orr-Ewing, A. J. Chem. Phys. Lett. 2000, 332, 487. (40) Romanescu, C.; Manzhos, S.; Boldovsky, D.; Clarke, J.; Loock, H.-P. J. Chem. Phys. 2004, 120, 767. (41) PGOPHER 2010, a Program for Simulating Rotational Structure, Western, C. M., University of Bristol, http://pgopher.chm.bris.ac.uk. (42) Callaghan, R.; Arepalli, S.; Gordon, R. J. J. Chem. Phys. 1987, 86, 5273. (43) Eppink, A. T. J. B.; Parker, D. H. Rev. Sci. Instrum. 1997, 68, 3477. Hydrogen Chloride – Water Dimer References 148 (44) Dribinski, V.; Potter, A. B.; Fedorov, I.; Reisler, H. J. Chem. Phys. 2004, 121, 12353. (45) Dribinski, V.; Ossadtchi, A.; Mandelshtam, V. A.; Reisler, H. Rev. Sci. Instrum. 2002, 73, 2634. (46) Demyanenko, A. V.; Dribinski, V.; Reisler, H.; Meyer, H.; Qian, C. X. W. J. Chem. Phys. 1999, 111, 7383. (47) Judge, R. H.; Clouthier, D. J. Comput. Phys. Commun. 2001, 135, 293. (48) Korolik, M.; Arnold, D. W.; Johnson, M. J.; Suchan, M. M.; Reisler, H.; Wittig, C. Chem. Phys. Lett. 1998, 284, 164. (49) Lanquetin, R.; Coudert, L. H.; Camy-Peyret, C. J. Mol. Spectrosc. 1999, 195, 54. (50) Sadlej, J.; Moszynski, R.; Dobrowolski, J. C.; Mazurek, A. P. J. Phys. Chem. A 1999, 103, 8528. (51) Lane, J. R.; Vaida, V.; Kjaergaard, H. G. J. Chem. Phys. 2008, 128, 034302. (52) Osborne, M. A.; McCaffery, A. J. J. Chem. Phys. 1994, 101, 5604. (53) McCaffery, A. J. Phys. Chem. Chem. Phys. 2004, 6, 1637. (54) Ewing, G. E. J. Phys. Chem. 1987, 91, 4662. (55) Ewing, G. E. J. Chem. Phys. 1980, 72, 2096. (56) Ewing, G. E. J. Chem. Phys. 1979, 71, 3143. (57) Reid, S. A.; Reisler, H. J. Phys. Chem. 1996, 100, 474. (58) Green, W. H.; Moore, C. B.; Polik, W. F. Annu. Rev. Phys. Chem. 1992, 43, 591. (59) Polik, W. F.; Moore, C. B.; Miller, W. H. J. Chem. Phys. 1988, 89, 3584. (60) Schinke, R.; Engle, V.; Andresen, P.; Häusler, D.; Balint-Kurti, G. G. Phys. Rev. Lett. 1985, 55, 1180. Hydrogen Chloride – Water Dimer References 149 (61) van Zee, R. D.; Pibel, C. D.; Butenhoff, T. J.; Moore, C. B. J. Chem. Phys. 1992, 97, 3235. (62) Schinke, R.; Vander Wal, R. L.; Scott, J. L.; Crim, F. F. J. Chem. Phys. 1991, 94, 283. (63) Pechukas, P.; Light, J. C. J. Chem. Phys. 1965, 42, 3281. (64) Zyrianov, M.; Sanov, A.; Droz-Georget, T.; Reisler, H. J. Chem. Phys. 1999, 110, 10774. (65) Potter, A. B.; Dribinski, V.; Demyanenko, A. V.; Reisler, H. J. Chem. Phys. 2003, 119, 7197. (66) Gross, A.; Mikkelsen, K. V.; Stockwell, W. R. Int. J. Quantum Chem. 2001, 84, 479. (67) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics: Theory and Experiments; Oxford University Press, Inc.: New York, 1996. (68) McCaffery, A. J.; Pritchard, M.; Reisler, H. Journal of Physical Chemistry A 2009, 114, 2983. (69) Soloveichik, P.; O’Donnell, B. A.; Lester, M. I.; Francisco, J. S.; McCoy, A. B. J. Phys. Chem. A 2009, 114, 1529. (70) Ni, H.; Serafin, J. M.; Valentini, J. J. J. Chem. Phys. 2000, 113, 3055. (71) Fraser, G. T.; Pine, A. S. J. Chem. Phys. 1989, 91, 633. (72) Farrell, J. J. T.; Suhm, M. A.; Nesbitt, D. J. J. Chem. Phys. 1996, 104, 9313. (73) Oudejans, L.; Miller, R. E. Chem. Phys. 1998, 239, 345. (74) Dribinski, V.; Potter, A. B.; Fedorov, I.; Reisler, H. J. Chem. Phys. 2004, 121, 12353. Hydrogen Chloride – Water Dimer References 150 (75) Ashfold, M. N. R.; Bayley, J. M.; Dixon, R. N. Chem. Phys. 1984, 84, 35. (76) Kuge, H. H.; Kleinermanns, K. J. Chem. Phys. 1989, 90, 46. (77) Uselman, B. W.; Boyle, J. M.; Anderson, S. L. Chem. Phys. Lett. 2007, 440, 171. (78) Dickinson, H.; Mackenzie, S. R.; Softley, T. P. Phys. Chem. Chem. Phys. 2000, 2, 4669. (79) Meijer, G.; ter Meulen, J. J.; Andresen, P.; Bath, A. J. Chem. Phys. 1986, 85, 6914. (80) Yang, C. H.; Sarma, G.; ter Meulen, J. J.; Parker, D. H.; Western, C. M. Phys. Chem. Chem. Phys. 2010, 12, 13983. (81) Hama, T.; Yokoyama, M.; Yabushita, A.; Kawasaki, M.; Andersson, S.; Western, C. M.; Ashfold, M. N. R.; Dixon, R. N.; Watanabe, N. J. Chem. Phys. 2010, 132, 164508. (82) Yang, C.-H.; Sarma, G.; ter Meulen, J. J.; Parker, D. H.; Buck, U.; Wiesenfeld, L. J. Phys. Chem. A 2010, 114, 9886. (83) Yuan, K.; Cheng, Y.; Cheng, L.; Guo, Q.; Dai, D.; Wang, X.; Yang, X.; Dixon, R. N. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 19148. (84) Parker, D. H.; Eppink, A. T. J. B. J. Chem. Phys. 1997, 107, 2357. W C d d e ex o co S p (0 M ca ch w F p fr + Water Dimer Chapt In th issociation espite grea nergy and xperimenta f the hydro ompared to urprisingly, rediction (C 000) is the Mainly, the alculation c hannel as w work has bee igure 5.1 hotoexcitin ragments in (000) and r er 5: W his chapter, energies of t interests i energy tra al challenges ogen-bonded o quasiclassi , although Chapter 2) 1 e major cha (000) + (0 captures tra well, which en publishe Vibrational ng the hydr n the ground (000) + (00 Water , the vibra f (H 2 O) 2 an in the water ansfer path s. Utilizing v d OH stretc ical trajecto our experi 1 and quasic annel, som 000) chann ajectories th h helps to e ed previousl l predissoc ogen-bonde d (000) and 00) were obs 151 r Dime ational pre d (D 2 O) 2 ar r dimer sinc ways have velocity ma ch of the w ory calculati imental res classical tra e other un nel with hig hat generat elucidate en ly. 2-4 iation of th ed OH stret bending ex served. er edissociation re reported ce decades not been ap imaging, water dimer ions and sta sults agree ajectory calc nusual chan gh rotation te high rota nergy trans he water d tch of the d xcited (010) n dynamics . As mentio ago, the dim measured vibrational has been i atistical pha e qualitative culations, in nnels have n. Interesti ation in the sfer pathwa dimer was dimer and ) state. Two Introdu s and accu oned previo mer dissocia directly du predissocia nvestigated ase space th ely with E n which (01 been obser ingly, trajec e (000) + ( ays. Part of investigate detecting w channels, ( ction urate ously, ation ue to ation d and eory. wing 10) + rved. ctory (000) f this d by water (010) Water Dimer Introduction 152 5.1 Introduction A general introduction, experimental setup and data analysis of hydrogen- bonded clusters have been presented in the previous chapters. Only information relevant to the (H 2 O) 2 and (D 2 O) 2 dimer will be presented in this chapter. The complex properties of water, which are due in large part to its hydrogen bond (H- bond) network, have fascinated and challenged chemists since the early 1920s. 5-10 In the gas phase, experimental emphasis has been placed on investigations of clusters in the cold environment of molecular beams, with most reports focusing on spectroscopy. 10,11 The mechanism of vibrational predissociation (VP) of H-bonded clusters are at present much less understood. 12 As the smallest cluster, the water dimer serves as a benchmark for both experiment and theory. 13,14 Studies of H-bond breaking in the dimer provide critical information on bond strength and energy relaxation, both of which are important in understanding these processes in complex water networks, such as clusters, liquids, solids, water chains and other unusual structures. 10,11,15-18 The atmospheric importance of the water dimer continues to be the subject of intense interest. 19-22 In this context, an accurate value of the bond dissociation energy (D 0 ) of the dimer is crucial in assessing the contributions of the water dimer to absorption in the atmosphere. 19 Pairwise interactions are also important in amorphous solid water, which is the most common form of water in the universe. 17 It is therefore quite surprising that so little is known about the VP dynamics of the water dimer. Water Dimer Introduction 153 Here, we report studies of VP following excitation of the H-bonded OH and OD stretch of (H 2 O) 2 and (D 2 O) 2 , respectively, and determine D 0 and correlated internal states of monomer fragments. Upon excitation of the dimer, two channels are energetically open for (H 2 O) 2 and (D 2 O) 2 : (1) (000) + (000) and (2) (000) + (010), where (000) and (010) are the ground and first bending vibrational states of the fragment, respectively. Experimental studies of state-specific energy transfer and H-bond breaking pathways of water-containing dimers are scarce because of difficulties in detecting water fragments. It is only recently that water fragments were detected state- selectively in VP of dimers, 2,23 and the D 0 of (H 2 O) 2 was reported with spectroscopic accuracy (1105 ± 10 cm -1 ), 2 in excellent agreement with theory (1103 ± 5 cm -1 [ref 24] and 1108.2 cm -1 [ref 14]). In this paper, we report for the first time the experimental determination of D 0 for (D 2 O) 2 . We also determine pair-correlated fragment state distributions (i.e., the cofragment state distribution correlated with a specific rovibrational state of the other monomer fragment) for (H 2 O) 2 and (D 2 O) 2 . Such pair-correlated distributions can provide rigorous tests of mechanisms. Recently, Czakó et al. 13 calculated D 0 = 1244 ± 5 cm -1 for (D 2 O) 2 and reported preliminary quasiclassical trajectory (QCT) calculations predicting that the predominant channel in the VP of (H 2 O) 2 and (D 2 O) 2 was (000) + (010). The theoretical calculations provide complementary information, which is partly inaccessible in experiments. For example, the calculations show that bending vibrational excitation is distributed equally between fragments corresponding to the donor (d) and acceptor (a) units. The new QCT calculations reported here Water Dimer Experimental Methods 154 provide for the first time fragment rotational distributions correlated separately with channels (1) and (2). This information is currently impossible to obtain experimentally. In addition, we analyze representative trajectories and report vector correlations in fragment rotations. The combined theoretical and experimental results reveal new insights about energy transfer and the VP mechanism. 5.2 Experimental Methods Two experimental methods of data collection were used: (i) time-of-flight mass spectrometry combined with 2 + 1 resonance-enhanced multiphoton ionization (REMPI) for spectroscopic investigations of water monomer fragments, and (ii) velocity map imaging for deriving internal energy distributions of cofragments (nondetected fragments) as well as determining D 0 of (H 2 O) 2 and (D 2 O) 2 . The experimental setup and procedures are similar to those used in the previous studies 2,23,25,26 and the details are discussed in Chapter 3. The dimers were formed in a pulsed supersonic molecular beam by expanding ~2% water in helium at a stagnation pressure of ~2 atm through the 0.5 mm orifice of a pulsed valve. Focused infrared (IR) radiation excited the hydrogen bonded OH and OD stretch of (H 2 O) 2 and (D 2 O) 2 at 3602 and 2634 cm -1 , respectively. Tightly focused ultraviolet (UV) radiation ionized state-selected H 2 O and D 2 O fragment, scanning through the 1 B 1 (000) ← 1 A 1 (000 or 010) bands using REMPI. The 1 B 1 excited state of H 2 O has a short lifetime due to predissociation, particularly for high ′ with high ′ Water Dimer Experimental Methods 155 levels, 27 which prevents us from detecting certain high rotational levels and makes the detection scheme more dependent on excitation conditions. For this reason, the H 2 O REMPI spectra are also noisier compared to those of D 2 O, which is less predissociative. On the other hand, the D 2 O spectra are more congested due to smaller spacings between rotational levels. Spectra were collected by alternating “IR on” and “IR off” conditions. IR laser conditions (timing, focusing, power) were optimized to ensure single-photon absorption. UV laser conditions were optimized for the best signal-to-noise ratio. Expansion conditions (water concentration, helium backing pressure) were optimized to maximize signal from the dimer. A cryopumping system cooled by liquid nitrogen was installed to reduce background water during data acquisition. The dimer hydrogen bonded OH and OD stretch is red-shifted by ~150 cm -1 from the monomer antisymmetric stretch, the trimer hydrogen bonded stretch is 40-70 cm -1 red-shifted from the trimer. 28,29 The combination of IR laser and expansion conditions allows excitation of water dimer without contributions from higher clusters. The combination of UV laser conditions and cryopumping maximizes detection of the water fragment upon dimer dissociation and minimizes background signals from water monomers. The velocity map imaging arrangement and data analysis methods have been described in Chapter 3. Two-dimensional projections of the velocity distributions were collected using event counting and reconstructed to give velocity or speed distributions using the BASEX method. 30 Water Dimer Computational Methods 156 5.3 Computational Methods The QCT calculations were performed with the ab initio HBB2 potential energy surface. 24 Standard normal-mode sampling was applied to prepare the initial quasiclassical states by giving harmonic zero-point energy to each mode and an extra quantum of excitation to the hydrogen-bonded OH and OD stretch fundamental, i.e., almost a local mode of the donor. The total rotational angular momentum of the dimers was set to zero. A total of 30,000 trajectories for each dimer were propagated for about 25 ps using a 0.25 fs time step. For (D 2 O) 2 we ran 10,000 longer (50 ps) trajectories as well. The product states of the fragments were analyzed for dissociation trajectories with O—O distance > 10 Å. At 25 ps about 84% of the (H 2 O) 2 trajectories dissociated, but only 25% of the (D 2 O) 2 trajectories did. This latter value increases to about 64% at 50 ps. We determined the normal mode quantum number for the water fragment pair using the procedure described previously. 13,31 The rovibrational distributions were computed by the efficient Gaussian binning procedure (1GB). 13,31 In the present implementation, 1GB means one Gaussian weight for each fragment based on its total vibrational energy; thus, the weight of a correlated state is the product of two Gaussians. 1 GB assigns small weights for trajectories in which either fragment violates zero point energy, thereby effectively addressing the well-known zero point energy issue of the quasiclassical trajectory method. (Note that the Gaussians have finite widths; in the present case the full width at half-maximum is 0.1, which Water Dimer Results and Discussion 157 corresponds to about 900 and 700 cm -1 for H 2 O and D 2 O, respectively. Thus, 1GB can allow small nonzero weights for energetically closed states.) 5.4 Results and Discussion IR action spectra of the excited dimers were obtained by monitoring H 2 O and D 2 O fragments in selected rovibrational states by REMPI while scanning the IR laser frequency. The positions and shape of the hydrogen-bonded OH and OD stretch bands, which indicate that the absorbed species are dimers, were similar to previously reported spectra. 28,32 A typical spectrum at 3585—3610 cm -1 obtained by monitoring H 2 O (010) J" KaKc = 3 2,1 is shown in Figure 5.2 (a). The (D 2 O) 2 spectrum at 2623—2645 cm -1 obtained by monitoring D 2 O (000) J" KaKc = 13 1,12 is shown in Figure 5.2 (b). Figure 5.2 Fragment yield IR spectra of (a) (H 2 O) 2 [monitoring H 2 O (010) J  Ka,Kc = 3 2,1 ] and (b) (D 2 O) 2 [monitoring a D 2 O (000) transition with a major contribution from J" Ka,Kc = 13 1,12 ]. The top (red) curves show dimer spectra obtained by monitoring the monomer fragment. The bottom (black) curves show background signal from monomers in the molecular beam under the same conditions. Water Dimer Results and Discussion 158 The lifetimes of excited (H 2 O) 2 and (D 2 O) 2 are 80 ps and 5 ns, respectively. Figure 5.3 shows REMPI spectra of H 2 O and D 2 O fragments in the C  1 B 1 (000) ← X  1 A 1 (000 and 010) bands. Spectral congestion and/or upper state predissociation prevent us from converting the REMPI spectra into complete rotational populations of the fragments. However, the spectra in Figures 5.3a, 5.3b and 5.3d were simulated fairly well with rotational temperatures of 250 ± 50, 250 ± 50 and 150 ± 50 K, respectively. No temperature gave a good fit to the spectrum in Figure 5.3c; specifically, several prominent peaks include unusually large contributions from J >11 (see below). Several isolated rotational transitions of H 2 O (000) and (010) fragments were used for imaging, as described before. 2 The REMPI spectrum of fragment D 2 O (000), with allowed transitions from J  = 0 - 16 (Figure 5.3c), is very congested, and we could find no unblended lines suitable for accurate determination of D 0 . Fortunately, the C  1 B 1 (000) ← X  1 A 1 (010) band has only few (J  ≤ 5) energetically allowed transitions, and images from isolated transitions of D 2 O (010) fragments were used for determination of D 0 . Water Dimer Results and Discussion 159 Figure 5.3. Fragment yield spectra of (H 2 O) 2 and (D 2 O) 2 . The black curves correspond to the fragments 2 + 1 REMPI enhancement spectra scanning the (a) H 2 O C  1 B 1 (000) ← X  1 A 1 (000) band; (b) H 2 O C  1 B 1 (000) ← X  1 A 1 (010) band; (c) D 2 O C  1 B 1 (000) ← X  1 A 1 (000) band; and (d) D 2 O C  1 B 1 (000) ← X  1 A 1 (010) band. The red curves correspond to PGOPHER simulations 33 with known spectroscopic parameters, 27 and using the labeled rotational temperatures. Assigned REMPI transitions selected for images are labeled. * denotes a blended transition with a major contribution from J  KaKc = 13 1,12 . Figure 5.4 shows representative velocity distributions obtained by VMI. The recorded two-dimensional projections of ionized fragments were reconstructed to three-dimensional images. 2,23,25,26 Reconstructed images in velocity space were obtained by summing over the isotropic angular distribution for each radius. The isotropy of the angular distributions reflects the slowness of the dissociation processes. The velocity distributions were used to determine the rotational Water Dimer Results and Discussion 160 populations of H 2 O and D 2 O cofragments pair-correlated with each monitored rovibrational state, as described before. 2,23,25,26 Fitting was accomplished by assigning a Gaussian-shaped curve to rotational levels 34,35 of each cofragment vibrational state. The positions of these Gaussians were determined by conservation of energy, E rot (dimer) + hν = D 0 + E T + E vib,rot (mon) + E vib,rot (cofrag) where E rot (dimer) is the dimer rotational energy estimated from IR spectra (5 and 7 ± 5 cm -1 for (H 2 O) 2 and (D 2 O) 2 , respectively); hν is the IR photon energy; E T is the measured center-of-mass (c.m.) translational energy ( α velocity 2 ); and E vib,rot (mon) (defined by REMPI) and E vib,rot (cofrag) are the rovibrational energies of the monitored fragment and the cofragment, respectively. The positions of the Gaussians were shifted together by adjusting D 0 until both the observed structure and the maximum velocity were well matched in all the images. The widths of the Gaussians (44 and 39 m/s for H 2 O and D 2 O fragments, respectively) were obtained from previous calibration experiments. 23 In all cases reasonable fits to the velocity distributions were obtained by using an exponentially decaying function for the heights of the Gaussians, corresponding to decrease in rotational population with increasing E T . However, to obtain best fits, state-to-state population fluctuations have to be included. For images in the (000) state, because of the overlap of two sets of rotational levels in the cofragment [cofragments in (000) and (010) states] and congestion of the J  KaKc levels, it was impossible to adjust the height of each Gaussian unambiguously for a detailed rotational population distribution. For images in the (010) state, where the Water Dimer Results and Discussion 161 cofragment is only allowed in the (000) state, the heights of the Gaussian curves were adjusted to obtain the best fit. As before, 2,23,25,26 we find that the D 0 value derived from fitting multiple images is narrowly constrained by the fits to unique structures in each image, which are determined by rotational level positions. The same D 0 value is obtained whether we use smooth population functions or adjust the height of each Gaussian to obtain the best fit to the overall velocity distribution. Figure 5.4. Velocity distributions from reconstructed images obtained by monitoring state-selected fragments. The red curves show experimental results of state-selected H 2 O or D 2 O fragments and the blue ones correspond to total integrated simulations. The Gaussians (black curves) in (b), (c) and (d) are the energetically allowed rotational levels of the cofragment. In (a), the Gaussians were integrated to obtain the green and purple curves for cofragment in the (000) and (010) state, respectively. A ratio of (000):(010) = 1:2 was used. Water Dimer Results and Discussion 162 Figure 5.4a shows a velocity distribution obtained by monitoring H 2 O (000) J  KaKc = 3 2,1 , where the cofragments are formed in both the (000) and (010) states. Best fits are obtained with a ratio of (000):(010) = 1:2 in the cofragments. Figure 5.4b shows the image obtained by monitoring J  KaKc = 3 2,1 , of (010). When monitoring rotational levels in D 2 O (000) up to J  = 5, both the (000) and (010) vibrational levels of the cofragment can be populated, but only the (000) level is allowed for J > 5. As described above, all spectral lines of D 2 O (000) are blended, and thus the exact ratio of (000):(010) in the cofragments cannot be determined from the images, but the fits show that a large fraction of the fragments are in the (010) state. Indeed, a REMPI spectrum of D 2 O (010) fragments was obtained (Figure 5.3d), and D 0 of (D 2 O) 2 was determined by fitting four images of isolated transitions of D 2 O (010). Figure 5.4d shows a representative velocity distribution. After internal energy and error corrections, these images give D 0 = 1244 ± 10 cm -1 , in excellent agreement with theory. 13 Images obtained by monitoring blended transitions of D 2 O (000) are consistent with this value (Figures 5.4c). Fitting the unique structures in the images puts the uncertainty of the fits at 2-8 cm -1 , depending on the signal-to-noise ratio in each image. The uncertainty in internal energy of the dimer is estimated to be ± 5 cm -1 , and IR frequency calibration adds another 1 cm -1 to the uncertainty. Taking weighted average of all our data and combining random and systematic uncertainties, we arrive at the uncertainty quoted above. Water Dimer Results and Discussion 163 The D 2 O (000) images confirm that the intense peaks in the REMPI spectrum that could not be fit by a 250 K rotational temperature include large contributions from high J s. For example, in Figure 5.3c, the high J  state gives rise to the prominent low-velocity features. Our inability to observe a comparable excess population in high J  levels of H 2 O (000) may be due to the faster predissociation of the C  1 B 1 state of H 2 O. 27 The experimental results give rotational distributions of the cofragments pair-correlated with specific H 2 O and D 2 O rovibrational levels, and these distributions encompass all the rotational states allowed by energy conservation. In spite of some fluctuations in state populations, they show consistent preferential population of high rotational levels that minimize translational energy release. The trajectory calculations, on the other hand, give the overall rotational distributions for each product rotational channel, as described below. Calculated channel-specific rotational distributions for (D 2 O) 2 are shown in Figure 5.5. The rotational distributions for the (000) + (010) channel are significantly colder than those for the (000) + (000) channel, as expected from the reduced available energy. The distributions are broad, each peaking at J  around of 4 and 7, respectively. (Note that for (000) + (010) the maximum allowed J  is 5, but non-zero computed populations for J  > 5 are possible owing to the highly asymmetric top nature of the monomers and the finite widths (about 700 cm -1 for D 2 O) of the Gaussians allowing a few hundred cm -1 ZPE violation, which is small relative to the ZPE of the monomers, but not small enough to force the threshold in the rotational distributions.) The rotational distributions corresponding to the donor and acceptor fragments in each Water Dimer Results and Discussion 164 channel are similar, and there is an equal likelihood that the bending excitation resides in the donor or acceptor fragments. 13 This indicates that energy is shared between the two monomers, even though the OD stretch excitation has been placed initially in the donor. The rotational distributions of the corresponding product channels in (H 2 O) 2 are similar to those from (D 2 O) 2 . The average rotational energy in each D 2 O fragment for the major (000) + (010) channel is 75  20 cm -1 . 36 This value is in good agreement with the experimental estimate of 100  40 cm -1 , obtained from the temperature simulation of the REMPI spectrum (Figure 5.3d). Figure 5.5. Calculated vibrational state-specific rotational distributions of D 2 O fragments from VP of (D 2 O) 2 . (a) Ground vibrational state products; (b) one bend- excited monomer fragment. Water Dimer Results and Discussion 165 Figure 5.6. Correlation between the relative center of mass velocity vector (v) and the total angular momentum vector (J) of either the donor (J d ) or the acceptor (J a ) fragment [(a) and (c)] as well as correlation between the J d and J a vectors [(b) and (d)]. We also examined vector correlations of the relative c.m. velocity vector (v) and the classical total angular momentum vector (J) integrated over the fragment states. The computed results show that v and J of either the donor or the acceptor fragment are correlated, since the scalar product of v and J shows a Gaussian-like distribution peaking at 0 (Figure 5.6). This indicates that both the donor and acceptor fragments are preferentially formed in rotational states with J vectors perpendicular, on average, to the relative velocity vector of the fragments. The J vectors of the two fragments are also correlated favoring an anti-parallel orientation that facilitates angular momentum conservation. Water Dimer Results and Discussion 166 More insight into the dissociation dynamics is obtained by examining the time evolution of trajectories that lead to dissociation, and a (H 2 O) 2 and a (D 2 O) 2 trajectory can be seen as animations. Snapshots of a representative (H 2 O) 2 are shown in Figure 5.7. As seen, the identity of the donor and acceptor switches, at later times and larger O-O distance the two monomers assume a quasi-planar geometry, and finally we see dissociated monomers. Exchanges of donor and acceptor occur several times during the trajectory, which explains the similar rotational distributions as noted above. This facile exchange is a consequence of the low barrier (the largest being roughly 620 cm -1 ) for isomerization of the water dimer to the eight equivalent minima, 37 which are accurately reproduced by the PES. Figure 5.7. Selected frames labeled in picoseconds in increasing time sequence of a (H 2 O) 2 trajectory leading to dissociation. Note the exchange of donor and acceptor (in the first picosecond) that occurs several times during the trajectory before dissociation occurs. The experimental and theoretical results described herein depict, for the first time, a detailed picture of the VP of the water dimer. Following excitation of the bonded OH and OD stretch of the donor, calculations show that vibrational energy is Water Dimer Results and Discussion 167 shared among the donor and acceptor vibrational levels. The major dissociation channel is (000) + (010) with equal probability of bending excitation in the donor and acceptor fragments, and the donor and acceptor have similar and broad rotational state distributions. The experimental pair-correlated distributions are also broad, with a nonstatistical rotational energy distribution in the cofragment biased in favor of high rotational levels that minimize translational energy release. There is also a clear preference for producing one fragment in the (010) state, in accordance with the momentum-gap law of energy transfer. 38 The initial energy transfer out of the OH and OD stretch could involve coupling to two quanta of intramolecular bend and one or more intermolecular vibrations, since there are near-resonant pathways for both (D 2 O) 2 and (H 2 O) 2 . For example, in (H 2 O) 2 the bound OH stretch (3601 cm -1 ) is nearly resonant with two quanta of intramolecular bend plus an intermolecular bend. 39 Of course this energy transfer must then decay to one involving excitation of the dissociative degree of freedom, which often leaves one quantum of bend excitation in a fragment. One can envision scenarios where the initial bending excitation resides in one water molecule or is shared between the two water molecules (i.e., formation of (020) or (010) + (010)). As seen from the trajectories, the coupling of at least one bending quantum to the intermolecular modes involves extensive intramolecular vibrational redistribution among the intermolecular modes, including the exchange of donor and acceptor, which explains their final broad and similar rotational state distributions. The coupling to the dissociation coordinate is apparently inefficient, Water Dimer Results and Discussion 168 as both experiment and theory show dimer lifetimes >10 ps. 13,28 However, while there is ample time for the energy to redistribute among the available vibrational states, only restricted paths lead eventually to dissociation. The result is that while the rotational energy distributions are broad, they are not statistical. In fact, the propensity to generate one water fragment in the (010) state as well as in high rotational levels indicates that the momentum gap law, which predicts a preference for final fragment states that minimize translational energy release, is still manifest despite the extensive intramolecular vibrational redistribution and long dissociation time. An intriguing aspect in the REMPI spectrum of D 2 O (000) is the enhanced population of high rotational levels whose energies lie within 100 cm -1 of the 1178 cm -1 J  KaKc = 0 0,0 level of D 2 O (010). The minor (000) + (000) channel may result in part from processes in which the excited dimer samples the repulsive part of the PES in an impulsive interaction, converting all the vibrational excitation into fragment rotation and translation, 40 thereby accessing high rotational levels. This, however, is a minor channel. Water Dimer Conclusion 169 5.5 Conclusion The theoretical calculations of D 0 of (H 2 O) 2 and (D 2 O) 2 are in excellent agreement with experiment, demonstrating the high quality of the water dimer PES. Trajectory calculations and experimental results both show broad rotational distributions of the monomer products. Theory and experiment both find the major channel to be (000) + (010) indicating that the vibrationally excited H-bonded OH stretch relaxes via a pathway that preferentially leads to bend excitation in the monomer. Dissociation is slow and involves extensive intramolecular vibrational energy distribution in the dimer but product state distributions are not statistical. In the future, we hope to extend these results to the cyclic water trimer – the smallest network of hydrogen bonds. Water Dimer References 170 Chapter 5 References (1) Ewing, G. E. J. Chem. Phys. 1980, 72, 2096-2107. (2) Rocher-Casterline, B. E.; Ch'ng, L. C.; Mollner, A. K.; Reisler, H. J. Chem. Phys. 2011, 134, 211101. (3) Ch’ng, L. C.; Samanta, A. K.; Czakó, G.; Bowman, J. M.; Reisler, H. J. Am. Chem. Soc. 2012, 134, 15430-15435. (4) Rocher, B. E. Velocity Map Imaging of the State-Specific Vibrational Predissociation of Water-Containing Hydrogen-Bonded Complexes, University of Southern California, 2011. (5) Latimer, W. M.; Rodebush, W. H. J. Am. Chem. Soc. 1920, 42, 1419-1433. (6) Pauling, L. Proc. Natl. Acad. Sci. U.S.A. 1928, 14, 359-362. (7) Bernal, J. D.; Fowler, R. H. J. Chem. Phys. 1933, 1, 515-548. (8) Pauling, L. The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry; Cornell University Press: New York, 1939. (9) Scheiner, S. Hydrogen Bonding: A Theoretical Perspective; Oxford University Press: New York, 1997. (10) Keutsch, F. N.; Saykally, R. J. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 10533- 10540. (11) Keutsch, F. N.; Cruzan, J. D.; Saykally, R. J. Chem. Rev. 2003, 103, 2533-2578. (12) Oudejans, L.; Miller, R. Annu. Rev. Phys. Chem. 2001, 52, 607-637. (13) Czakó, G.; Wang, Y.; Bowman, J. M. J. Chem. Phys. 2011, 135, 151102. Water Dimer References 171 (14) Leforestier, C.; Szalewicz, K.; van der Avoird, A. J. Chem. Phys. 2012, 137, 014305. (15) Rey, R.; Møller, K. B.; Hynes, J. T. Chem. Rev. 2004, 104, 1915-1928. (16) Bakker, H. J.; Skinner, J. L. Chem. Rev. 2010, 110, 1498-1517. (17) Smith, R. S.; Petrik, N. G.; Kimmel, G. A.; Kay, B. D. Acc. Chem. Res. 2011, 45, 33-42. (18) Paesani, F.; Xantheas, S. S.; Voth, G. A. J. Phys. Chem. B 2009, 113, 13118- 13130. (19) Vaida, V. J. Chem. Phys. 2011, 135, 020901. (20) Scribano, Y.; Goldman, N.; Saykally, R. J.; Leforestier, C. J. Phys. Chem. A 2006, 110, 5411-5419. (21) Goldman, N.; Leforestier, C.; Saykally, R. J. J. Phys. Chem. A 2004, 108, 787- 794. (22) Goldman, N.; Fellers, R. S.; Leforestier, C.; Saykally, R. J. J. Phys. Chem. A 2000, 105, 515-519. (23) Rocher-Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2011, 115, 6903-6909. (24) Shank, A.; Wang, Y.; Kaledin, A.; Braams, B. J.; Bowman, J. M. J. Chem. Phys. 2009, 130, 144314. (25) Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2010, 114, 9774-9781. (26) Mollner, A. K.; Casterline, B. E.; Ch'ng, L. C.; Reisler, H. J. Phys. Chem. A 2009, 113, 10174-10183. Water Dimer References 172 (27) Yang, C. H.; Sarma, G.; ter Meulen, J. J.; Parker, D. H.; Western, C. M. Phys. Chem. Chem. Phys. 2010, 12, 13983-13991. (28) Paul, J. B.; Provencal, R. A.; Saykally, R. J. J. Phys. Chem. A 1998, 102, 3279- 3283. (29) Paul, J. B.; Collier, C. P.; Saykally, R. J.; Scherer, J. J.; O'Keefe, A. J. Phys. Chem. A 1997, 101, 5211-5214. (30) Dribinski, V.; Ossadtchi, A.; Mandelshtam, V. A.; Reisler, H. Rev. Sci. Instrum. 2002, 73, 2634-2642. (31) Czakó, G.; Bowman, J. M. J. Chem. Phys. 2009, 131, 244302. (32) Huang, Z. S.; Miller, R. E. J. Chem. Phys. 1989, 91, 6613-6631. (33) PGOPHER 2009, a Program for Simulating Rotational Structure, Western, C. M., University of Bristol, http://pgopher.chm.bris.ac.uk. (34) Tennyson, J.; Zobov, N. F.; Williamson, R.; Polyansky, O. L.; Bernath, P. F. J. Phys. Chem. Ref. Data 2001, 30, 735-831. (35) Mellau, G.; Mikhailenko, S. N.; Starikova, E. N.; Tashkun, S. A.; Over, H.; Tyuterev, V. G. J. Mol. Spectrosc. 2004, 224, 32-60. (36) The average rotational energy of 75 cm -1 was obtained by using 1GB and giving zero weights to trajectories in which the sum of the rotational energies of the fragments is larger than the maximum available rotational energy of 210 cm -1 . Without this rotational energy constraint, 1GB provides an average rotational energy of 180 ± 20 cm -1 . Note that the error bars correspond to statistical uncertainties (without considering systematic uncertainties). Water Dimer References 173 (37) Tschumper, G. S.; Leininger, M. L.; Hoffman, B. C.; Valeev, E. F.; Schaefer Iii, H. F.; Quack, M. J. Chem. Phys. 2002, 116, 690-701. (38) Ewing, G. E. J. Phys. Chem. 1987, 91, 4662-4671. (39) Note that the vibrational levels are measured or calculated for ground state dimer and not for a dimer with one quantum of OH and OD stretch. Because most of the values are taken from matrix isolation data, they differ slightly from gas phase values. Also, the floppiness of the dimer may give values that deviate from the average equilibrium values. (40) Pritchard, M.; Parr, J.; Li, G.; Reisler, H.; McCaffery, A. J. Phys. Chem. Chem. Phys. 2007, 9, 6241-6252. Water Trimer Introduction 174 Chapter 6: Water Trimer In this chapter, the vibrational predissociation dynamics and the dissociation energy of the (H 2 O) 3 → H 2 O + (H 2 O) 2 dissociation channel are investigated. Due to large density of states of the water trimer, there is a high probability of intramolecular vibrational redistributions. In addition, the rovibrational density of states of the (H 2 O) 2 fragments are much higher than the monomer fragments, such as HCl and H 2 O. Therefore, the product energy distributions of the (H 2 O) 3 → H 2 O + (H 2 O) 2 channel may be statistical-like compared to that of (H 2 O) → 2 H 2 O. The measured translational energy distributions can be fit well with energy distributions simulated by using statistical phase space theory. The energy distributions calculated by quasiclassical trajectory calculations also agree with statistical predictions. The availability of the low-lying intermolecular vibrational levels in the dimer fragment is likely to facilitate energy transfer before dissociation occurs, leading to statistical-like product state distributions. Part of the work described in this chapter has been published previously [DOI: 10.1021/jp401155v]. Figure 6.1 Vibrational predissociation of the water trimer involves intramolecular vibrational redistribution and sequential bond breaking. The dissociation channel, (H 2 O) 3 → H 2 O + (H 2 O) 2 , was investigated by detecting the H 2 O fragment. Water Trimer Introduction 175 6.1 Introduction A general introduction, experimental setup and data analysis of hydrogen- bonded clusters have been presented in the previous chapters. Only information relevant to the water trimer will be presented in this chapter. Since the first description of the hydrogen bond (H-bond) in water in the early 1920s, the study of water has been an area of intense research efforts. 1-6 Water and its H-bond network is an exceedingly complicated system that is still not understood completely. The unique properties of water, such as its unusual density and high boiling point, are mainly due to the intermolecular forces that act among water molecules both in pairwise and non-pairwise additive interactions. As the smallest water cluster with a complete H-bond network, the cyclic water trimer serves as a prototype for examination of cooperative (nonadditive) interactions. This can help to understand the complex nature of larger water networks, such as liquids, solids, water chains, etc. The structure, vibrational frequencies, potential energy surface (PES), three- body effects, binding energies and tunneling motions of the water trimer have been studied extensively by theory. 7-12 Work up to 2003 is summarized in an exhaustive review, 12 and additional work has been published since then. 13-19 In gas phase experiments, emphasis has been placed on investigations of the trimer in cold molecular beams, with most reports focusing on structure and spectroscopy. In particular, the detailed, high-resolution spectroscopic studies of Saykally and coworkers mapped the vibrational, rotational, and tunneling (VRT) states of the Water Trimer Introduction 176 trimer and estimated the barriers between different conformations. 12,20 In addition, the intra- and intermolecular vibrational modes were characterized in molecular beams, He droplets and matrix isolation experiments. 21-29 Despite the fundamental interest in the nature of the cooperative interactions in the H-bond network and their influence on the H-bond strength, 6,7,12,30-33 no experimental measurements of the dissociation energy (D 0 ) of the trimer have been reported. Likewise, studies of energy transfer and H-bond breaking pathways of water clusters are scarce, partly because of difficulties in detecting water fragments. Our recent success in detecting internally excited water fragments in the vibrational predissociation (VP) of the water dimer paved the way for studying bond breaking in larger water clusters. Recently, D 0 of the water dimers (H 2 O) 2 and (D 2 O) 2 , whose binding is dominated by pairwise interactions, were determined accurately at 1105 and 1244 ± 10 cm -1 , 34,35 respectively, in excellent agreement with the corresponding calculated values of 1104 and 1244 ± 5 cm -1 . 36,37 Quasiclassical trajectory (QCT) calculations using an accurate full-dimensional PES were in accord with the experiments and helped to elucidate dissociation mechanisms. 35 Due to the larger number of available fragment quantum states, experimental investigations of (H 2 O) 3 are much more challenging. The excellent agreement between theory and experiment for D 0 of the water dimer has defined this system as a benchmark for theory. Subsequently, Wang and Bowman 38 calculated D 0 of (H 2 O) 3 and (D 2 O) 3 using an ab initio full-dimensional PES together with Diffusion Monte Carlo calculations. The calculated D 0 values for the Water Trimer Introduction 177 (H 2 O) 3 → H 2 O + (H 2 O) 2 and (H 2 O) 3 → 3 H 2 O dissociation channels are 2726 ± 30 cm -1 and 3855 ± 20 cm -1 , respectively. 38 The issue of non-pairwise additivity was investigated theoretically and its contribution to the value obtained by simply doubling the dimer’s D 0 (1105 x 2 = 2210 cm -1 ) was estimated at about 500 cm -1 . An experimental confirmation of the cooperative interaction modeled by theory is highly desirable. An agreement would also help to increase the confidence level for calculations of higher clusters with similar types of H-bond networks. In this chapter we report the first experimental determination of D 0 of (H 2 O) 3 by exciting the H-bonded OH-stretch fundamental at 3536 cm -1 . We can obtain D 0 only for the H 2 O + (H 2 O) 2 channel, as the excitation energy is insufficient to break all three H-bonds. We also examine the pair-correlated fragment state distributions; i.e., the (H 2 O) 2 cofragment (undetected fragment) state distribution correlated with a specific rotational state of the monitored H 2 O fragment. Following excitation of the H-bonded OH-stretch of (H 2 O) 3 , H 2 O fragments can be formed only in the ground vibrational state, whereas all the intermolecular vibrational modes of the (H 2 O) 2 fragment can be populated (but not the intramolecular modes). Our previous experimental and theoretical investigations of energy transfer in the water dimer found predominant bending excitation in the monomer fragment upon H-bond breaking. A preference for final fragment rotational states that minimize translational energy release was also observed. Since the H 2 O fragment bending excitation is energetically forbidden in VP of (H 2 O) 3 via excitation of the H- bonded OH-stretch, vibrational population can only reside in the intermolecular Water Trimer Introduction 178 modes of (H 2 O) 2 . Due to the large density of states in the (H 2 O) 2 fragment, its energy distributions might be more statistical compared to the corresponding behavior in fragments of (H 2 O) 2 dissociation and other small water-containing dimers. 34,35,39-41 The energy distributions in the trimer’s fragmentation are compared here to the results of QCT calculations and statistical predictions. The water trimer adopts six low-lying stationary points (Figure 6.1). Among these, the global minimum consists of three H-bonds, and has a cyclic structure that is conventionally denoted as “up-up-down” depending on the orientations of the free OH-bonds relative to the plane defined by the three oxygen atoms. 12,42 (H 2 O) 3 has one weaker H-bond due to repulsion of the two “up” OH-bonds, giving two different H-bonded OH-stretch fundamentals that differ in energy by 12 –15 cm - 1 . 19,28 Figure 6.1. Configurations of the up-up-down (uud) global minimum and other low- lying stationary points of the water trimer. See reference 42 for the energies of these stationary points, which are less than 1 kcal/mol (350 cm -1 ) above the global minimum except for the planar ppp saddle point. Water Trimer Experimental Methods 179 6.2 Experimental Methods Vibrational predissociation of (H 2 O) 3 formed in a pulsed supersonic molecular beam was studied following pulsed infrared (IR) laser excitation. Two experimental methods of data collection were used: (i) time-of-flight mass spectrometry combined with 2 + 1 resonance-enhanced multiphoton ionization (REMPI) for spectroscopic investigations of H 2 O fragments, and (ii) velocity map imaging (VMI) for deriving internal energy distributions of (H 2 O) 2 cofragments (undetected fragments) as well as determining D 0 for the (H 2 O) 3 → H 2 O + (H 2 O) 2 channel. Figure 6.2 illustrates the experimental scheme. Upon excitation of the H- bonded OH-stretch, VP occurs following coupling of energy to the dissociation coordinate. The excess energy can be distributed among center-of-mass (c. m.) translation and rotational and rovibrational states of the H 2 O and (H 2 O) 2 fragments, respectively. The experimental procedures are similar to those used in previous studies. 35,39-41 (H 2 O) 3 was formed in a pulsed supersonic molecular beam by expanding ~1% water in helium (Gilmore, 99.9999%) at a stagnation pressure of 1.4 atm through the 0.5 mm orifice of a pulsed valve (~ 150 μs opening time) operating at 10 Hz. Samples were prepared by transferring H 2 O by vacuum distillation to an evacuated reservoir followed by adding helium. Expansion conditions (water concentration, helium backing pressure) were optimized to maximize signal from the trimer and minimize higher clusters. The skimmed molecular beam was intersected at right angles by two counter-propagating laser Water Trimer Experimental Methods 180 beams in the interaction region. IR radiation (5 mJ/pulse, ~0.4 cm -1 linewidth) excited the H-bonded OH-stretch of (H 2 O) 3 at 3536 cm -1 . Focusing the IR radiation increases the enhancement from multiphoton absorption of higher clusters and therefore was avoided in this experiment. 41 IR radiation was generated by an optical parametric oscillator/ amplifier (OPO/OPA) system (LaserVision) pumped by the fundamental of a seeded Nd:YAG laser (Continuum Precision II 8000). The IR frequency was calibrated by measuring the well-known absorption spectrum of gaseous H 2 O. Figure 6.2. Experimental scheme for vibrational predissociation of (H 2 O) 3 . An IR photon (hν IR ) excites the H-bonded OH-stretch of (H 2 O) 3 . Some of the excess energy (E Excess ) can be distributed in intermolecular vibrational levels (fundamentals, overtones and combination bands) of (H 2 O) 2 . Blue horizontal lines show the vibrational states of the dimer fragment (calculated using harmonic approximation and published vibrational frequencies) 43 as a function of excess energy. H 2 O fragments in the ground vibrational state are detected by REMPI via the -state. C  Water Trimer Experimental Methods 181 Ultraviolet (UV) radiation at 248.24 – 248.55 nm was generated by frequency-doubling (Inrad Autotracker III) the output of the dye laser (Continuum ND 6000, Coumarin 500) pumped by a Nd:YAG laser (Continuum Surelite III) and frequency calibrated by the known REMPI spectrum of H 2 O. 44 Tightly focused UV radiation (0.4 – 0.6 mJ/pulse, lens focal length (f. l.) = 20 cm; ~ 0.4 cm -1 linewidth) ionized state-selected H 2 O fragment, scanning through the 1 B 1 (000) ← 1 A 1 (000) band using REMPI. Tighter focusing of the UV beam was achieved by expanding it using an additional negative lens (f. l. = -100 cm) placed 137 cm before the focusing lens. Spectra were collected by alternating “IR on” and “IR off” conditions at each frequency. In “IR on”, the IR laser was fired 70 ns before the UV laser. The REMPI spectra were simulated using the program PGOPHER 45 with rotational constants from Yang et al. 44 IR laser conditions (timing, focusing, power) were optimized to ensure single-photon absorption. UV laser conditions were optimized for the best signal-to-noise ratio. The timing of the lasers was adjusted by delay generators (Stanford, DG535) controlled through a GPIB interface (National Instruments). A cryopumping system cooled by liquid nitrogen served to reduce background water during data acquisition. The VMI arrangement has been described in detail previously. 46,47 In brief, it consists of a four-electrode ion acceleration assembly, a 60 cm field-free drift tube, and a microchannel plate (MCP) detector coupled to a phosphor screen (Beam Imaging Solutions, Inc. BOS-40-6) that is monitored by a charge-coupled device (CCD) camera (LaVision, Imager). In the VMI mode, the two-dimensional projections were collected using an event counting method (DaVis) and reconstructed to three- C  X  Water Trimer Theoretical Methods 182 dimensional images using the BASEX method. 48 Speed distributions were obtained by summing over the angular distribution for each radius, and were converted to c. m. translational energy distributions using momentum conservation, the appropriate Jacobian (proportional to E T -1/2 , where E T is the translational energy) and calibration constants obtained from previous calibration experiments. 39 6.3 Theoretical Methods Quasiclassical trajectories were run essentially as described previously for analogous predissociation studies of the water dimer. 35 Initial conditions were expressed in the normal modes of the trimer by giving harmonic zero-point energy (ZPE) to each mode, except for the IR-bright H-bonded OH-stretch. That normal mode, depicted in Figure 6.3, was excited to an energy equal to the experimental fundamental (see below). We use the experimental energy instead of the harmonic one; the difference between the two is roughly 100 cm -1 . 42 The normal mode coordinates and momenta were sampled randomly subject to the given mode energy. The transformation from normal coordinates and momenta to standard Cartesian coordinates and momenta was then done, followed by a small purification that subtracted any residual angular velocity in the Cartesian coordinate and momenta in order to have zero total angular momentum at t = 0 to ensure zero total angular momentum. Then the trajectories were propagated in Cartesian coordinates using the Verlet propagator with a time step of 0.1 fs. A total of roughly 25,000 trajectories were propagated using the WHBB PES. 42 Of these, roughly 20,000 dissociated to a monomer plus dimer. The dissociation criterion was based on the Water Trimer Theoretical Methods 183 distance of the second largest OO being at least 10 bohr. We chose the second largest distance to ensure that dissociation occurred. Final product analysis was done in the standard way. The internal energy and rotational angular momenta of the dimer and monomer were determined as well as the relative translational energy of the fragments. As we discuss below, the trimer complex is long-lived before dissociating and thus there is significant energy relaxation over most, if not all, of the vibrational modes. This suggests that the harmonic description of initial conditions is not a major concern. This long lifetime also offers some justification in using a quasiclassical trajectory approach, instead of quantum one (which is not feasible) as quantum coherence is likely not significant for such long-lived complexes. Figure 6.3. Depiction of the H-bonded OH-stretch (mass-scaled) normal mode that is excited. Water Trimer Results and Discussion 184 6.4 Results and Discussion The fundamental transition of the H-bonded OH-stretch of (H 2 O) 3 has previously been assigned and characterized in gas phase, He droplets and inert matrix environment. 21,22,26,28,29 In the gas phase molecular beam experiments, Huisken et al. 21 assigned the H-bonded OH-stretch fundamentals of (H 2 O) 2 , (H 2 O) 3 , and (H 2 O) 4 at 3601, 3533, and 3416 cm -1 , respectively. The observed bands are well isolated and red-shifted by >50 cm -1 from the H 2 O monomer stretch. The trimer band appears with a broad shoulder to the blue (3552 cm -1 ), assigned by Paul et al. as a higher cluster band. 22 This has recently been confirmed as the double donor absorption of the hexamer, 29 whose intensity diminishes under conditions where larger clusters are disfavored. There is a tendency to create higher clusters with high backing pressure and high water vapor concentration. 22 Therefore, in our experiments the expansion conditions are carefully optimized to minimize higher cluster formation. In addition, the IR radiation fluence is kept sufficiently low in order to minimize multiphoton absorption. These optimizations, while reducing signal-to-noise levels, ensure that the detected H 2 O fragments are produced from a single photon absorption of the (H 2 O) 3 species. The signal is further reduced by the large number of accessible fragment monomer states and upper state predissociation of the H 2 O REMPI state. 44 For REMPI spectra and VMI measurements, the H-bonded OH-stretch of (H 2 O) 3 is excited at 3536 cm -1 , which is sufficient only to induce (H 2 O) 3 → H 2 O + (H 2 O) 2 dissociation. The H 2 O fragments are detected state-selectively by REMPI. IR Water Trimer Results and Discussion 185 enhancement in the REMPI spectra (IR on – IR off) can be observed only when there is absorption of IR radiation by the trimer that leads to production of H 2 O fragments in the monitored J" KaKc level. The signal enhancement in the spectral region where the trimer absorbs ensures that the observed products are produced from VP of (H 2 O) 3 and not from other clusters. Due to their rotational envelopes, it is impossible to distinguish, with our experimental resolution, between the two types of H-bonds in (H 2 O) 3 , which differ in energy by 12 –15 cm -1 . 19,28 It is therefore believed that the detected H 2 O monomer fragments are formed by breaking of both types of H-bonds. Little is known about the lifetime of (H 2 O) 3 excited to the H-bonded OH- stretch. In the He droplet spectrum, the trimer’s absorption peak appears slightly broader than the dimer’s peak (the dimer’s lifetime is 80 ps). 26,49 The calculated lifetime is discussed below. Figure 6.4 shows the fragment yield REMPI spectrum of H 2 O fragments in the 1 B 1 (000) ← 1 A 1 (000) band produced by VP of (H 2 O) 3 at 3536 cm -1 . The spectrum is simulated fairly well with a rotational temperature of 230 ± 70 K, which gives an average energy in rotation of 160 ± 50 cm -1 . Upon VP, the estimated excess energy of 810 cm -1 (3536 cm -1 – 2726 cm -1 ) can populate H 2 O fragment rotational levels up to J" = 8 (or J" KaKc = 7 2,5 ). Several isolated rotational transitions (J' KaKc ←J" KaKc = 2 0,2 ← 2 2,1 , 2 0,2 ← 3 2,1 and 4 0,4 ← 4 2,3 ) of H 2 O fragments were used for imaging. From the rotational temperature of background H 2 O in the molecular beam, C  X  Water Trimer Results and Discussion 186 determined from the 1 B 1 (000) ← 1 A 1 (000) REMPI spectrum, we estimate the parent trimer temperature at 14 ± 5 K. Figure 6.4. Fragment yield rotational spectrum of (H 2 O) 3 . The top (black) curve corresponds to the fragments 2 + 1 REMPI enhancement spectrum obtained by scanning the H 2 O 1 B 1 (000) ← 1 A 1 (000) band. The bottom (red) curve shows a PGOPHER 45 simulation with known spectroscopic parameters 44 at 230 K rotational temperature. Assigned REMPI transitions selected for imaging are labeled. Figure 6.5 shows speed distributions obtained by VMI by monitoring specific rotational states of the H 2 O fragments. Note that in Fig. 6.5(c), the 4 2,3 level has a minor contribution from the 4 0,4 level, which has a lower rotational energy. The recorded two-dimensional projections of ionized H 2 O fragments were reconstructed to three-dimensional images as described above. Reconstructed images in speed (velocity) space (m/s) were obtained by summing over the isotropic angular distribution for each radius. The isotropy of the angular distributions reflects the slowness of the dissociation processes. In contrast to the speed distributions obtained in the VP of H 2 O and D 2 O dimers, as well as water dimers with other small C  X  C  X  Water Trimer Results and Discussion 187 molecules, 34,35,39-41 which show distinct structures in the speed distributions, the speed distributions in Figure 6.5 are smooth and do not exhibit reproducible structural features. In determining the precise value for D 0 of dimers, we were able to fit distinct and state-specific structures in several speed distributions. In the trimer case, we do not have such structures to rely on, and therefore our estimated value is less precise (see below). The difficulty in estimating D 0 is augmented by the small number of isolated water monomer levels available for imaging. Note that the large fragment signal near zero velocity is associated with background water in the monitored rotational level. In studies of the VP of the water dimer, 35 it has been shown that the product energy distributions are nonstatistical and generally agree with the energy gap law, 50 resulting in a propensity to populate fragment vibration over rotation over translation. Thus, water monomer fragments with bending excitation were favored over ground state products, and fits to the data demonstrated that the rotational population decreased with increasing translational energy release. As mentioned above, product energy distributions in VP of (H 2 O) 3 are likely to be more statistical due to the large density of states in the dimer fragment intermolecular vibrational modes, and therefore we decided to compare the measured distributions to simulations using the statistical Phase Space Theory (PST), 51-54 as well as to QCT calculations. In the PST calculations D 0 was the only parameter used in the fits, and we selected a value that best fit both the shapes of the distributions and their cutoff values. W F H 3 cu T a 4 J" co le T Water Trime igure 6.5. S H 2 O fragmen 00 cm -1 , re urves corre Theory (PST ngular mom 4 m/s. In " KaKc = 4 2,3 ontribution Fittin evels of eac The position r Speed distr nts in J" KaKc espectively. espond to th T, which as mentum are c) 4 2,3 * den 3 . The exte n from the n g was accom ch (H 2 O) 2 co ns of these G ibutions fro = a) 2 2,1 , b Black curv he total integ ssumes tha e equally pr notes a ble ended popu earby trans mplished by ofragment v Gaussians w 188 om reconstr ) 3 2,1 and c ves show e grated simu t all energ robable) wi ended trans ulation bey sition 4 4,0 wh y assigning vibrational s were determ ructed imag c) 4 2,3 * level experiment ulations obt etically allo th D 0 = 264 sition with yond ~550 hose energy a Gaussian state, as we ined by con Result ges obtained ls with E rot tal measure tained by us owed states 40 cm -1 and a major co 0 m/s may y is 222 cm - -shaped cur e have done nservation o ts and Discu d by monito = 135, 212 ements and sing Phase S s that cons d a resolutio ntribution y be due -1 . rve to rotat e before. 34,35 of energy, ssion oring 2 and d red Space serve on of from to a ional 5,39-41 Water Trimer Results and Discussion 189 hν IR + E rot (trimer) = D 0 + E rot (mon) + E vib,rot (dimer) + E T where E rot (trimer) is the trimer rotational energy estimated from the IR spectra and beam temperature (10 ± 10 cm -1 ; since there may be a difference in the cooling efficiency of H 2 O and (H 2 O) 3 , the uncertainty of the internal energy is higher); hν IR is the IR photon energy (3536 cm -1 ); E T is the measured center-of-mass (c. m.) translational energy (proportional to speed 2 ); and E rot (mon) and E vib,rot (dimer) are the rotational energies of the monitored H 2 O fragment and the rovibrational energies of the (H 2 O) 2 cofragment, respectively. E rot (mon) is defined by the selected REMPI transition. Vibrational energies of (H 2 O) 2 were determined by using the harmonic approximation and the fundamental frequencies from ab initio calculations. 43 The rotational energies were generated by PGOPHER 45 using known rotational constants. 55,56 For H 2 O in J" KaKc = 2 2,1 , 3 2,1 and 4 2,3 , (H 2 O) 2 cofragments are allowed up to J" KaKc = 60 1,60 , 57 0,57 and 53 1,53 , respectively. The widths of the Gaussians (full width at half-maximum of 44 m/s) were obtained from previous calibration experiments. 39 Population distributions were calculated using PST, which assumes that all energetically allowed states that conserve angular momentum are equally probable. 51-54 The vibrational densities of states in the (H 2 O) 2 cofragment were calculated by the Beyer-Swinehart algorithm. 54,57 All pair-correlated translational energy distributions show energy distribution profiles that vary smoothly with no unique structures in the images. The translational energy distributions were converted to speed distributions and each rovibrational level in the simulation was Water Trimer Results and Discussion 190 assigned a Gaussian width of 44 m/s. A best fit D 0 and uncertainty were obtained for each image. Taking a weighted average of all our data, we arrive at a value of D 0 = 2640 ± 140 cm -1 . Adding the (H 2 O) 3 internal energy of 10 ± 10 cm -1 , a final value of D 0 = 2650 ± 150 cm -1 is obtained. There are two major sources of uncertainties: 1) 140 cm -1 obtained from fitting the shapes and cutoffs of the images; 2) 10 cm -1 obtained from the internal energy correction. The experimental estimate of D 0 is in good agreement with the calculated value of 2726 ± 30 cm -1 . 38 Therefore, a cooperative (nonadditive) effect of 450-500 cm -1 is indeed involved in stabilizing the cyclic structure of (H 2 O) 3 . The good agreement between the measured and calculated D 0 for the water dimer and trimer lends confidence in the high accuracy of the ab initio calculations for D 0 for breaking all three H-bonds of (H 2 O) 3 , which is 3855 ± 20 cm -1 . This value is 1129 cm -1 higher than the calculated value for breaking two H-bonds. This difference is similar to the value of breaking the single H-bond of (H 2 O) 2 (1104 ± 5 cm -1 ), indicating that the cooperative effect is in fact dominated by the cyclic structure and the (H 2 O) 3 → H 2 O + (H 2 O) 2 dissociation channel. While the agreement of the speed distributions with PST is good, it is by no means unique. We can get equally good fits by assuming models in which the rotational distributions obey the energy gap law; i.e., are described with smooth population functions, − (where C is a fitting parameter), in which the rotational population decreases with increasing translational energy, and the vibrational distributions have several different forms. We can, however, confirm the statistical W n T m o d sh o re m J" fr th im F V b Water Trime ature of th The QCT tra methods to a ne with no ifference am hown below nly those espective (h m. translatio " KaKc = 3 2,1 le ragments ar hus a fairl mproving st igure 6.6. VMI by detec y QCT (hard r he observed anslational e account for o constraint mong the m w was obtai trajectories harmonic) Z onal energy evel and th re in J" = 2 y large nu tatistics. Th Comparison cting H 2 O fr d ZPE const d distributio energy distr r the ZPE co t, all show methods is in ined with “h s where th ZPE. Figure distributio e distributi – 4. These umber of t e agreemen n of the c. m ragment in traint), whe 191 ons by com ribution wa onstraint in a peak at n the high-e hard zero-p he monome 6.6 shows a n obtained ons obtaine rotational l trajectories nt between t m. translatio the J" KaKc = re H 2 O frag mparing them as calculated the fragme around 50 energy tail o point constr er and dim a compariso in VMI by d ed by QCT c levels have are assoc theory and onal energy 3 2,1 level (b ments are in Result m to the Q d using sev ents. The re 0 cm -1 or le of the distrib aint”, that i mer each h on between detecting H calculations maximum ciated with experiment y distributio black curve n J" = 2 – 4 ts and Discu QCT calculat veral establi esults, inclu ess. The m bution. The s, by proces has at least the measur H 2 O fragmen s where the population them, the t is good. on measure ) and calcu (red curve) ssion tions. ished uding major e one ssing t the red c. nts in e H 2 O , and ereby ed by lated . Water Trimer Results and Discussion 192 Table 1. Average vibrational, rotational and translational energies (in cm -1 ) obtained from QCT (hard ZPE constraint) calculations and PST (correlated with J" = 2 – 4 of the H 2 O monomer fragment). The average rotational energy of H 2 O fragment (all J") obtained from temperature fit is also listed. QCT Calculations PST Temperature Fit (H 2 O) 2 Vibration (J" = 2 – 4) 342 412 (H 2 O) 2 Rotation (J" = 2 – 4) 151 145 H 2 O Rotation (All J") 229 160 ± 50 Translation (J" = 2 – 4) 143 142 Figure 6.7 shows the (hard ZPE constraint) QCT results for the total rotational and translational energy distributions in the (H 2 O) 2 dimer fragment and compares them with the PST predictions. Note that the energy distributions calculated by using QCT have not been quantized, whereas the PST calculations are quantized and are presented normalized to the total number of trajectories. All PST and QCT distributions agree fairly well, confirming the statistical nature of the energy distributions. Table 1 shows the average vibrational, rotational and translational energies obtained from the QCT calculations, PST for the (H 2 O) 2 fragment, and a Boltzmann temperature fit (cm -1 ) to the measured rotational distribution of the monomer fragment. All average energies, except the vibrational energy, are in good agreement. Quantizing the vibrational energy distributions Water Trimer Results and Discussion 193 calculated from QCT will exclude energetically forbidden states at low energy, which will increase the average vibrational energy and get a result closer to PST. Figure 6.7. Comparison of (H 2 O) 2 a) rotational and b) translational energy distributions, where the H 2 O fragments are in J" = 2 – 4, obtained from QCT (hard ZPE constraint) and PST calculations. It is evident that the translational energy release can be well fit by PST as well as by the QCT calculations. In addition, the QCT calculations suggest a statistical-like distribution in the other degrees of freedom. This result is easily rationalized by the large vibrational density of states in the (H 2 O) 2 fragment. The harmonic intermolecular vibrational energies of the dimer range from 90 to ~600 cm -1 , with 4 of the 6 intermolecular vibrational modes being below 300 cm -1 . 42,43 Water Trimer Results and Discussion 194 The density of vibrational states can reach > 8 /cm -1 for (H 2 O) 2 fragments with low rotational and translational energies. As mentioned previously, the product energy distributions in VP of the water dimer are nonstatistical and agree with the energy gap law. 35 For (H 2 O) 3 , the product energy distributions are more statistical due to the large density of states of the products. For future experiments, it will be interesting to examine and compare the energy distributions of the (H 2 O) 3 → 3 H 2 O dissociation channel. Are product energy distributions less statistical due to the lower product density of states? The experimental work cannot distinguish between a mechanism in which the H-bonds are broken sequentially, or several bonds are broken simultaneously; however, the QCT calculations can shed light on this (see below). Next consider the internal and rotational distributions of the dimer and monomer obtained by QCT. It is worth examining these using the various ZPE constraints (and also no constraint), and so we show results with the indicated constraints and also with no constraints. Figure 6.8 shows the internal energy of the dimer. With no constraint the distribution is quite broad with about 30% of trajectories leading to the dimer with less than the (harmonic) ZPE. A very similar distribution is seen for the “soft ZPE” constraint, in which the sum of internal energies of the fragments must be at least the sum of the ZPEs. Hard constraints on either the monomer or the dimer basically “slice” the no-constraint distribution in the expected ways. Finally, the hard-constraint produces a fairly narrow distribution, which shows a peak at around 400 cm -1 above the dimer ZPE. There Water Trimer Results and Discussion 195 are intermolecular modes in the dimer with harmonic frequencies below 400 cm -1 (ref. 42 for example), and so we predict that some internal excitation of these dimer modes is likely. (The large reduction in the number of accepted trajectories for the hard-constraint condition compared to the “no-constraint” case implies that many trajectories need to be run and this underscores the need to have an analytical PES available for the calculations.) Figure 6.8. Internal energy of the dimer under indicated treatments of zero-point energy (ZPE). The harmonic ZPE of the dimer is 10,157 cm -1 . See text for details of the various ZPE constraints. Water Trimer Results and Discussion 196 Figure 6.9. Rotational angular momentum of the dimer under indicated treatments of zero-point energy (ZPE). See text for details of the various ZPE constraints. Figure 6.9 shows the dimer rotational angular momentum distribution for the various treatments of the ZPE. In this case, as was noted above for the translational energy distribution, there is much less sensitivity on how the ZPE is treated compared to the internal (mostly vibrational) energy distribution of the dimer. As seen, the J distribution is fairly broad with a maximum in the range 10 – 15. The corresponding distribution for the monomer is shown in Figure 6.10, where the maximum is predicted to be at roughly 4. (We do not show the monomer Water Trimer Results and Discussion 197 vibrational distribution because with the hard constraint there is not sufficient internal energy to excite any normal mode, based on any standard histogram method to assign excited quantum states to classical energy.) In the experiment (Figure 6.4), we observed water monomer fragments mostly in rotational levels J" = 2 – 5, which agrees with the QCT calculations. Figure 6.10. Rotational angular momentum distribution of the monomer under indicated treatments of zero-point energy (ZPE). See text for details of the various ZPE constraints. Water Trimer Results and Discussion 198 The trajectories show, as expected, much internal isomerization of the trimer prior to dissociation. Snapshots of one trajectory, shown in Figure 6.11, illustrate this. The full animation in mpg format is available. Inspection of the trajectories tells us that the ring opens early in the trajectory, indicating the breaking of one H-bond. It reforms and breaks and reforms and breaks (often with different H-bonds breaking) until finally the second H-bond breaks and fragmentation is seen. The evolution described by the water trimer trajectories is similar to what was inferred from spectroscopic studies of trimers of HF, 58 DF 59 and HCl. 60 In these studies it was concluded that the first step in the dissociation is opening of the ring, followed by further intramolecular vibrational redistribution and finally elimination of a monomer fragment. The timescales, however, differ from case to case, reflecting differences in ring strain, vibrational levels, etc. Finally, to obtain an estimate of the QCT lifetime of dissociation to the dimer + monomer we simply kept track of the three OO distances and used the dissociation criterion mentioned above to record the time for dissociation. From the distribution of lifetimes for nearly 20,000 trajectories (with no constraints) that dissociated, 84% did so within 10.5 ps. This is shorter than the reported comparable percentage for the water dimer (using the same PES) following OH-stretch excitation, which was reported as “At 25 ps about 84% of the (H 2 O) 2 trajectories dissociated”. 35 It must be noted that the criterion for dissociation in the two cases are not identical but certainly comparable, and differences between them would account for a fraction of a picoseconds uncertainty in the comparisons. Water Trimer Summary and Conclusions 199 Figure 6.11. Snapshots of a trajectory (~ 100 ps) of an initially excited trimer (1) (as described in the text) that dissociates to the dimer + monomer depicted in frame (6). Frames (2) – (5) depict the intermediate (in increasing time) distortions of the trimer including a nearly linear configuration (4) and compressed reformed trimer (5). The full animation in mpg format is available. 6.5 Summary and Conclusions The present joint experimental-theoretical study of the VP of the water trimer provides the first experimental determination of D 0 of the trimer upon excitation of the H-bonded OH stretch fundamental, and an estimation of the contributions of cooperative interactions to the H-bonding network. The experimental value, D 0 = 2650 ± 150 cm -1 for (H 2 O) 3 → H 2 O + (H 2 O) 2 , derived from fitting images of selected rotational levels of the water monomer fragment, agrees well with the calculated value (D 0 = 2726 ± 30 cm -1 ), and places the cooperative Water Trimer Summary and Conclusions 200 contribution for this channel at about 450 cm -1 , again in good agreement with theory. It appears, therefore, that most of the cooperativity is captured by breaking off one water molecule from the cyclic trimer. The QCT calculations provide the first description of the dissociation mechanism of the trimer. The trajectories show that the trimer lives on average for >10 ps before dissociating, allowing ample time for intramolecular vibrational energy redistribution. Indeed, complex vibrational motions are observed that include, among others, isomerization of the H-bonded and free hydrogens, partial breaking and reformation of H-bonds, etc. The trajectories show that the ring opens first by breaking one H-bond, and after many subsequent vibrational motions, the second bond breaks as well, liberating a water monomer. In addition, the QCT calculations provide the c. m. translational energy distribution, as well as the rotational energy distributions in the monomer and dimer fragments. Good agreement is obtained between the QCT calculations and PST predictions, as well as with the experimentally measured pair-correlated speed distributions. We conclude that the fairly long dissociation times and large density of states leads to statistical-like energy distributions. A nearly statistical outcome is also in accordance with what is seen in the trajectories, which favor a mechanism in which most dissociation events involve stepwise H-bond breaking, facilitating energy redistribution among the intermolecular vibrations of the dimer and the reaction coordinate. Water Trimer Summary and Conclusions 201 The statistical-like behavior of the VP of the water trimer stands in contrast to the corresponding behavior of the water dimer, in which the fragment rovibrational energy distributions are nonstatistical even though the dimer’s lifetime is longer than the trimer’s. The difference can be attributed partly to the existence of low-lying (< 300 cm -1 ) intermolecular vibrational levels in the dimer fragment that facilitate energy transfer in the trimer. We do not know whether the dimer fragment vibrational energy distribution is statistical but the QCT calculations show that a large fraction of the available energy is deposited in dimer fragment vibration. We conclude that the energy gap law is not as important in the VP of the trimer as it is for the dimer. Water Trimer References 202 Chapter 6 References (1) Latimer, W. M.; Rodebush, W. H. J. Am. Chem. Soc. 1920, 42, 1419-1433. (2) Pauling, L. Proc. Natl. Acad. Sci. U.S.A. 1928, 14, 359-362. (3) Pauling, L. The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry; Cornell University Press: New York, 1939. (4) Bernal, J. D.; Fowler, R. H. J. Chem. Phys. 1933, 1, 515-548. (5) Scheiner, S. Hydrogen Bonding: A Theoretical Perspective; Oxford University Press: New York, 1997. (6) Keutsch, F. N.; Saykally, R. J. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 10533- 10540. (7) Fowler, J. E.; Schaefer, H. F., III J. Am. Chem. Soc. 1995, 117, 446-452. (8) Xantheas, S. S.; Burnham, C. J.; Harrison, R. J. J. Chem. Phys. 2002, 116, 1493- 1499. (9) Wales, D. J. J. Am. Chem. Soc. 1993, 115, 11180-11190. (10) Takahashi, M.; Watanabe, Y.; Taketsugu, T.; Wales, D. J. J. Chem. Phys. 2005, 123, 044302. (11) Mas, E. M.; Bukowski, R.; Szalewicz, K. J. Chem. Phys. 2003, 118, 4386-4403. (12) Keutsch, F. N.; Cruzan, J. D.; Saykally, R. J. Chem. Rev. 2003, 103, 2533-2578. (13) Anderson, J. A.; Crager, K.; Fedoroff, L.; Tschumper, G. S. J. Chem. Phys. 2004, 121, 11023. (14) Santra, B.; Michaelides, A.; Scheffler, M. J. Chem. Phys. 2007, 127, 184104. (15) van der Avoird, A.; Szalewicz, K. J. Chem. Phys. 2008, 128, 014302. Water Trimer References 203 (16) Kiss, P. T.; Baranyai, A. J. Chem. Phys. 2009, 131, 204310. (17) Salmi, T.; Kjaergaard, H. G.; Halonen, L. J. Phys. Chem. A 2009, 113, 9124-9132. (18) Czakó, G.; Kaledin, A. L.; Bowman, J. M. Chem. Phys. Lett. 2010, 500, 217-222. (19) Salmi, T.; Sälli, E.; Halonen, L. J. Phys. Chem. A 2012, 116, 5368-5374. (20) Pugliano, N.; Saykally, R. J. Science 1992, 257, 1937-1940. (21) Huisken, F.; Kaloudis, M.; Kulcke, A. J. Chem. Phys. 1996, 104, 17-25. (22) Paul, J. B.; Collier, C. P.; Saykally, R. J.; Scherer, J. J.; O'Keefe, A. J. Phys. Chem. A 1997, 101, 5211-5214. (23) Braly, L. B.; Liu, K.; Brown, M. G.; Keutsch, F. N.; Fellers, R. S.; Saykally, R. J. J. Chem. Phys. 2000, 112, 10314-10326. (24) Braly, L. B.; Cruzan, J. D.; Liu, K.; Fellers, R. S.; Saykally, R. J. J. Chem. Phys. 2000, 112, 10293-10313. (25) Keutsch, F. N.; Braly, L. B.; Brown, M. G.; Harker, H. A.; Petersen, P. B.; Leforestier, C.; Saykally, R. J. J. Chem. Phys. 2003, 119, 8927-8937. (26) Slipchenko, M. N.; Kuyanov, K. E.; Sartakov, B. G.; Vilesov, A. F. J. Chem. Phys. 2006, 124, 241101. (27) Ceponkus, J.; Uvdal, P.; Nelander, B. J. Phys. Chem. A 2008, 112, 3921-3926. (28) Burnham, C. J.; Xantheas, S. S.; Miller, M. A.; Applegate, B. E.; Miller, R. E. J. Chem. Phys. 2002, 117, 1109-1122. (29) Moudens, A.; Georges, R.; Goubet, M.; Makarewicz, J.; Lokshtanov, S. E.; Vigasin, A. A. J. Chem. Phys. 2009, 131, 204312. (30) Mó, O.; Yáñez, M.; Elguero, J. J. Chem. Phys. 1992, 97, 6628-6638. Water Trimer References 204 (31) González, L.; Mó, O.; Yáñez, M.; Elguero, J. J. Mol. Struc. (Theochem) 1996, 371, 1-10. (32) Glendening, E. D. J. Phys. Chem. A 2005, 109, 11936-11940. (33) Ohno, K.; Okimura, M.; Akai, N.; Katsumoto, Y. Phys. Chem. Chem. Phys. 2005, 7, 3005-3014. (34) Rocher-Casterline, B. E.; Ch'ng, L. C.; Mollner, A. K.; Reisler, H. J. Chem. Phys. 2011, 134, 211101. (35) Ch’ng, L. C.; Samanta, A. K.; Czakó, G.; Bowman, J. M.; Reisler, H. J. Am. Chem. Soc. 2012, 134, 15430-15435. (36) Shank, A.; Wang, Y.; Kaledin, A.; Braams, B. J.; Bowman, J. M. J. Chem. Phys. 2009, 130, 144314. (37) Czakó, G.; Bowman, J. M. J. Chem. Phys. 2009, 131, 244302. (38) Wang, Y.; Bowman, J. M. J. Chem. Phys. 2011, 135, 131101. (39) Rocher-Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2011, 115, 6903-6909. (40) Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2010, 114, 9774-9781. (41) Mollner, A. K.; Casterline, B. E.; Ch'ng, L. C.; Reisler, H. J. Phys. Chem. A 2009, 113, 10174-10183. (42) Wang, Y.; Shepler, B. C.; Braams, B. J.; Bowman, J. M. J. Chem. Phys. 2009, 131, 054511. (43) Kalescky, R.; Zou, W.; Kraka, E.; Cremer, D. Chem. Phys. Lett. 2012, 554, 243- 247. Water Trimer References 205 (44) Yang, C. H.; Sarma, G.; ter Meulen, J. J.; Parker, D. H.; Western, C. M. Phys. Chem. Chem. Phys. 2010, 12, 13983-13991. (45) PGOPHER 2010, a Program for Simulating Rotational Structure, Western, C. M., University of Bristol, http://pgopher.chm.bris.ac.uk. (46) Eppink, A. T. J. B.; Parker, D. H. Rev. Sci. Instrum. 1997, 68, 3477-3484. (47) Dribinski, V.; Potter, A. B.; Fedorov, I.; Reisler, H. J. Chem. Phys. 2004, 121, 12353. (48) Dribinski, V.; Ossadtchi, A.; Mandelshtam, V. A.; Reisler, H. Rev. Sci. Instrum. 2002, 73, 2634-2642. (49) Paul, J. B.; Provencal, R. A.; Chapo, C.; Petterson, A.; Saykally, R. J. J. Chem. Phys. 1998, 109, 10201-10206. (50) Ewing, G. E. J. Phys. Chem. 1987, 91, 4662-4671. (51) Light, J. C. J. Chem. Phys. 1964, 40, 3221-3229. (52) Pechukas, P.; Light, J. C. J. Chem. Phys. 1965, 42, 3281-3291. (53) Pechukas, P.; Light, J. C.; Rankin, C. J. Chem. Phys. 1966, 44, 794-805. (54) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics: Theory and Experiments; Oxford University Press, Inc.: New York, 1996. (55) Fraser, G. T. Int. Rev. Phys. Chem. 1991, 10, 189-206. (56) Zwart, E.; ter Meulen, J. J.; Leo Meerts, W.; Coudert, L. H. J. Mol. Spectrosc. 1991, 147, 27-39. (57) Beyer, T.; Swinehart, D. F. Commun. ACM 1973, 16, 379. (58) Michael, D. W.; Lisy, J. M. J. Chem. Phys. 1986, 85, 2528-2537. Water Trimer References 206 (59) Suhm, M. A.; Farrell, J. J. T.; Ashworth, S. H.; Nesbitt, D. J. J. Chem. Phys. 1993, 98, 5985-5989. (60) Farnik, M.; Nesbitt, D. J. J. Chem. Phys. 2004, 121, 12386-12395. Future Work Introduction 207 Chapter 7: Future Work Our goal is to study energy transfer at the molecular level and extend our studies to larger systems. The Reisler group has studied the vibrational predissociations of the HCl-HCCH, DCl-HCCH, NH 3 -HCCH, HCl-H 2 O, NH 3 -H 2 O, (H 2 O), (D 2 O) 2 dimers and the water trimer. The successful experimental investigation of the water trimer lends confidence to study other mixed trimers, such as (HCl) 2 H 2 O, HCl(H 2 O) 2 , etc. The proposed experiments for the mixed trimers have been discussed previously. 1 Can we extend our studies to larger clusters, such as tetramers and pentamers? We learned from our previous studies that it is challenging to analyze the speed distributions upon vibrational predissociation of the water trimer due to extensive band overlaps, which limit our ability to extract information. Therefore, it may not be feasible to study clusters larger than trimers using a similar technique. Alternatively, we could explore larger systems by studying dimers trimers with larger subunits, such as organic molecule-water dimers. The extended studies on the HCl-H 2 O and NH 3 -H 2 O dimers and a proposed experiment on the methanol-water dimer are discussed below. Figure 7.1 Mixed water clusters (HCl-H 2 O, NH 3 -H 2 O) and methanol-water dimer discussed in this Chapter. Future Work Extended Studies on the Dimers 208 7.1 Extended Studies on Dimers Given that we are familiar with the systems we studied, and the rovibrational levels of the cofragment are resolved (or partially resolved) in the pair-correlated velocity distributions in dimers’s predissociation, reinvestigating some of the dimers will provide valuable information and a more complete picture of their predissociation dynamics. Section 7.1.1 and 7.1.2 discuss possible experiments for the HCl-H 2 O and NH 3 -H 2 O dimers, respectively. 7.1.1 Hydrogen Chloride-Water Dimer In our studies, the HCl stretch of the HCl-H 2 O dimer was excited and both the HCl and H 2 O fragments were detected in two separate experiments. 2,3 In this case, the vibrational modes of the fragments were energetically forbidden. To examine the V-V channel, we can excite the free OH stretch of the HCl-H 2 O dimer at ~3760 cm -1 to induce vibrational predissociation. 4 After breaking the hydrogen bond [dissociation energy (D 0 ) = 1334 ± 10 cm -1 ], the excess energy is sufficient to populate the H 2 O bending level (1594.75 cm -1 ) when the HCl fragment rotation is J" ≤ 11. Figure 7.2 shows the two dissociation channels where the H 2 O fragments are in the (000) and (010) states. The corresponding simulations of the speed distributions are shown in Figure 7.3. F F p th T F d G si st a Future Work igure 7.2 V hotoexcitin he ground v The correspo igure 7.3 S etected frag Gaussians o imulations, tates, repre nd d), the ro k Vibrational ng the free O vibrational onding simu Speed distr gments and of the rota respectivel esented by otational lev predissoci OH stretch o state and t ulations of t ibutions sim d states are ational lev ly. In a), the the purple vels of the H 209 ation of th of the dimer the H 2 O frag the speed di mulated by labeled. Bl vels of the e cofragmen and green HCl cofragm Exte e HCl-H 2 O r. The HCl fr gments in t istributions an expone ack and red e cofragme nt is allowed curves (2:1 ments are lab ended Studie dimer can fragment ca the (000) a s are shown ential smoot d curves co ents and t d in the H 2 O 1 ratio), res beled in pur es on the Di be achieve n be detect nd (010) st in Figure 7 th function. orrespond to total integr O (000) and spectively. rple. mers ed by ed in tates. .3. . The o the rated (010) In b) Future Work Extended Studies on the Dimers 210 As shown in Figure 7.3, speed distributions acquired from detecting the H 2 O fragments are rotationally resolved, whereas the ratio H 2 O (000) : (010) can be extracted directly from the speed distributions acquired by detecting the HCl fragments. In addition, the differences in excess energy from detecting the fragments in different rovibrational states allow the examination of the correlation between excess energies and population distributions. It can be determined by examining the fitting parameters used in the exponential smooth function. 7.1.2 Ammonia-Water Dimer In the vibrational predissociation of the NH 3 -H 2 O dimer, there was no evidence of major population in the H 2 O (010) state, even though it was energetically accessible. The hydrogen bonded OH stretch of the water was excited at 3485 cm -1 and the NH 3 fragments were detected in the ν 2 = 0, 1 + and 2 + states. 5 The excess energy after dissociation (D 0 = 1538 ± 10 cm -1 ) is ~1947 cm -1 . The NH 3 fragments were detected in the r S 0 (5) rotational levels in the ground vibrational state, which left ~1650 cm -1 excess energy for rovibrational excitation of the H 2 O fragments. For this case, merely ~55 cm -1 excess energy could be distributed in H 2 O rotation if the bending level (1594.75 cm -1 ) of the H 2 O fragments was populated. The overlap of rotational levels correlated with the H 2 O (010) and (000) states in the velocity distribution limits our ability to determine whether the H 2 O (010) state was populated. Future Work Methanol-Water Dimer 211 With the detection scheme for internally excited H 2 O at hand, we can now detect the H 2 O (010) state directly. This experiment will confirm the vibrational state- specificity upon vibrational predissociation of the NH 3 -H 2 O dimer. 7.2 Methanol-Water Dimer Understanding the interactions of water with organic molecules have been of general interests, because the interactions dominated by hydrogen bonds are central to life sustaining process. As a starting point, we can study small organic molecule-water complexes, such as the methanol-water, phenol-water dimers, etc. These systems will provide insights into vibrational state-specificity and energy distributions of larger hydrogen bonded dimers. The larger number of accessible vibrational modes may give rise to statistical-like energy distributions. However, the energy distributions may be less statistical compared to that of the water trimer depending on the vibrational density of states of the predissociation fragments. In addition, we can examine angular momentum restrictions of the relatively heavy organic molecules, whose moment of inertias are larger than those of the diatomic to tetra-atomic molecules. The hydrogen bonds among alcohol-water mixed clusters are of fundamental interest, and major studies have focused on the conformational populations, donor/acceptor preferences and binding energies of the clusters, and the vibrational frequency shifts due to hydrogen bond interactions. 9-18 Future Work Methanol-Water Dimer 212 Theoretical studies predicted two major methanol-water dimer geometries. Figure 7.4 shows the optimized geometries where the water molecule acts as a hydrogen bond donor (wm) and the hydrogen bond acceptor (mw). Both geometries have been observed in matrix isolation experiment. 19 A combined of Raman and infrared studies in the slit jet gas phase experiments reveal the vibrational frequencies of the water/methanol clusters and mixed clusters. The agreement between theory and experiment confirms that the wm geometry, where the water molecule acts as a hydrogen bond donor, is the most stable conformer. 9 Suhm and coworkers 20 measured the energy of the tunneling motion between two enantiomers. The Raman measurement placed the energy of the tunneling splitting at ~2.5 cm -1 , which is indistinguishable in infrared spectroscopy due to extensive rotational contour. 20 Figure 7.4 Structures of the methanol-water dimer, mw and wm configurations. The vibrational predissociation of wm can be induced by exciting the hydrogen bonded OH stretch of the water unit at 3567 cm -1 , 20 which is well shifted from the other methanol/water pure and mixed clusters. 20-23 Table 7.1 shows the Future Work Methanol-Water Dimer 213 vibrational frequencies of the nearby methanol/water clusters. Although the mw OH stretch is not observed in gas phase experiments, matrix isolation experiments confirm that the mw and wm hydrogen bonded OH stretches are well separated. 19 Table 7.1 Experimental vibrational energies (in cm -1 ) of the hydrogen bonded OH stretch of methanol/water pure and mixed clusters in gas phase environment. 20-23 Assignment Vibrational energies (cm -1 ) Water trimer 3533 wm 3567 Methanol dimer 3577 Water dimer 3601 mw Not observed (calculated value ~3620) The methanol-water dimer is an interesting system that may serve as a bridge between the water dimer and the water trimer [(H 2 O) 3 → H 2 O + (H 2 O) 2 ] in terms of product energy distributions. The wm dimer is similar to the water dimer in the sense that one can imagine the hydrogen bond of a water dimer acceptor unit being replaced by a methyl group. Because methyl is an electron donating group, the hydrogen bond of wm is expected to be stronger than the water dimer. The hydrogen bonded OH stretch of the water unit was determined to be 3567 cm -1 , 20 which is less red-shifted than the hydrogen bonded OH stretch of ammonia-water dimer (3485 cm -1 ) 5 and more than the water-water dimer (3601 cm -1 ). 22 Therefore, the D 0 is expected to be between those of ammonia-water and water-water dimer at 1538 and 1105 ± 10cm -1 , 5,24 respectively, which places a very rough D 0 estimate of wm at 1400 cm -1 . Moskowitz and Bacˇic applied flexible methyl and hydroxyl group and Diffusion Monte Carlo simulation with CHARMM potential and calculated D 0 for Future Work Methanol-Water Dimer 214 wm at 1567.5 ± 0.3 cm -1 . 12 Figure 7.5 shows a tentative experimental scheme of the vibrational predissociation of wm. Upon vibrational predissociation, the excess energy of ~2000 cm -1 (3567 – 1567 cm -1 ) is sufficient to populate the bending level of the water fragment and eight vibrational modes (fundamentals, overtones, combination bands) of the methanol fragment. The calculated vibrational energies of methanol are shown in Table 7.2. Figure 7.5 Experimental scheme for the vibrational predissociation of wm (methanol-water dimer). An IR photon (hν IR ) excites the hydrogen bonded stretch of the dimer to initiate dissociation, which has a dissociation energy of D 0 . REMPI with UV photons detects the water fragments in the (000) and (010) states. E Excess corresponds to the excess energy available for rovibration of both fragments and translation. Eight vibrational modes of the methanol fragment are energetically accessible when water fragment is in the (000) state. Only one vibrational mode of Future Work Methanol-Water Dimer 215 the methanol fragment is accessible when water fragment is in the (010) state. Blue lines show the energetically accessible vibrational levels of the methanol fragment including overtones and combination bands. Table 7.2 Calculated vibrational energies (in cm -1 ) of methanol. 25 Vibrational modes of methanol Calculated energy (cm -1 ) τ (OH) 299 ν (CO) 1043 r (CH 3 ) 1070 r (CH 3 ) 1168 δ (OH) 1356 δ (CH 3 ) 1480 δ (CH 3 ) 1495 δ (CH 3 ) 1506 ν (CH 3 ) 2989 ν (CH 3 ) 3036 ν (CH 3 ) 3112 ν (OH) 3846 Similar to the water dimer, the water fragment upon predissociation of the methanol-water dimer can be detected in the (000) and (010) states to reveal the D 0 of the dimer and the energy distributions of the fragments. Comparing to the water dimer, this proposed experiment seeks to answer the following questions: 1. How does the increase in energetically accessible vibrational modes affect the product energy distributions? Is there vibrational state-specificity? How does the ratio of the (000) : (010) states compare to that of water dimer? 2. Is there angular momentum restriction due to high moment of inertia of the methanol fragment? Future Work Methanol-Water Dimer 216 3. Does the geometry upon dissociation and the lower moment of inertia of the H 2 O fragment than the methanol fragment favor high rotational excitation in the H 2 O fragment? 4. Can we gain more insights into the dissociation mechanisms by examining the wm internal modes that are in resonant with its hydrogen bonded OH mode that lead to dissociation? Another interesting aspect of this system is that wm has the exact same number of atoms as the water trimer. Therefore, there is equal number of vibrational modes in the parent molecules as well as the fragments as shown below: For case (1), the water dimer fragment has a total of twelve vibrational modes, in which six intermolecular vibrational modes have energies below 600 cm -1 . For case (2), there are only intramolecular vibrational modes in the methanol fragment with only one vibrational mode with energy below 1000 cm -1 and the bending level in the water fragment. The vibrational density of states of the methanol cofragment [case (2)] is clearly much lower than the water dimer cofragment [case (1)] (see Figure 7.5 and 3.10 for comparison). This proposed experiment also seeks to answer the following question: Comparing to the water trimer, does the decrease in vibrational Future Work Methanol-Water Dimer 217 density of states of the methanol cofragment give rise to less statistical energy distributions? Note that the vibrational predissociation of the water trimer involves a two- step sequential bond-breaking process, which favors statistical energy distributions in the fragment. Therefore, having less statistical energy distributions for wm may or may not be directly correlated with the decrease in vibrational density of states. However, detecting water fragments in the (000) and (010) states upon vibrational predissociation of wm will reveal valuable information about energy transfer mechanisms. The excess energy for populating H 2 O fragments in the (000) and (010) states are ~2200 and 600 cm -1 , respectively. The corresponding numbers of energetically accessible vibrational states of the methanol fragments are 27 and 2, respectively. Future Work References 218 Chapter 7 References (1) Rocher, B. E. Velocity Map Imaging of the State-Specific Vibrational Predissociation of Water-Containing Hydrogen-Bonded Complexes, University of Southern California, 2011. (2) Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2010, 114, 9774-9781. (3) Rocher-Casterline, B. E.; Mollner, A. K.; Ch’ng, L. C.; Reisler, H. J. Phys. Chem. A 2011, 115, 6903-6909. (4) Skvortsov, D.; Lee, S. J.; Choi, M. Y.; Vilesov, A. F. J. Phys. Chem. A 2009, 113, 7360-7365. (5) Mollner, A. K.; Casterline, B. E.; Ch'ng, L. C.; Reisler, H. J. Phys. Chem. A 2009, 113, 10174-10183. (6) Wang, Y.; Bowman, J. M. J. Chem. Phys. 2011, 135, 131101. (7) Perchard, J. P. Chem. Phys. 2001, 273, 217-233. (8) Salmi, T.; Kjaergaard, H. G.; Halonen, L. J. Phys. Chem. A 2009, 113, 9124-9132. (9) Stockman, P. A.; Blake, G. A.; Lovas, F. J.; Suenram, R. D. J. Chem. Phys. 1997, 107, 3782-3790. (10) Fileti, E. E.; Chaudhuri, P.; Canuto, S. Chem. Phys. Lett. 2004, 400, 494-499. (11) Masella, M.; Flament, J. P. J. Chem. Phys. 1998, 108, 7141-7151. (12) Moskowitz, J. W.; Bacic, Z.; Sarsa, A.; Schmidt, K. E. J. Chem. Phys. 2001, 114, 10294-10299. (13) Mandal, A.; Prakash, M.; Kumar, R. M.; Parthasarathi, R.; Subramanian, V. The Journal of Physical Chemistry A 2010, 114, 2250-2258. Future Work References 219 (14) Fileti, E. E.; Castro, M. A.; Canuto, S. Chem. Phys. Lett. 2008, 452, 54-58. (15) Fileti, E. E.; Canuto, S. Int. J. Quantum Chem. 2005, 104, 808-815. (16) Iosue, J. L.; Benoit, D. M.; Clary, D. C. Chem. Phys. Lett. 1999, 301, 275-280. (17) Galano, A.; Narciso-Lopez, M.; Francisco-Marquez, M. J. Phys. Chem. A 2010, 114, 5796-5809. (18) Campen, R. K.; Kubicki, J. D. J. Comput. Chem. 2010, 31, 963-972. (19) Bakkas, N.; Bouteiller, Y.; Loutellier, A.; Perchard, J. P.; Racine, S. J. Chem. Phys. 1993, 99, 3335-3342. (20) Nedi ć, M.; Wassermann, T. N.; Larsen, R. W.; Suhm, M. A. Phys. Chem. Chem. Phys. 2011, 13, 14050-14063. (21) Buck, U.; Huisken, F. Chem. Rev. (Washington, DC, U. S.) 2000, 100, 3863-3890. (22) Keutsch, F. N.; Braly, L. B.; Brown, M. G.; Harker, H. A.; Petersen, P. B.; Leforestier, C.; Saykally, R. J. J. Chem. Phys. 2003, 119, 8927-8937. (23) Keutsch, F. N.; Cruzan, J. D.; Saykally, R. J. Chem. Rev. 2003, 103, 2533-2578. (24) Rocher-Casterline, B. E.; Ch'ng, L. C.; Mollner, A. K.; Reisler, H. J. Chem. Phys. 2011, 134, 211101. (25) Gonzalez, L.; Mo, O.; Yanez, M. J. Chem. Phys. 1998, 109, 139-150. Appendix A REMPI Cell 220 Appendix A: REMPI Spectroscopy of Water using a REMPI Cell Resonance-enhanced multiphoton ionization (REMPI) is a sensitive and state-selective spectroscopy technique applied to the detection of atoms or molecules. A REMPI cell was built to acquire H 2 O REMPI spectra at various temperatures. The details of the H 2 O REMPI spectroscopy are found in Chapter 3.3. The schematic diagram of the REMPI cell is shown in Figure A1. Figure A1. Schematic diagram of REMPI cell. Appendix A REMPI Cell 221 Two conflat cross flanges (Stainless Steel, 4 way crosses with 5.12” width and length, NW 40 flange, OD: 1.5”) were connected using Kwik flanges (KF NW 40, OD: 1.5”). The outlet was connected to a liquid nitrogen trap via flexible metal hose (Stainless Steel, NW 40, OD: 1.5”) and pumped by a mechanical pump and evacuated to ~7 mTorr. Room temperature water vapor was ionized via 2 + 1 REMPI by focused ultraviolet (UV) radiation (0.15 - 0.30 mJ/pulse, 20 cm f.l., 80,640 – 80,970 cm -1 ). The UV radiation passed through the CaF compression port window (OD: 1.8125”, window diameter 1.25”, compression port length: 2.00”) and the center of the electrodes. The ions were collected by setting the electrode bias at 200 - 500 V and the ion signals captured by an oscilloscope were recorded using the LabVIEW program. The cell pressure was monitored by a thermocouple gauge connected to a pressure gauge. The cell pressure was kept below 1 Torr to achieve nearly collisionless conditions during the ~7 ns laser pulse duration. 1 The flow rate and cell pressure were carefully optimized to maximize signal-to-noise ratio. Cell pressures in the range of 100 - 750 mTorr with various flow rates were mainly used to optimize the conditions. High flow rates reduced the detectable ions significantly, whereas low flow rates and static cell conditions increased background signals. Similarly, high cell pressures tend to increase background signal. For medium flow rates, the signal-to-noise ratio decreased over time as water vapor condensed on the windows where the UV radiation passed through. Figure A2 shows a 2 + 1 REMPI spectrum of 1 B 1 (000) ← 1 A 1 (000) band acquired using REMPI cell at room temperature. The cell pressure was maintained at 500 mTorr with a medium flow rate. UV radiation with 0.25 mJ/pulsed focused by Appendix A REMPI Cell 222 a 20 cm f.l. lens was applied to achieve REMPI of the H 2 O molecules. A bias of 300 V was applied to the electrode to collect the ion signal. Unsuccessful attempts were made to heat the REMPI cell utilizing heating tape to produce hot water molecules. Spectra obtained by heating the cell to various temperatures gave inconsistent rotational temperatures (PGOPHER fits). Figure A2. Black curves show measured 2 + 1 REMPI spectrum of H 2 O 1 B 1 (000) ← 1 A 1 (000) band. Red curves show PGOPHER 2 simulation using 300 K rotational temperature with published spectroscopic constants. 3 Measuring REMPI spectra utilizing the REMPI cell is a good method to calibrate the laser frequency and to develop REMPI spectra. The major disadvantage of the REMPI cell is that major time has to be spent on optimizing the cell pressure and flow rate for each species in order to obtain a reasonable signal-to-noise ratio. Appendix A REMPI Cell 223 In addition, the detected molecules are not mass-selected and therefore any contamination can contribute to the spectra. Introduction References 224 Appendix A References (1) Rosa, M. D. D.; Farrow, R. L. J. Quant. Spectrosc. Radiat. Transfer 2001, 68, 363-375. (2) PGOPHER 2010, a Program for Simulating Rotational Structure, Western, C. M., University of Bristol, http://pgopher.chm.bris.ac.uk. (3) Yang, C. H.; Sarma, G.; ter Meulen, J. J.; Parker, D. H.; Western, C. M. Phys. Chem. Chem. Phys. 2010, 12, 13983-13991.

Abstract (if available)

Abstract The state-to-state vibrational predissociation (VP) dynamics of water clusters were studied following excitation of a vibrational mode of each cluster. Velocity-map imaging (VMI) and resonance-enhanced multiphoton ionization (REMPI) were used to determine pair-correlated center-of-mass translational energy distributions. Product energy distributions and dissociation energies were determined. ❧ Following vibrational excitation of the HCl stretch fundamental of the HCl-H₂O dimer, HCl fragments were detected by 2 + 1 REMPI via the ƒ³∆₂(ν′ = 0) ← X¹Σ⁺ (ν″ = 0) and V¹Σ⁺ (ν′ = 11 and 12) ← X¹Σ⁺ (ν″ = 0) transitions. REMPI spectra clearly show HCl from dissociation produced in the ground vibrational state with J″ up to 11. The fragments' center-of-mass translational energy distributions were determined from images of selected rotational states of HCl and were converted to rotational state distributions of the water cofragment. All the distributions could be fit well when using a dimer dissociation energy of bond dissociation energy D₀ = 1334 ± 10 cm⁻¹. The rotational distributions in the water cofragment pair-correlated with specific rotational states of HCl appear nonstatistical when compared to predictions of the statistical phase space theory. A detailed analysis of pair-correlated state distributions was complicated by the large number of water rotational states available, but the data show that the water rotational populations increase with decreasing translational energy. H₂O fragments of this dimer were detected by 2 + 1 REMPI via the C̃¹B₁(000) ← X̃¹A₁(000) transition. REMPI clearly shows that H₂O from dissociation is produced in the ground vibrational state. The fragment’s center-of-mass translational energy distributions were determined from images of selected rotational states of H₂O and were converted to rotational state distributions of the HCl cofragment. The distributions gave D₀ = 1334 ± 10 cm⁻¹ and show a clear preference for rotational levels in the HCl fragment that minimize translational energy release. The usefulness of 2 + 1 REMPI detection of water fragment is discussed. ❧ The hydrogen bonding in water is dominated by pair-wise dimer interactions, and the predissociation of the water dimer following vibrational excitation is reported. The measured D₀ values of (H₂O)₂ and (D₂O)₂, 1105 and 1244 ± 10 cm⁻¹, respectively, are in excellent agreement with the calculated values of 1103 and 1244 ± 5 cm⁻¹. Pair-correlated water fragment rovibrational state distributions following vibrational predissociation of (H₂O)₂ and (D₂O)₂ were obtained upon excitation of the hydrogen bonded OH and OD stretch fundamentals, respectively. Quasiclassical trajectory calculations, using an accurate full-dimensional potential energy surface, are in accord with and help to elucidate experiment. Experiment and theory find predominant excitation of the fragment bending mode upon hydrogen bond breaking. A minor channel is also observed in which both fragments are in the ground vibrational state and are highly rotationally excited. The theoretical calculations reveal equal probability of bending excitation in the donor and acceptor subunits, which is a result of interchange of donor and acceptor roles. The rotational distributions associated with the major channel, in which one water fragment has one quantum of bend, and the minor channel with both water fragments in the ground vibrational state are calculated, and are in agreement with experiment. ❧ The predissociation dynamics of the water trimer following excitation of the hydrogen bonded OH-stretch fundamental were investigated. The D₀ for the (H₂O)₃→ H₂O + (H₂O)₂ dissociation channel is determined from fitting the speed distributions of selected rovibrational states of the water monomer fragment using velocity map imaging. The experimental value, D₀ = 2650 ± 150 cm⁻¹, is in good agreement with the previously determined theoretical value, 2726 ± 30 cm⁻¹, obtained using an ab initio full-dimensional potential energy surface (PES) together with Diffusion Monte Carlo calculations [Wang and Bowman, J. Chem. Phys., 2011, 135, 131101]. Comparing this value to D₀ of the dimer places the contribution of non-pairwise additivity to the hydrogen bonding at 450-500 cm⁻¹. Quasiclassical trajectory (QCT) calculations using this PES help elucidate the reaction mechanism. The trajectories show that most often one hydrogen bond breaks first, followed by breaking and reforming of hydrogen bonds (often with different hydrogen bonds breaking) until, after many picoseconds, a water monomer is finally released. The translational energy distributions calculated by QCT for selected rotational levels of the monomer fragment agree with the experimental observations. The product translational and rotational energy distributions calculated by QCT also agree with statistical predictions. The availability of low-lying intermolecular vibrational levels in the dimer fragment is likely to facilitate energy transfer before dissociation occurs, leading to statistical-like product state distributions.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Dissociation energy and dynamics of HCl and aromatic-water clusters

PDF

Imaging the state-specific vibrational predissociation of hydrogen bonded complexes

PDF

Development and implementation of methods for sliced velocity map imaging. Studies of overtone-induced dissociation and isomerization dynamics of hydroxymethyl radical (CH₂OH and CD₂OH)

PDF

Photodissociation dynamics and energetics of HCl-(H₂O)₃

PDF

Photodissociation dynamics of atmospherically relevant small molecules in molecular beams

PDF

Molecular orientation and structure of hydrogen bonds at water interfaces

PDF

Vibrational sum frequency spectroscopy of molecules on metal, semiconductor, and aqueous surfaces

PDF

Photoelectron and ion imaging investigations of spectroscopy, photoionization, and photodissociation dynamics of diazomethane and diazirine

PDF

A multifaceted investigation of tris(2-phenylpyridine)iridium

PDF

An investigation of morphology and transport in amorphous solid water via guest-host interactions

PDF

New electronic structure methods for electronically excited and open-shell species within the equation-of-motion coupled-cluster framework

PDF

Surface plasmon resonant enhancement of photocatalysis

PDF

Understanding the mechanism of oxygen reduction and oxygen evolution on transition metal oxide electrocatalysts and applications in iron-air rechargeable battery

PDF

Nucleophilic fluorination of bisphosphonates and its application in PET imaging

PDF

Development of robust ab initio methods for description of excited states and autoionizing resonances

PDF

Multicomponent synthesis of optically pure aminodicarboxylic acids in water and total synthesis of 15-EPI-benzo-lipoxin A4 and aspirin-triggered neuroproctectin D1/protectin D1

PDF

The effect of microhydration on ionization energy and proton transfer in nucleobases: analysis and method development

PDF

Temperature-dependent photoionization and electron pairing in metal nanoclusters

PDF

Liquid phase photoelectron spectroscopy as a tool to probe excess electrons in liquid ammonia along with Birch chemistry carbanions: from dilute electrolytic solutions to the metallic regime

PDF

Exploring new frontiers in catalysis: correlating crystal chemistry and activity in layered silicates

Asset Metadata

Creator Ch'ng, Lee Chiat (author)

Core Title Dissociation energy and dynamics of water clusters

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Publication Date 07/26/2013

Defense Date 05/09/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag dimer,hydrogen bond,OAI-PMH Harvest,velocity map imaging,vibrational predissociation,water trimer

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Reisler, Hanna (committee chair), Bradforth, Stephen E. (committee member), Shing, Katherine (committee member)

Creator Email lchng@usc.edu,leecchng@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-301043

Unique identifier UC11293209

Identifier etd-ChngLeeChi-1848.pdf (filename),usctheses-c3-301043 (legacy record id)

Legacy Identifier etd-ChngLeeChi-1848.pdf

Dmrecord 301043

Document Type Dissertation

Format application/pdf (imt)

Rights Ch'ng, Lee Chiat

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA