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Rovibrational spectroscopy in helium droplets

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Rovibrational spectroscopy in helium droplets

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Content ROVIBRATIONAL SPECTROSCOPY IN HELIUM DROPLETS by Dmitry S. Skvortsov A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CHEMISTRY) August 2008 Copyright 2008 Dmitry S. Skvortsov ii Dedication To my parents and my sister To my wife iii Acknowledgements I would like to thank my scientific advisor Professor Andrey Vilesov for all his efforts and support during my studies at UCS. He has shared all his encyclopedic knowledge and tremendous experimental experience which has allowed me to develop different research skills as well as grow as an individual scientist. I attribute the most of my success in the laboratory to his constant guidance and his enthusiasm. I am very grateful to Professor Hanna Reisler for her constant support and wisdom and to Professor Curt Wittig for his inspiration and strong personality. I would like to thank Professor Stephen Bradforth for long scientific discussions on the spectroscopy. It is my pleasure to thank Professor Howard Taylor for his advice and participation in my scientific career. I would like to thank Professor Vitaly Kresin for all his help and advice. My special thanks go to our postdoc Myong Yong Choi whom I had great pleasure to work with. I would like to say great thanks to Mikhail Slipchenko, Kirill Kuyanov, and Vadim Mozhayskiy for all their efforts and help in the laboratory. I would like also thank Russell Sliter and Luis Gomez for proof-reading this manuscript and for their help during the experiments. It is my great pleasure to thank all of the graduate students from the Chemistry and Physics departments whom I have interacted with, borrowed iv equipment from, and had fruitful conversations with: Boris Karpichev, Mikhail Rayzanov, Igor Fedorov, Laura Edwards, and Andrew Mallner from the group of Hanna Reisler; Daniil Stolyarov, Elena Polyakova, Sergey Malyk, Anton Zadorozhny, and Chris Nemirow from the group of Curt Wittig; Askat Jailaubekov and Chris Rivera from the group of Stephen Bradforth; Roman Rabinovich and Chunlei Xia from the group of Vitaly Kresin; and to Nikolay Markovskii from the group of Chi Mak. I would like to thank Dr. Boris Sartakov for fruitful scientific discussions. I am grateful to Professor Takamasa Momose for his help with cw laser. I would like to thank all the personal of the USC Machine shop, especially Victor Jordan and Don Wiggins, for their valuable work. My special thanks go to Heather Connor, Michele Dea, Yuki Yabuta, and Valery Childress for their professionalism and willingness to help with all the paperwork, purchase orders, etc. and for making my life easier. v Table of Contents Dedication ii Acknowledgements iii List of Tables viii List of Figures x Abstract xv Chapter I: Introduction 1 1. The Scope of the Work 1 2. Content of the Chapters 2 3. Chapter I References 6 Chapter II: Experimental Setup 7 1. Introduction 7 2. Experimental Setup Outline 7 3. Helium Droplets Production 9 4. Pick-up Process 13 5. Mass Spectrometer Detection and Depletion Technique 15 6. Laser system 16 7. Chapter II References 17 Chapter III: Rotation of CX 4 and SiX 4 (X = H, D) Molecules in He Droplets 18 1. Introduction 18 2. Experimental Details 20 3. Results 21 3.1. Intensity of the Lines 23 3.2. Spectrum of SiH 4 26 3.3. Line Widths 27 3.4. Spectroscopic Constants 27 4. Discussion 31 5. Conclusions 34 6. Chapter III References 36 vi Chapter IV: Large Enhancement of the Intramolecular Coupling in SiH 4 in Liquid Helium 38 1. Abstract 38 2. Introduction 39 3. Experimental Details 40 4. Results 41 5. Discussion 44 6. Chapter IV References 50 Chapter V: Study of HCl Clusters in Helium Nanodroplets: Experiments and Ab Initio Calculations as Stepping Stones from Gas Phase to Bulk 52 1. Introduction 52 2. Experimental Technique 53 3. Results 54 3.1. Ab Initio Calculations 54 3.2. Spectra of (HCl) n in He Droplets 56 4. Discussion 61 4.1. Monomer 61 4.2. Dimer 63 4.3. (HCl) n , n = 3-6, Clusters 64 4.4. Large (HCl) n clusters 67 5. Conclusion 69 6. Supporting Information 70 7. Chapter V References 80 Chapter VI: Interchange-Tunneling Splitting in HCl Dimer in Helium Nanodroplets 84 1. Introduction 84 2. Experimental Details 86 3. Results and Discussion 87 3.1. Monomer 87 3.2. Dimer 89 4. Conclusion 96 5. Chapter VI References 98 Chapter VII: Measurement of the relative energy of the conformers in 2-chloroethanol in helium droplets 101 1. Abstract 101 2. Introduction 101 3. Experimental Details 103 4. Results 104 5. Discussion 109 6. Conclusions 111 7. Chapter VII References 112 vii Chapter VIII: Rotation of CO 2 Isotopomers in Helium Droplets 114 1. Introduction 114 2. Experimental Details 115 3. Results 116 4. Discussion 119 5. Conclusions 123 6. Chapter VIII References 124 Chapter IX: Conclusions and Future Work 125 1. Conclusions 125 2. Spherical Top Molecules 125 3. Study of the Conformers of the Large Biomolecules 126 4. Study of the HCl-(H 2 O) n Complexes 127 5. Chapter IX References 128 Alphabetized Bibliography 129 viii List of Tables Table 2.1. 9 Typical pressures in the different parts of the He droplet apparatus. Table 3.1. 24 Frequencies, line widths, and integral intensities of the ν 3 band of CH 4 and CD 4 lines observed in this work in He droplets. For comparison frequencies in the gas phase and from previous He droplet study are shown. Table 3.2. 25 Frequencies, line widths, and integral intensities of the SiH 4 and SiD 4 lines observed in this work in He droplets. For comparison frequencies in the gas phase are shown. Table 3.3. 29 Molecular constants of the CH 4 and CD 4 molecules in He droplets and in the gas phase frequencies. The values in parenthesis are single standard deviations of the last significant digits. Table 3.4. 30 Molecular constants of the SiH 4 and SiD 4 molecules in He droplets and in the gas phase frequencies. The values in parenthesis are single standard deviations of the last significant digits. Position of the R(2) line of SiD 4 was not used for the fitting procedure. Table 5.2. 62 Frequency of (HCl) n (n = 1-6) clusters in He droplets and in the gas-phase. The frequencies are in wavenumbers (cm -1 ). The gas-phase frequencies are for H 35 Cl molecules and corresponding clusters. Table 5.S1. 72 Optimized geometries of the (HCl) n (n = 2-6) at the MP2 level of theory with an aug-cc-pVDZ basis set. Table 5.S2. 73 Optimized geometries of the (HCl) n (n = 2-6) at the MP2 level of theory with a 6-311++G(d,p) basis set. ix Table 5.S3. 74 Optimized geometries of the (HCl) n (n = 2-6) at the MP2 level of theory with a 6-311++G(3df,3pd) basis set. Table 5.S4. 75 A summary of the calculated harmonic vibrational frequencies (cm -1 ) and intensities (km/mol) for (HCl) n (n = 2-6) using the MP2 level of theory with various basis sets [aug-cc-pVDZ, 6-311++G(d,p) and 6-311++G(3df,3pd)]. Table 5.S5. 76 A summary of the calculated harmonic vibrational frequencies (cm -1 ) and intensities (km/mol) for (HCl) n (n = 2-6) using the B3LYP level of theory with various basis sets [aug-cc-pVDZ, 6-311++G(d,p) and 6-311++G(3df,3pd)]. Table 6.3. 90 Frequencies (cm -1 ) of the HCl dimer v 1 and v 2 bands, in helium and in gas-phase. Error limits (1 σ) for frequencies in He are ± 0.1 cm -1 and ± 0.5 cm -1 for v 2 and v 1 bands, respectively. Table 8.4. 121 Comparison of the molecular constants of the CO 2 isotopes obtained in this work in He droplets and previous results in the gas phase. Error bar for absolute and relative frequency measurement are 0.2 cm -1 and 0.01 cm -1 . x List of Figures Figure 2.1. 8 Schematic diagram of the He droplet apparatus. See text for details. Figure 2.2. 12 Averaged He droplet size and mean diameter measured at different stagnation pressures as the function of nozzle temperature. Red dots correspond to the expansion conditions realized in this work. Cartoons suggest droplets formation mechanisms. Figure 2.3. 14 Examples of Poisson distributions for k = 0-3. Vertical arrow shows what will be the probability distribution to find k foreign species inside He droplets if on average only 〈1〉 (one) is picked-up. Figure 3.1. 22 Spectra of the ν 3 bands of: a) CH 4 ; b) CD 4 ; c) SiH 4 , and d) SiD 4 in helium droplets. The mass spectrometer was set to masses of CH 3 + (M = 15 u), CD 3 + (M = 18 u), SiH + (M = 29 u), and SiD + (M = 30 u), respectively, which was found to originate predominantly from the single molecules in He droplets. Weak peaks marked by asterisks in panels (a) and (b) are assigned to the dimers of (CH 4 ) 2 and (CD 4 ) 2 , respectively. Vertical lines are drawn as guides to eyes. Figure 3.2. 26 Schematic energy level diagram and rovibrational transitions observed during the experiments. Figure 3.3. 32 Reduction of the rotational constant for all four molecules vs. gas phase values of B. Dashed line are just for guidance. Figure 3.4. 33 Dependence of the effective D constant vs. the effective B constant for all four molecules. Red straight line is the proposed fit. xi Figure 4.1. 42 Spectra of silane in the opto-acoustic cell (a), and in helium droplets obtained with the mass spectrometer detection of SiH + (M = 29 u) (b) and of SiH 3 + (M = 31 u) (c). Laser pulse energy was 65 μJ. Figure 4.2. 45 Spectrum of silane in He droplets measured at different laser pulse energies of 1mJ (a), 400 μJ (b), and 65 μJ (c) and at the same pickup pressure corresponding to capture of about 0.5 molecules per droplet. Figure 4.3. 46 Schematic diagram of the rotational energy levels of the ν 1 and ν 3 vibrational states of silane. Rotational levels of the ν 3 state are sorted according to the vibrational angular momentum sublevels F (-) , F (0) , and F (+) . 29 Circles show the upper levels of the observed lines. The arrows show the upper levels of the Q2 and R1 lines. Figure 5.1. 55 The global minimum structures of (HCl) n (n = 2-6) clusters calculated at the MP2 level with an 6-311++G(3df,3pd) basis set using Gaussian 03. Figure 5.2. 58 Spectra of HCl molecules and clusters in He droplets of 4000 atoms measured at different pressures of HCl in the pickup cell, (a) 2.1 × 10 -6 ; (b) 8.5 × 10 -6 ; (c) 1.7 × 10 -5 ; (d) 3.4 × 10 -5 ; (e) 6.8 × 10 -5 ; (f) 4.7 × 10 -5 ; (g) 1.0 × 10 -4 mbar. The numbers in brackets show the average number of molecules captured by the He droplets. The band marked with an asterisk is assigned to H 2 O-HCl complexes. The upper spectra (f) and (g) with <n> = 20 and <n> = 500 have been measured in larger He droplets of 1.6 × 10 4 and 2.5 × 10 6 atoms, respectively. Figure 5.3. 59 (a) A spectrum of (HCl) n clusters in He droplets for the average cluster size of <n> = 2. (b) The scaled ab initio frequencies for the monomers, dimers, trimers, and tetramers are shown by down triangle, square, triangle, and circle, respectively. xii Figure 5.4. 60 (a) A high resolution (δν = 0.08 cm -1 ) spectrum of (HCl) n clusters in He droplets; <n> = 4. The stick spectra are the results of calculations for the cyclic hexamers (b) and pentamers (c) using the MP2/aug-cc-pVDZ level of theory. Panel (d) shows the spectrum of the tail (4+1) isomer of the pentamer calculated with the same basis set. Figure 5.5. 66 An average frequency shift of the bonded HCl vibration with respect to the band origin of the single HCl molecules vs. cluster size n. The squares with solid line are the experimental results of this work. Filled circles, up triangles and down triangles are results of the MP2 level of theory with aug-cc-pVDZ, 6-311++G(d,p) and 6-311++G(3df,3pd) basis sets. Figure 5.S1. 71 The optimized global minimum structures of (HCl) n (n = 4-6) clusters, calculated at the MP2 level of theory with a 6-311++G(d,p) (a), and 6-311++G(3df,3pd) (b) basis set using Gaussian 03. Figure 5.S2. 77 The optimized structures and relative energies of the low- lying energy isomers of HCl pentamer and hexamer from calculations at the MP2 level with an aug-cc-pVDZ basis set. The values in the brackets are energies relative to the global minimum in kJ/mol with/without a harmonic zero point energy correction. Figure 5.S3. 78 Pick-up cell pressure dependencies of the bands of monomer through trimer. The intensity represents the maxima of the corresponding cluster bands. Figure 5.S4. 79 (a) A spectrum of (HCl) n clusters in He droplets; <n> = 4. The stick spectra are the results of calculations using the MP2/aug-cc-pVDZ level of theory. Panel (b) shows the spectrum of the global minimum cyclic hexamer. Panels (c-e) show the spectra of the low-lying energy isomers. The values in brackets give the energies relative to the global minimum in kJ/mol with/without a harmonic zero point energy correction. xiii Figure 6.1. 86 The energy level diagram of the (H 35 Cl-H 37 Cl) heterodimers. 20 Solid and dotted lines show the fully allowed and “broken symmetry” transitions, respectively. The insert shows the equilibrium geometry of the HCl dimer. Transitions observed in this work are marked with filled circles. Figure 6.2. 88 A survey spectrum of the HCl molecules and dimers in He droplets for the average cluster size of <n> = 2 with spectral resolution of 1 cm -1 . The higher resolution scans (0.08 cm -1 ) of the monomer, and dimer v 1 and v 2 bands are shown in panels (b), (c) and (d), respectively. Figure 7.1. 105 The structure of the conformers of 2-chloroethanol molecule calculated at the CCSD/cc-pVDZ level of theory. Numbers are relative energies in units of kcal/mol, which take into account different zero point energy of the conformers. Figure 7.2. 106 Spectra of the 2-CLE molecules in the *CH 2 asymmetric stretch of the CH 2 Cl group (a) and in the OH stretch region (b) measured at four different temperatures of the pickup cell as indicated in each panel. Spectral resolution is 0.08 cm -1 and 1 cm -1 in a) and b), respectively. Figure 7.3. 108 Temperature dependence of the intensity ratio of the G g ' and T bands. Results for OH band and *CH 2 asymmetric stretching band of the CH 2 Cl group are shown by solid squares and open circles, respectively. Lines are the results of the least square fitting of the data. Dashed lines are asymptotic behavior at infinite temperature. Figure 8.2. 116 Schematic diagram of the experimental setup for the production of mixed ( 16 OC 18 O) carbon dioxide. The volume of the stainless cylinder is about 1 liter. The gases (CO and O 2 ) has been premixed according to the stoichiometric ratio of the reaction 2CO + O 2 → 2CO 2 . xiv Figure 8.2. 118 Spectra of 16 OC 16 O (a), 16 OC 18 O (b), and 18 OC 18 O (c) molecules embedded in helium droplets. Spectra were measured at pickup pressure of the mixed gas of 6 ⋅10 -6 mbar. Figure 8.3. 119 Spectrum of 16 OC 16 O molecules embedded in helium droplets. Spectra were measured at pickup pressure of the mixed gas of 6 ⋅10 -6 mbar. Feature at 3611.0-3611.5 is a clear signature of CO 2 dimer xv Abstract This thesis covers different aspects of the spectroscopy of molecules and molecular clusters embedded in helium droplets. The interaction between the trapped molecules and the host He clusters as well as the use of helium as a media for novel matrix isolation spectroscopy experiments will be discussed. The rovibrational spectroscopy of spherical top molecules in helium droplets shows the matrix effect on the free rotation. The effect of the both intrinsic moment of inertia as well as increase of the anisotropy of the helium-molecule interaction potential is discussed. Large enhancement of the intramolecular coupling in silane molecules trapped inside He cluster was observed. The deperturbation analysis shows increase of the interaction coefficient between ν 1 and ν 3 vibrational modes by a factor of 100 in liquid helium as compared to the gas phase. Study of HCl clusters in helium droplets shows the formation of the cyclic structures up to the hexamers. These results indicate a non-planar twisted structure for tetramers, an envelope-like structure for pentamers and a pseudo bi-pyramid for hexamers. The absence of the bands due to free H-Cl stretches in the spectrum of large (HCl) n clusters (n > 20) is consistent with either branched structures with the surface. Observation of the “broken symmetry” band in HCl dimer (H 35 Cl - H 37 Cl) allows the interchange-tunneling (IT) splitting of Δν = 2.7 ± 0.2 cm -1 in the ν 2 xvi vibrationally excited state to be obtained, from which the matrix element of β = 0.85 ± 0.15 cm -1 was estimated. This coupling value is about a factor of two smaller than in the free dimers. 2-chloroethanol molecules at temperature in the range of 300 – 600 K have been captured by helium droplets and studied via infrared spectroscopy in the range of O-H and C-H stretching bands. We found that the intensity ratio of the bands due to trans- and gauche- conformers follows the Arrhenius dependence, giving the enthalpy of interconversion, ΔH 0 = 1.12 ± 0.09 kcal/mol. The effect of isotopic substitution on molecular rotations of CO 2 have been studied via infrared spectroscopy in helium droplets. In the spectral region of 2ν 2 + ν 3 (3500 - 3700 cm -1 ), rovibrational spectra of 16 OC 16 O, 16 OC 18 O, and 18 OC 18 O have been obtained showing significant participation of surrounding helium in rotations. Enhancement of coupling of molecular rotations with helium has been observed for the asymmetric CO 2 and attributed to increasing number of the interacting levels for 16 OC 18 O molecules as compared to symmetric CO 2 isotopic species, where odd rotational levels are missing. 1 Chapter I: Introduction 1. The Scope of the Work This work can be separated into projects in three major areas. The first one is devoted to the study of the interaction of between molecules and superfluid helium droplets. This study includes the ro-vibrational spectroscopy of spherical top molecules embedded into He clusters. The observation and analysis of the rotational structure of ν 3 vibrational modes of CH 4 , CD 4 , SiH 4 , and SiD 4 allows for the thorough investigation of the effects of the helium onto the rotation of these molecules. 1 This effect is described in terms of the increase of the effective moment of inertia of the trapped molecules and is quantitatively studied as a function of intrinsic moment of inertia and as a function of the anisotropy of the interaction potential between spherical tops and surrounding helium. Besides that, an unexpected large enhancement of the interaction of the close lying IR inactive ν 1 and IR active ν 3 vibrational modes is observed in SiH 4 molecules in liquid helium. 2 In addition, another aspect of this project was the study of the coupling between rotational states of the different isotopomers of the CO 2 molecules with the states of the liquid helium. The second project is devoted to the study of the formation of the hydrogen bond network in the clusters of hydrochloric acid (HCl) n . 3 This study shows textbook examples of hydrogen bonding molecules as they form the cyclic structures for clusters up to the hexamers. Obtained spectra of HCl clusters (up to 500 HCl 2 molecules) correlates well with the onset of the folded cyclic structure and with the full development of hydrogen bonding in such large clusters. Furthermore, we have studied the effect of the helium environment onto the interchange-tunneling (IT) motion of the HCl dimer. Observed spectroscopic features are described in terms of the increase of the tunneling barrier and quenching of the IT level splitting. 4 The third project was devoted to the development of the novel experimental approach for obtaining relative energies of the conformers of large organic molecules. The use of the He droplets as a host for matrix isolation spectroscopy is tested on the study of the conformers of 2-chloroethanol (2CLE). 5 He droplets allow for the instant entrainment of the population distribution of the conformers. Measurement of the series of vibrational spectra at different temperatures results in the determination of the ΔH 0 values for two low energy conformers of 2CLE. 2. Content of the Chapters Chapter II describes the construction and operation of the experimental setup in detail. Brief overview and thorough explanation of the each part of the He droplet beam apparatus follows by the insights on the principles of the formation, doping, and detection of helium clusters used in this work. The dependence of the He cluster size vs. stagnation pressure of the helium and temperature of the nozzle are outlined and discussed. Chapter III is devoted to the study of the rotation of the spherical top molecules, such as methane, silane, and their deuterium substituted derivatives, inside He droplets. Observed rovibrational transitions in the υ 3 region allowed 3 identification of spectroscopic constants, such as rotational constants in ground and vibrationally excited states, centrifugal distortion constants, and vibrational band origin. In general, reduction of the rotational constant B and increase of the centrifugal distortion constant has been observed in agreement with previous measurements. We can clearly separate effects on the B constant due to the deuterization of molecules, thus increasing moment of inertia, and change of the strength of the interaction potential as we change the central atom from carbon to silicon. It should be noticed, that the centrifugal distortion constant for spherical top molecules are affected differently by helium as compared to D constant for other molecules measured in He droplets. In Chapter IV the study of the unusual large enhancement of the intramolecular coupling in silane (SiH 4 ) molecules is discussed. The observed spectrum of the υ 3 vibrational band shows significant enlargement of the coupling between IR inactive υ 1 and IR active υ 3 vibrational modes. This enhancement of the coupling of the closed lying (2.3 cm -1 ) vibrational bands manifests itself as the appearance of the satellites of the R(1) and Q(2) rotational lines of nearly same intensity as parent lines. Deperturbation analysis shows that the interaction coefficient is increased by a factor of 100 in He droplets as compared to the gas phase value. In Chapter V, we report the results of a joint theoretical and infrared laser spectroscopic study of the hydrogen chloride clusters formed in helium nanodroplets. The H-Cl stretching bands of the dimers, trimers, and tetramers show a large increase in the infrared intensity and low frequency shift with respect to that in a single HCl 4 molecule. The average frequency of the bands for clusters of <n> = 4-500 remains approximately constant at about 2770 cm -1 . We have identified absorption bands of clusters up to hexamers. Both calculations and experiments indicate that pentamers have an envelope like structure, while a folded chain geometry resembling a bi- pyramid is identified for hexamers. Chapter VI describes infrared spectra of the free and hydrogen bonded stretches of the HCl dimers solvated in He nanodroplets. In the case of the ν 2 vibration (hydrogen bonded stretch), the bands due to the isotopomers of the HCl dimers, (H 35 Cl) 2 , (H 35 Cl - H 37 Cl) and (H 37 Cl) 2 , have been resolved. Observation of the “broken symmetry” band in heterodimers allows the IT splitting of Δν = 2.7 ± 0.2 cm -1 in the ν 2 vibrationally excited state of the HCl dimers to be obtained, from which the IT matrix element of β = 0.85 ± 0.15 cm -1 was estimated. This coupling value is about a factor of two smaller than in the free dimers. The partial quenching of the IT splitting of the HCl dimers provides further information on the interaction of the large amplitude molecular motion with liquid helium. In Chapter VII we report the spectroscopic study of the conformers of the 2- chloroethanol in He droplets. Infrared spectra of the molecule obtained in the regions of OH and CH 2 vibration at different temperatures (300 – 600 K) allows for determination of the relative energy of two dominant conformers (G g ' and T), which has been found to be ΔH 0 = 1.12 ± 0.09 kcal/mol. The He droplets played the crucial role in trapping the population distribution of conformers at different temperatures. Chapter VIII devoted to the study of the effect of isotopic substitution on molecular rotations of CO 2 via infrared spectroscopy in helium droplets. In the 5 spectral region of 2ν 2 + ν 3 (3500 - 3700 cm -1 ), rovibrational spectra of 16 OC 16 O, 16 OC 18 O, and 18 OC 18 O have been obtained showing significant participation of surrounding helium in rotations. Enhancement of coupling of molecular rotations with helium has been observed for the asymmetric CO 2 . This observation can be described in terms of the increasing number of interacting levels for 16 OC 18 O molecules as compared to symmetric CO 2 isotopic species, where, due to the bosonic statistics of oxygen atoms, odd rotational levels are missing. 6 3. Chapter I References (1) Hoshina H., S. D., Sartakov B., Vilesov A. In preparation 2008. (2) Skvortsov, D.; Marinov, D.; Sartakov, B.; Vilesov, A. In preparation 2008. (3) Skvortsov, D.; Choi, M. Y.; Vilesov, A. F. Journal of Physical Chemistry A 2007, 111, 12711. (4) Skvortsov, D.; Sliter, R.; Choi, M. Y.; Vilesov, A. F. Journal of Chemical Physics 2008, 128. (5) Skvortsov D. S., Vilesov A. F. In preparation 2008. 7 Chapter II: Experimental Setup 1. Introduction The experimental setup described in this section is similar to the He droplet machine performed in other groups. 1,2 Here, a detailed description of the most recent modifications of the apparatus is given. However, a brief description as well as parameters for each experiment is discussed in the corresponding chapters. This chapter is divided into the four sections covering each part of the helium droplet machine: helium droplet production, pick-up cells, laser system, and quadrupole mass spectrometer detection. But first the brief outline of the whole apparatus is presented. 2. Experimental Setup Outline The helium droplet apparatus diagram is presented in Figure 2.1. The overall experimental setup can be divided into four major chambers marked by following numbers: 1) helium droplet source, 2) differentially pumped pick-up cell, 3) main or interaction chamber, and 4) quadrupole mass spectrometer chamber. The helium droplet source chamber (1) is used to prepare a beam of helium droplets in which the central part of the beam is collimated by use of a skimmer. The differentially pumped pick-up chamber (2) is 13 cm long chamber with gas introduction port. Main or interaction chamber (3) is used for holding additional pick-up chambers and for increasing the interaction length of the He droplet beam 8 with counter-propagating laser radiation. Chamber (4) holds the quadrupole mass spectrometer for signal detection. The He droplet source chamber (1) is pumped by a diffusion pump (P1) with 5000 l/s pump speed, which is backed by a roots blower pump followed by mechanical pump. The differentially pumped pick-up chamber (2) is pumped by turbo-molecular pump (P2) with 400 l/s pumping speed and backed by mechanical pump. Main chamber (3) is pumped by a turbo-molecular pump (P3) with 500 l/s speed, which is backed by the same mechanical pump as in the pick-up chamber 3 A B C E F G X-Y Z D H 2 1 4 P1 P2 P3 P4 Figure 2.1. Schematic diagram of the He droplet apparatus. See text for details. 9 turbo pump (P2). In order to reduce the residual water vapor pressure, this chamber (3) has a liquid nitrogen (LN 2 ) trap (E). The volume of this trap is about 2 liters, which under normal operation conditions, is enough to work for up to seven hours. Finally, ultra-high vacuum chamber (4) is equipped with 350 l/s turbo-molecular pump (P4) which is backed by a mechanical pump with azeolite oil trap to reduce the presence of mechanical oil vapors into the chamber. All four chambers are equipped with ion gauges and thermo-electrical gauges are used to measure fore-vacuum pressure for all mechanical pumps. Typical values for high vacuum in all parts of the He apparatus are given in Table 2.1. 3. Helium Droplets Production Helium droplets can be produced by supersonic expansion of precooled helium gas or liquid helium into vacuum. Both cw 2,3 and pulsed 4 nozzles can be used in the expansion. In all experiments described in this work cw He droplet beams were utilized. Precooled (T nozzle = 8-20 K) pressurized (P =20 bar) helium gas (or Table 2.1. Typical pressures in the different parts of the He droplet apparatus. Pressure in chambers, mbar Source (1) Pick-up (2) Main (3) Mass spec (4) Without He droplets a) 6-7 · 10 -6 6-7 · 10 -7 2-3 · 10 -7 7-9·10 -10 b) With He droplets c) 5-8 · 10 -5 4-5 · 10 -6 4-5 · 10 -7 1-3 · 10 -8 d) a) Values are given for the case when the nozzle at room temperature. b) Valve between main chamber (3) and mass spectrometer chamber (4) is closed. c) Values are given for the case when T nozzle = 15-20 K. LN 2 in main chamber. d) Valve between main chamber (3) and mass spectrometer chamber (4) is open. 10 liquid) was expanded through the 5 μm nozzle into the vacuum (10 -6 mbar). Characteristic parameters of He droplets produced depend on the expansion conditions as shown in Figure 2.2. One can see that there are three distinct regimes for He droplets production: 1) Sub critical – when He droplets are produced from condensation of the cooled gas. Corresponding nozzle temperatures are 10-20 K for stagnation pressure P = 20 bar. 2) Critical – When the nozzle temperature is about 10 K 3) Super critical – when He droplets are produced by breaking of the liquid helium jet. Corresponding nozzle temperatures are 8-10 K for stagnation pressure P = 20 bar. Production of He droplets at sub critical regime yields to the smaller average droplet size of about 10 3 – 10 4 atoms (T nozzle = 17-11 K). This regime was used for the majority of the measurements of the depletion signal of single molecules and small clusters (2-7 molecules). For molecular clusters consisting of larger number of molecules (up to 1000) super critical regime is more suitable, since it leads to the production of significantly larger droplets (several millions of He atoms). Such large droplets will not be destroyed during the pick-up process as compared to the smaller He droplets. The size of the He droplet under sub critical expansion conditions follows log-normal distribution 5,6 : () ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − − = 2 2 N 2 σ μ lnN exp N σ 2 π 1 NP, 11 where σ is called shape parameter and μ is called location parameter. An average number of atoms in the droplet depends on these parameters as follow: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = 2 σ μ exp N 2 . The full width at half maximum (FWHM) of the log-normal distribution is comparable with value of 〈N〉. The nozzle assembly (B) is attached to the second stage of the helium closed cycle refrigerator (A) (Sumitomo Cryocooler, SRDK–408 DW). This second stage is resistively heated in order to control the temperature of the nozzle. Silicon diode temperature sensor is directly attached to the nozzle assembly. A polished aluminum radiation shield mounted to the first stage of the Cryocooler is used to prevent heating of the nozzle by radiation from diffusion pump (P1) located underneath. Overall Cryocooler assembly with the nozzle can be positioned in X-Y plane by sliding it on the o-ring over the polished surface. Also, by adding an expandable bellow for the suspension of Cryocooler, it is possible to adjust the position of the nozzle in the Z direction. As a result, one can precisely direct the He droplet beam through the length of the apparatus. The cw nozzle assembly consists of a massive copper reservoir with the detachable 5 μm diameter nozzle. The precooled helium gas is first introduced into the reservoir and later is expanded into the vacuum. The reservoir is used to thermally equilibrate significant amount of helium gas before expansion. The skimmer (C) is mounted to the wall between source (1) and pick-up (2) chambers downstream the helium beam. The purpose of it is to collimate the central 12 part of the He droplet beam. During most of the experiments two different skimmer sizes were used: 0.6 and 1.2 mm in diameter. Figure 2.2. Averaged He droplet size and mean diameter measured at different stagnation pressures as the function of nozzle temperature. 2 Red dots correspond to the expansion conditions realized in this work. Cartoons suggest droplets formation mechanisms. 13 4. Pick-up Process The pick-up process of foreign species by He droplets occur upon the collision. Experimentally, it is done by passing He droplet beam through the pick-up chamber containing vapor of the chromophore under investigation. In order to pick- up low-vapor pressure species, suck as some liquids or metals, one can use heated cells. In principle, the pick-up cross section is close to the geometrical cross section of the He droplet. Thus, low vapor pressure (10 -5 – 10 -6 mbar) is required in order to pick-up single molecule in the 13 cm long cell. This fact also leads to the strict requirement on the residual gas pressure in main chamber (3), which has the length of about 80 cm. In order to avoid the contamination of the He beam by water in main chamber, the pressure should be kept better than 2-4 · 10 -7 mbar. The control over the number of embedded species is done by varying the pressure of the gas inside pick-up chamber or cell. It has been known that the pick- up process obeys Poisson statistics. 2,7 This means that the probability to have k molecules in the droplet picked-up in the cell of length L is defined by following equation: ( ) () L n k L n P k k ⋅ ⋅ − ⋅ ⋅ = σ σ exp ! , where n is number density of the gas in pick-up chamber and σ is He droplet cross section. The probability distributions for different k values are shown on Figure 2.3. The 13 cm long differentially pumped pick-up chamber (2) has been used in most of the experiments described in this work. The pressure inside the chamber was monitored by ionization pressure gauge. Foreign species were introduced by means 14 of a standard ¼” stainless steel tube, connected by a leak valve and pressure regulator to the gas cylinder or to a small container, in the case of liquid samples. Another smaller pick-up cell (D) has been installed inside main chamber (3). This cell is 4 cm long and 2 cm in diameter made from stainless steel. The cell can be heated by Thermocoax in the temperature range of 300-700 K. The temperature was monitored by K-type thermocouple. This cell has been used for the experiments with 2-chloroethanol described in detail in Chapter VII. 012 3 4 0.0 0.2 0.4 0.6 0.8 1.0 k = 0 k = 1 k = 2 k = 3 I k Number of embedded molecules <1> Figure 2.3. Examples of Poisson distributions for k = 0-3. Vertical arrow shows what will be the probability distribution to find k foreign species inside He droplets if on average only 〈1〉 (one) is picked-up. 15 5. Mass Spectrometer Detection and Depletion Technique In all of the experiments described in this work, mass depletion technique has been implemented for signal detection. The total flux of the He droplets beam is detected by quadrupole (G) mass spectrometer (Extranuclear Laboratories). The spectrometer is equipped with electron beam impact ionizer and “venetian blind” type electron multiplier. Quadrupole mass spectrometer can work into two different operational modes: single mass detection and all mass transmission. In the case of single mass detection both DC and RF AC voltages are applied to the quadrupole mass filter resulting in the stabilization of a unique m/z species. In the other case, only DC voltage is applied to the mass filter which allows all ions heavier than certain ones (defined by DC) to be transmitted. In the depletion technique the counter-propagating laser beam entering through the long focus (f=75 cm, CaF 2 ) collimating lens (H) is aligned with the He droplet beam to increase the effective interaction length. If trapped inside helium chromophores absorb the laser radiation, the subsequent vibrational relaxation results in the evaporation of several hundred He atoms. This reduction of the He droplet size can be detected by monitoring mass spectrometer signal before and right after the laser pulse. In most cases it is more convenient to monitor reduction of the signal on all splitter ions of He droplet – He n + . For this purpose, the mass filter is set to transmit all the masses higher than 6 amu in order to eliminate large background signal from He + ions. In some cases, when the sample gas contains several isotopic species, it is more convenient to detect depletion signal on specific single masses. 16 This prevents the scrambling of the absorption spectrum by the simultaneous signal due to the different isotopes. 6. Laser system The laser setup implemented in all of the described experiments consists of custom built infra-red OPO/OPA system (LaserVision) pumped by pulsed Nd:YAG laser (Continuum Inc., PowerLite II 8020). The normal linewidth of the OPO/OPA system output is 0.08 cm -1 and 1 cm -1 with the injection seeder of the Nd:YAG laser on and off, respectively. The pump power (1064 nm) needed for normal operation for OPO/OPA system is about 750 mJ, which is somewhat higher that manufacturer suggested (550 mJ). This is due to the less than perfect beam profile of our 20Hz Nd:YAG system compared to manufacturer’s requirements for the pump source. The output wavelength of the IR system can be continuously tuned in the ranges of 1350- 2200 nm and 2200-5000 nm. The absolute frequency was calibrated by absorption spectra of the known gas in photo-acoustic cell. For some experiments the Raman para-hydrogen shifter 8 has been used to extend the available wavelength to 8 micron. 17 7. Chapter II References (1) Stienkemeier, F.; Vilesov, A. F. The Journal of Chemical Physics 2001, 115, 10119. (2) Toennies, J. P.; Vilesov, A. F. Angewandte Chemie-International Edition 2004, 43, 2622. (3) Choi, M. Y.; Douberly, G. E.; Falconer, T. M.; Lewis, W. K.; Lindsay, C. M.; Merritt, J. M.; Stiles, P. L.; Miller, R. E. International Reviews in Physical Chemistry 2006, 25, 15. (4) Slipchenko, M. N.; Vilesov, A. F. Abstracts of Papers of the American Chemical Society 2002, 223, C63. (5) Harms, J.; Toennies, J. P.; Dalfovo, F. Physical Review B 1998, 58, 3341. (6) Lewerenz, M.; Schilling, B.; Toennies, J. P. Chemical Physics Letters 1993, 206, 381. (7) Lewerenz, M.; Schilling, B.; Toennies, J. P. Journal of Chemical Physics 1995, 102, 8191. (8) Kuyanov, K. E.; Momose, T.; Vilesov, A. F. Applied Optics 2004, 43, 6023. 18 Chapter III: Rotation of CX 4 and SiX 4 (X = H, D) Molecules in He Droplets 1. Introduction Study of the interaction of molecules with quantum liquids has become possible with recent advances of molecular spectroscopy in 4 He droplets. 1-4 Infrared spectra of molecules in helium droplets show well resolved ro-vibrational structure, 1-3 which have been nicely fitted using ro-vibrational Hamiltonian characteristic for free molecules. For heavy molecules, such as SF 6 , OCS, 5 and CO 2 , 6 rotational constants in liquid helium, B He , were found to decrease by about a factor of three as compared to those for free molecules. In contrast, a very small reduction of the rotational constants of the order of 5% have been observed for light molecules, such as CH 4 and C 2 H 2 . 7 Renormalization of the rotational constants for heavy rotors was quantitatively accounted for by a rigid coupling of the molecular rotation to the local non-superfluid helium density that is induced by molecular interaction. 8-10 Spectroscopic constants of heavy molecules have recently been calculated by the projector operator imaginary time spectral evolution method, 8-11 in good agreement with experiments. On the other hand, theoretical calculations have shown that the local helium density can not adiabatically follow the motion of the rapidly rotating light molecules. 8,12 The centrifugal distortion constants, D He , of heavy molecules in liquid helium were found to be about three orders of magnitude larger than those for free molecules, about 10 -2 of the value of the B He constants. Much less 19 information is available on the D He constants of light molecules in helium. Higher rotational energy levels, which are required for determination of the D He constants have exceedingly small population at the temperature of He droplets of T = 0.38 K. 3 Exceptions are molecules, for which the rotational relaxation of the low levels is prohibited because they belong to different nuclear spin symmetry species, such as in the case of acetylene - C 2 H 2 and methane - CH 4 . For C 2 H 2 , B He = 1.04 cm -1 , and D He = 2·10 -2 cm -1 have been obtained 7 , which can be compared to the corresponding gas phase values of B gas = 1.17 cm -1 , and D gas = 1.6·10 -6 cm -1 . The large value of D He in C 2 H 2 in He has been explained by coupling of the molecular rotation with roton collective excitations in liquid helium, which have slightly higher energy than J = 2 level of acetylene in He. 13,14 For methane molecule, B He = 5.0 cm -1 , and D He = 3.3 10 -3 cm -1 has been obtained, as compared to the gas phase values of B gas = 5.24 cm -1 , and D gas = 9.3·10 -6 cm -1 . 15 Thus, the relatively small value of D He for methane is in accord with small change of rotational constant in He droplets. Apparently, the effect of the coupling of the molecular rotation with the liquid He environment depends on a number of factors, such as strength and morphology of the molecular interaction with He atoms as well as on the magnitude of the molecular rotational constant. Therefore it is difficult to compare the extensive results obtained for different molecules, each heaving its unique blend of coupling parameters. In this work we attempted to circumvent this problem by studying a series of isotopomers of homologous molecules such as CH 4 , CD 4 SiH 4 , and SiD 4 . This series of molecules covers a large range of the magnitudes of rotational constants from 5 cm -1 for CH 4 to 1.4 cm -1 for SiD 4 . On the other hand, 20 CD 4 and SiH 4 have very similar rotational constants and morphology of the interaction, but different strength of the interaction with He atoms. In this work we re-investigated spectra of CH 4 and studied spectra of CD 4 , SiH 4 , and SiD 4 molecules in He droplets. In all cases large values of D He have been found. These results led to a conclusion that the mechanism of change of rotational constants in liquid helium includes angular momentum coupling of the molecule and its first helium solvation shell, which is similar for both heavy and light rotors. The results are rationalized in the framework of the coupling of methane molecule with its He shell, both of which can be represented by spherical tops. 2. Experimental Details The spectra were measured using the molecular beam apparatus similar to that used previously. 3 The helium droplets, having about 3000 atoms, were formed by an adiabatic expansion of helium gas from a 5 μm orifice at a stagnation pressure of 20 atm at a temperature of 16 K. Helium droplets were doped with CH 4 (99.99 %, Matheson Tri-Gas), CD 4 (99 %, Cambridge Isotope Laboratories, Inc.) SiH 4 (99.998 %, Sigma-Aldrich Corp.) or SiD 4 (98%, Cambridge Isotope Laboratories, Inc.) in a separate, differentially pumped, 13 cm long pick-up chamber, equipped with an ionization pressure gauge. In the case of the deuterated silane spectrum measurements, the output of the near infrared laser was then Raman shifted by 4150 cm -1 in a cryogenic parahydrogen crystal. The laser frequency was calibrated by the absorption lines of the CH 4 , CD 4 , CO or NH 3 gases in an opto-acoustic cell. 21 3. Results Figure 3.1 (a) through (d) shows the IR depletion spectra of the ν 3 bands of the CH 4 , CD 4 , SiH 4 , and SiD 4 molecules in He droplets, respectively. In order to minimize the interference of the spectra of dimers, the measurements have been performed at low pickup pressure. Moreover the mass filter was set to masses of the corresponding deprotonated molecules. In Figure 3.1 the residual weak dimer features in the spectra are marked by asterisks. The frequencies, linewidths (FWHM), and the intensities of the observed lines of methanes and silanes are summarized in Tables 3.1 and 3.2, respectively. The error of the observed transition frequency was estimated to be 0.04 cm -1 as a mean square root deviation of the frequencies of the CH 4 and CD 4 lines in the opto-acoustic cell from the high resolution FTIR frequencies. 16 22 1595.0 1597.5 1600.0 1602.5 1605.0 Q(2) R(2) SiD 4 wavenumber, cm -1 P(2) P(1) Q(1) R(0) R(1) 2180 2185 2190 2195 2200 R(1)' Q(2)' SiH 4 Depletion, a.u. P(2) P(1) Q(1) R(0) R(1) 2250 2255 2260 2265 2270 b) CD 4 P(2) P(1) Q(1) R(0) R(1) 3000 3010 3020 3030 3040 c) a) a) a) CH 4 P(2) P(1) Q(1) R(0) R(1) d) Figure 3.1. Spectra of the ν 3 bands of: a) CH 4 ; b) CD 4 ; c) SiH 4 , and d) SiD 4 in helium droplets. The mass spectrometer was set to masses of CH 3 + (M = 15 u), CD 3 + (M = 18 u), SiH + (M = 29 u), and SiD + (M = 30 u), respectively, which was found to originate predominantly from the single molecules in He droplets. Weak peaks marked by asterisks in panels (a) and (b) are assigned to the dimers of (CH 4 ) 2 and (CD 4 ) 2 , respectively. Vertical lines are drawn as guides to eyes. 23 3.1. Intensity of the Lines In the absence of the nuclear spin relaxation in He droplets the population of the lowest rotational levels of J = 0, 1 and 2 should be in the ratio of 5 : 9 : 2 for CH 4 and 5 : 18 : 4 for CD 4 17 , which equals to the population ratio of the A, F and E nuclear spin symmetry species at room temperature. Thus the intensity of the P(2):P(1):Q(1):Q(2):R(0):R(1):R(2) lines should be in the ratio of 2: 5: 15: 3.3: 25: 25: 4.7 and 2.4: 6: 18: 4: 15: 30: 5.6 for CH 4 (SiH 4 ) and CD 4 (SiD 4 ), respectively. Tables 3.1 and 3.2 show that the intensity ratios of all of the measured lines are in reasonable agreement with the results of the above calculations. In case of deuterated species (CD 4 and SiD 4 ) renormalization of the integral intensities have been done by setting intensity of R(1) line to the theoretical value of 30. For CH 4 and SiH 4 , R(0) lines has been chosen as a reference and set to the theoretical value of 25. Some small deviations of the measured intensity of the lines from the calculated values are due to partial laser power saturation of the transitions. With the exception of the spectrum of the SiD 4 molecule we were not able to identify Q(2) and R(2) lines in the spectra. The Q(2) line is expected to have a complete overlap with the stronger Q(1) line, and thus could not be separated. The lack of any obvious R(2) lines in the spectra most probably indicates its large breadth. 24 Table 3.1. Frequencies, line widths, and integral intensities of the ν 3 band of CH 4 and CD 4 lines observed in this work in He droplets. For comparison frequencies in the gas phase and from previous He droplet study 18 are shown. Molecule Line Frequency, cm -1 Line width a) Intensity, a.u. CH 4 in He droplets a) in He droplets Ref. 18 in gas phase b) FWHM, cm -1 Experiment c) Theory P(2) 3001.70 2999.033 0.24 1.3 2 P(1) 3010.24 3010.31 3009.026 0.41 4.9 5 Q(1) 3019.69 3019.61 3018.837 0.38 19 d) 15 R(0) 3029.10 3029.07 3028.765 0.36 25 25 R(1) 3038.10 3038.13 3038.511 2.03 29 25 CD 4 P(2) 2252.02 2250.400 0.12 1.7 2.4 P(1) 2255.68 2254.820 0.18 7.0 6 Q(1) 2259.72 2259.195 0.16 21 d) 18 R(0) 2263.78 2263.594 0.17 15 15 R(1) 2266.91 2267.943 0.26 48 30 a) results of this work in He droplets. Accuracy of frequencies is ±0.04 cm -1 . b) Results of the gas phase FTIR measurements. 16 c) Intensity of the lines are normalized to give the calculated intensity of the R(0) line. d) Sum of the intensities of the Q(1) and Q(2) lines. 25 Table 3.2. Frequencies, line widths, and integral intensities of the SiH 4 and SiD 4 lines observed in this work in He droplets. For comparison frequencies in the gas phase are shown. Molecule Line Frequency, cm -1 Line width a) Intensity SiH 4 in He droplets a) in gas phase b) FWHM, cm - 1 Experiment c) Theory P(2) 2182.42 2177.80 2.2 2 P(1) 2185.85 0.11 5.3 5 Q(2) 3.3 Q(1) 2190.31 0.13 14.5 d) 15 R(0) 2194.85 2194.75 0.14 25 25 R(1) 2198.29 2200.36 0.15 11.4 25 ν 1 Q(2)’ 2188.04 0.35 1.8 ν 1 R(1)’ 2196.02 0.33 12 SiD 4 P(2) 1595.57 0.13 3.2 2.4 P(1) 1597.13 0.13 7.4 6 Q(2) 1598.68 0.13 3.1 4 Q(1) 1599.03 0.14 20 18 R(0) 1600.99 0.15 15 15 R(1) 1602.30 0.12 26 30 R(2) 1603.02 0.12 5.1 5.6 a) Results of this work in He droplets. Accuracy of frequencies is ±0.05 cm -1 . b) From reference 19 c) Intensity of the lines are normalized to give the calculated intensity of the R(1) line. d) Sum of the intensities of the Q(1) and Q(2) lines. 26 3.2. Spectrum of SiH 4 The spectrum of silane molecules contains some additional lines, which are marked by R(1)’ and Q(1)’ in Figure 3.1(c). These lines could not be assigned to the ro-vibrational transitions of the ν 3 band. Most probably these extra lines come through the interaction with the energy levels of the close lying energy levels of the ν 1 vibrational state. Further discussion on the nature of these transitions will be presented in Chapter 5. Figure 3.2. Schematic energy level diagram and rovibrational transitions observed during the experiments. 27 3.3. Line Widths Tables 3.1 and 3.2 show that some of the lines, such as the R(1) line of CH 4 have width, which is larger than the laser line width of 0.1 cm -1 . Most likely this indicates lifetime broadening due to rotational relaxation of the molecules in the ν 3 state. The energy level diagram of the CH 4 molecules is shown in Figure 3.2. The R(0), P(2), and P(1) transitions of CH 4 and SiH 4 populate the lowest level of the A, E and F nuclear spin manifolds in the ν 3 state, respectively and the rotational relaxation in the upper vibrational state is not feasible. Therefore the broadening may be assigned to vibrational relaxation in the upper state. The large linewidth of the R(1) line may indicate efficient rotational relaxation of the upper J’ = 2, F - state or some splitting of this level due to interaction with He surrounding. Note, that because the J’ = 2, F - state has only one component of the F 1 symmetry, this level can not be split under the T d symmetry due to rotational-vibrational Hamiltonian of the CH 4 molecule. It is seen that the width of the R(1) line of the CD 4 is about seven times smaller as compared with that for CH 4 . Other lines of CD 4 are a factor of three narrower as compared with corresponding lines of CH 4 . 3.4. Spectroscopic Constants The frequency of the P(1), Q(1), R(0), and R(1) lines are in good agreement with the previous He droplet study. 18 Owing to the good signal to noise ratio in the present measurements, we observed an additional weak P(2) line. We were not able to observe R(2) lines in the spectra of both molecules, which may indicate their large linewidth. From the molecular constants obtained in Ref. 20 the frequency of the P(2) 28 line can be calculated to be 3000.77 cm -1 , which is about 1 cm -1 lower than that observed in this work. This difference indicates that the value of D He of CH 4 molecules in He droplets is much larger than derived previously. 18 The energy levels of the CH 4 molecules in the ground (E g ) and the triply degenerate vibrationally excited (E e ) states, which are shown in Figure 3.3, can be expressed as, 21 2 2 g 1) (J DJ - 1) J(J B E + + ′ ′ = (1) ) (F : 1) (J DJ ζJ B 2 1) J(J B ν E 2 2 3 e + + − ′ + + ′ + = (2) ) (F : 1) (J DJ ζ B 2 1) J(J B ν 0 2 2 3 + − ′ + + ′ + (3) ) (F : 1) (J DJ 1) ζ(J B 2 1) J(J B ν - 2 2 3 + − + ′ − + ′ + (4) where 3 ν is the vibrational frequency, B” and B’ are the rotational constants in the ground and vibrationally excited states, respectively, and D is the centrifugal distortion constant, which is taken to be the same for the ground and the excited states, and ζ is Coriolis constant. Equations (2)-(4) are for the l = 1 (F + ), l = 0 (F 0 ), and l = -1(F - ) sublevels, respectively, where l stands for the vibrational angular momentum quantum number. Table II shows the parameters 3 ν , B ′ ′ , B′ , and D obtained from the least squares fitting of the observed transition frequencies to Eqs. (1)-(4). The values of Coriolis constants were assumed to be the same as in free molecules. For the sake of comparison, the gas phase values of the spectroscopic constants have been derived in the same way from the gas phase frequencies. The full fit in Ref. 22 , which included a much larger number of lines, provided very similar values of rotational constants. Table 3.3 shows that rotational constants of the CH 4 and CD 4 molecules in He droplets are about 4.4% for ground state, 2.2% for excited and 4.0% for ground state, 7.1% for excited, respectively, smaller than those in the gas phase. On the other hand the D- constants are more than two orders of magnitude 29 larger than those in the gas phase and amount to about 0.5% and 1% of the corresponding rotational constants. Large values of the D –constants in helium indicate coupling of the molecular rotational states with some states of local rotational motion of surrounding helium atoms. Table 3.3. Molecular constants of the CH 4 and CD 4 molecules in He droplets and in the gas phase frequencies. The values in parenthesis are single standard deviations of the last significant digits. CH 4 in He droplets a) in gas phase a) 3 ~ ν (cm -1 ) 3020.15 3019.512 B” (cm -1 ) 5.01 5.245 B’ (cm -1 ) 5.09 5.205 D” (cm -1 ) D’ (cm -1 ) 0.027 0.00000929 ζ 0.05583 b) 0.05583 b) CD 4 in He droplets a) in gas phase a) 3 ~ ν (cm -1 ) 2260.63 2260.065 B” (cm -1 ) 2.52 2.622 B’ (cm -1 ) 2.43 2.610 D” (cm -1 ) D’ (cm -1 ) 0.027 0.00009195 ζ 0.162 b) 0.162 b) a) Rotational constants are deduced from the gas phase frequencies in Table 3.1 using equations (1) - (4) b) ζ taken to be the same as in the gas phase for CH 4 and CD 4 from Refs. 23 and 24 , respectively. 30 Table 3.4. Molecular constants of the SiH 4 and SiD 4 molecules in He droplets and in the gas phase frequencies. The values in parenthesis are single standard deviations of the last significant digits. Position of the R(2) line of SiD 4 was not used for the fitting procedure. SiH 4 in He droplets a) in gas phase b) 3 ~ ν (cm -1 ) 2190.39 2189.193 B” (cm -1 ) 2.37 2.8388 B’ (cm -1 ) 2.36 2.8559 D” (cm -1 ) D’ (cm -1 ) 0.044 0.000028 ζ 0.011091 b) 0.011091 b) SiD 4 3 ~ ν (cm -1 ) 1599.25 1598.21 B” (cm -1 ) 1.06 1.4273 B’ (cm -1 ) 1.10 1.4338 D” (cm -1 ) D’ (cm -1 ) 0.021 0.00000079 ζ 0.068992 b) 0.068992 b) a) rotational constants are deduced from the gas phase frequencies in Table 3.2 using eqs. (1-4) b) ζ taken to be the same as in the gas phase for SiH 4 and SiD 4 from Refs. 19 31 4. Discussion Reduction of the rotational constants (B gas /B He ) for all four molecules vs. the value of the rotational constant in the gas phase (B gas ) is plotted on the Figure 3.3. The effective rotational constants of the molecules embedded in helium droplets are reduced with decreasing value of the gas phase rotational constant as was expected. 25 For the large number of studied molecules there is little or no reduction of the rotational constant for the range of B gas > 2 cm -1 . As the value of B gas is approaching 1 cm -1 , the value of the effective rotational constant starts to decrease noticeable and for the heavy molecules (B gas < 1 cm -1 ) B He can be decreased by 3-6 times. In this work we observed the molecules with B gas lying in the range of 1.4 for SiD 4 to 5.2 cm -1 for CH 4 . As expected, helium droplets do not affect the rotation of the methane (B gas = 5.205 cm -1 ) leaving the rotational constant almost unchanged B He = 5.09 cm -1 . For deuterated methane and normal silane we can start to see large changes of the rotational constant. Effective rotational constants are reduced to the values of 2.43 cm -1 (B gas = 2.610 cm -1 ) and 2.36 cm -1 (B gas = 2.856 cm -1 ) for CD 4 and SiH 4 respectively. Reduction of the B constant is even more significant for the deuterated silane: B gas / B He = 1.3. Clearly we can separate the observed effects of the reduction of the rotational constant into two categories. First one is the effect of deuterization of the molecule, when light hydrogen atom is substituted with the twice heavier deuterium atom leading to the decrease in the rotational constant by two times in the gas phase. In the helium droplets this substitution brings the B gas / B He ratios from 1.02 to 1.07 and 32 from 1.21 to 1.30 for methane and silane molecules respectively. The second effect is the change of the interaction of the molecule and surrounding helium droplet. Substituting the carbon atom in methane with silicon results in the increase of the Van-der-Waals interaction in helium droplet. In our case the effect of changing the central atom is clearly seen when we are going from deuterated methane to the normal silane. Even though B gas is larger for the CD 4 than for SiH 4 , the reduction of the rotational constant is more significant for the silane where the silicon atom creates a larger interaction potential. 12 34567 1.0 1.2 1.4 1.6 1.8 2.0 B gas /B He B gas , cm -1 SiD 4 SiH 4 CH 4 CD 4 Figure 3.3 Reduction of the rotational constant for all four molecules vs. gas phase values of B. Dashed line are just for guidance. 33 Centrifugal distortion constant D increases significantly (about 10 3 times) for all four molecules as compared to their gas phase value. In the case of CH 4 , SiH 4 , and SiD 4 molecules, the increase of D constant is almost the same for each and equals to about 855. On the other hand, the increase of the D constant for CD 4 is about 3000 times. It has been proposed that there is strong dependence of the D constant on the value of rotational constant in the helium. Value of the centrifugal distortion constant vs. the rotational constant B in helium is presented on Figure 3.4. The red line is proposed power law fit from Reference 25 . As it can be seen from Figure 3.4 all values of D constant for spherical rotors under investigation do not 110 0.01 0.1 D eff , cm -1 B eff , cm -1 SiD 4 SiH 4 CD 4 CH 4 Figure 3.4 Dependence of the effective D constant vs. the effective B constant for all four molecules. Red straight line is the proposed fit from Ref. 25 34 follow the proposed equation. There is no unique explanation for the behavior of the D constant in the helium droplets. The increase of the angular anisotropy for higher J levels, increased interaction with He as the populated rotational levels approach phonon/roton excitations of the helium are the most common explanations for larger increase of D constant for light rotors. 5. Conclusions In this work we report rovibrational spectra of spherical top molecules (CH 4 , CD 4 , SiH 4 , and SiD 4 ) embedded in He droplets. Spectra have been obtained in the region of ν 3 vibrational band for all four molecules. Observed rovibrational transitions allowed identification of spectroscopic constants, such as rotational constants in ground and vibrationally excited states, centrifugal distortion constants, and vibrational band origin. The constants obtained in helium are compared to those obtained previously in the gas phase. In general, reduction of the rotational constant B and increase of the centrifugal distortion constant has been observed in agreement with previous measurements. The effect of helium environment on the rotational constant B can be explained in terms of change of the effective moment of inertia of the molecule due to the non-adiabatic following of the surrounding helium. We can clearly separate effects on the B constant due to the deuterization of molecules, thus increasing moment of inertia, and change of the strength of the interaction potential as we change the central atom from carbon to silicon. It should be noticed, that the centrifugal distortion constant for spherical top molecules are affected differently by helium as compared to D constant for other molecules measured in He droplets. It is 35 clear that sophisticated theoretical modeling is needed in order to understand the physics of the coupling between rotations of the molecule and surrounding helium environment. 36 6. Chapter III References (1) Toennies, J. P.; Vilesov, A. F. Ann. Rev. Phys. Chem. 1998, 49, 1. (2) Callegari, K.; Lehmann, K. K.; Schmied, R.; Scoles, G. J. Chem. Phys. 2001, 115, 10090. (3) Toennies, J. P.; Vilesov, A. F. Angew. Chem. Int. Ed. 2004, 43, 2622. (4) Stienkemeier, F.; Vilesov , A. F. J. Chem. Phys. 2001, 115, 10119. (5) Grebenev, S.; Hartmann, M.; Havenith, M.; Sartakov, B.; Toennies, J. P.; Vilesov, A. F. J. Chem. Phys. 2000, 112, 4485. (6) Nauta, K.; Miller, R. E. J. Chem. Phys. 2001, 115, 10254. (7) Nauta, K.; Miller, R. E. J. Chem. Phys. 2001, 115, 8384. (8) Kwon, Y.; Huang, P.; Patel, M. V.; Blume, D.; Whaley, K. B. J. Chem. Phys. 2000, 113, 6469. (9) Paesani, F.; Whaley, K. B. J. Chem. Phys. 2004, 121, 5293. (10) Paesani, F.; Kwon, Y.; Whaley, K. B. Onset of superfluidity in small CO 2 ( 4 He) N clusters, preprint 2004. (11) Tang, J.; McKellar, A. R. W.; Mezzacapo, E.; Moroni, S. Phys. Rev. Lett. 2004, 92, 1455031. (12) Patel, M. V.; Viel, A.; Paesani, F.; Huang, P.; Whaley, K. B. J. Chem. Phys. 2003, 118, 5011. (13) Zillich, R. E.; Whaley, K. B. Phys. Rev. B 2004, 69, 104517. (14) Zillich, R. E.; Kwon, Y.; Whaley, K. B. Physical Review Letters 2004, 93, 250401. (15) Nauta, K.; Miller, R. E. Chemical Physics Letters 2001, 350, 225. (16) Momose, T. Personal communications. (17) Herzberg, G. Molecular spectra and molecular structure, II Infrared and Raman spectra of polyatomic molecules; Van Nostrand: Princeton, New Jersey, London, 1968. (18) Nauta, K.; Miller, R. E. Chem. Phys. Lett. 2001, 350, 225. 37 (19) Willetts, D. V.; Jones, W. J.; Robiette, A. G. Journal of Molecular Spectroscopy 1975, 55, 200. (20) Yamamoto, T.; Kataoka, Y.; Okada, K. J. Chem. Phys. 1977, 66, 2701. (21) Bernath, P. F. Spectra of Atoms and Molecules; Oxford University Press: New York, 1988. (22) Herranz, J.; Stoicheff, B. P. Spectrochimica Acta 1961, 17, 1125. (23) Barnes, W. L.; Susskind, J.; Hunt, R. H.; Plyler, E. K. J. Chem. Phys. 1972, 56, 5160. (24) Brodersen, S.; Gray, D. L.; Robiette, A. G. Molecular Physics 1977, 34, 617. (25) Choi, M. Y.; Douberly, G. E.; Falconer, T. M.; Lewis, W. K.; Lindsay, C. M.; Merritt, J. M.; Stiles, P. L.; Miller, R. E. International Reviews in Physical Chemistry 2006, 25, 15. 38 Chapter IV: Large Enhancement of the Intramolecular Coupling in SiH 4 in Liquid Helium 1. Abstract The 3 ν vibrational band (2190 cm -1 ) of SiH 4 molecules was studied in helium droplets. Interaction with helium environment induces a factor of about 50 increase in the non-diagonal matrix elements of the rotation-vibration interaction between close laying ν 1 and 3 ν states of SiH 4 as compared to that in free molecule. As a result of this coupling the Q2 and R1 rotational lines of the band were found to have satellites shifted by about 2.3 cm -1 towards low frequency with respect to the parent line and having same intensity. 39 2. Introduction Large number of experimental 1-7 and theoretical 8-14 works are now available on molecules trapped in 4 He droplets. Molecules were discovered to experience free rotation in 4 He droplets and the rotationally resolved spectra were established as novel microscopic probes for superfluidity in finite systems. In heavy top molecules such as SF 6 and OCS 15,16 the effective moment of inertia increases in He as compared to free molecules by about a factor of three. On the other hand the light top molecules such as CH 4 , H 2 O and NH 3 show only a few percents increase of the moments of inertia. 17-20 Phenomenologically, the renormalization of the moments of inertia in helium can be described as a correction to diagonal matrix-elements of molecular rotational-vibrational Hamiltonian. In spite of the large activity, the physics of the rotational coupling of the molecule with its He environment is not understood completely. 8-14 Quantum mechanical origin of the effect must include the coupling of molecular rotation with some, yet undefined, local excitations in helium. Additional source of information on the effective symmetry as well as on the angular momentum and other characteristics of those excitations can be obtained from the non-diagonal matrix elements (NDME) in the rotational-vibrational Hamiltonian of the embedded molecule. So far very few observations of molecular perturbations, which could be connected with NDME in He have been made. In particular, the Fermi-dyad 02 0 1 and 10 0 1 bands of CO 2 in He were found to have the same splitting of about 102 cm -1 as in the gas phase, which indicates that the possible effect of He is much weaker than the strong intramolecular interaction. 21 In search of a more sensitive 40 probe of NDME in helium we turned to silane (SiH 4 ). SiH 4 is a spherical top molecule which totally symmetric stretching ( ν 1 , a 1g ) and anti-symmetric stretching ( ν 3 , t 2u ) modes are in close resonance (2.3 cm -1 ). In free molecules these modes are coupled by a weak vibration-rotation interaction 22,23 of about 0.02 cm -1 which would be virtually unobservable in helium. Surprisingly, we have found that the rotational structure of 3 ν band in helium shows pronounced anomalies. Both Q2 and R1 lines have satellites residing at about 2.3 cm -1 lower frequency and borrowing about one half of the intensity from each of the corresponding parent line. Deperturbation analysis shows that the strength of the coupling of some of the ro-vibrational levels of ν 1 and ν 3 states increases in helium by about a factor of 50. We suggest that the interaction is mediated by some rotational-vibrational states of helium environment, which can be classified in terms of the point symmetry group of the embedded molecule. 3. Experimental Details The molecular beam apparatus has been described elsewhere. 24,25 Helium droplets, consisting of about 3000 atoms, were formed by an adiabatic expansion of helium gas from a 5 μm orifice at a stagnation pressure of 20 bar at a temperature of 15 K. The droplets were doped with SiH 4 (99.0 %) molecules in a separate pick-up chamber. The laser frequency was calibrated using the absorption lines of silane gas in an opto-acoustic cell. The spectral purity of the laser radiation was additionally controlled by a monochromator. 41 4. Results Figure 4.1 shows the comparison of the spectrum of silane in a photo- acoustic cell (a) with that in He droplets (b). An insert in Figure 4.1 (b) shows a part of the spectrum in the range of 2185 – 2191 cm -1 , which was obtained with a factor of four longer averaging. In order to minimize the contribution from dimers, the spectrum (b) was measured at low pick-up pressure with the mass filter set at mass M = 29 u (SiH + ). The relative intensity of the lines in this spectrum remained constant as the average number of the captured molecules per droplet was changed in the range of 〈n〉 = 0.3 - 2. Thus we concluded that all the lines in the spectrum (b) originate from the single molecules and not from the dimers or the complexes of silane with some impurities. For comparison, spectrum (c) was obtained with the mass spectrometer set to M = 31 u (SiH 3 + ) and has the largest contribution from dimers. The gas phase spectrum in Figure 4.1(a) has a regular progression of nearly equally spaced P- and R- lines ( ΔJ = -1 and ΔJ = +1) of 28 SiH 4 molecules, which are labeled by the rotational quantum numbers in the ground state. 26 The Q-branch lines ( ΔJ = 0) in the central part of the spectrum are not resolved. The spectrum (b) in He shows well-resolved ro-vibrational lines which originate from the lowest rotational levels of the ground state J'' = 0, 1, 2. The levels of J'' = 1, 2 remain populated in He droplets due to the conservation of the nuclear spin of molecules in helium droplets as observed previously in SF 6 , 27 CH 4 , 17 C 2 H 2 , 18 NH 3 , 19 and H 2 O. 20 The spectrum of 42 silane in helium has two additional lines which are marked in Figure 4.1(b) by Q2' and R1'. From the frequencies of the P1, Q1 and R0 lines (Figure 4.1(b)) the band origin and the rotational constant of 28 SiH 4 in helium were obtained to be ν 3 = 2190.34±0.02 cm -1 and B = 2.28±0.02, as compared to ν 3 = 2189.19 cm -1 and (B 0 + 2170 2180 2190 2200 2210 Wavenumber, cm -1 M=31 Q1 Q2' P1 Q1 R1' R0 R1 R2 P2 P3 Q2' R1 P2 R0 M=29 Depletion signal P1 Q1 Q2' P1 2186 2188 2190 Q c) b) a) Figure 4.1. Spectra of silane in the opto-acoustic cell (a), and in helium droplets obtained with the mass spectrometer detection of SiH + (M = 29 u) (b) and of SiH 3 + (M = 31 u) (c). Laser pulse energy was 65 μJ. 43 B 3 )/2 = 2.864 cm -1 in the gas phase. 28 Here we used the rigid rotor approximation as well as the gas phase value of the Coriolis constant ζ 3 = 0.011. 28 The integrated line intensities in the spectrum of Figure 4.1(b), which was measured at low laser pulse energy, were found to be in the ratio of P2 : P1 : Q2′ : Q1 : R0 : R1′ : R1 = 2.2 : 5.3 : 1.8: 14.5 : 25 : 12 : 11.4. The measured relative intensity of the P2, P1, Q1, and R0 lines is the same within the experimental error of about ±10% to the calculated ratio of 2 : 5 : 15 : 25. 29 On the other hand, the R1 and R1' components are making total of (23.5 ± 2.0), in good agreement with the calculated intensity of the R1 line of 25. The intensity of the Q2′ line of (1.8 ± 0.9) is smaller than expected for the Q2 line of 3.3. The Q1 line has some weak high frequency shoulder, which can be tentatively assigned to the Q2 line. The intensity of the last is difficult to measure due to overlap with the strong Q1 line. Figure 4.2 shows the spectra of silane molecules in helium droplets measured at different laser pulse energies. At highest laser pulse energy of 1 mJ (a) the R1′ and R1 lines have the same peak intensity and are stronger than the R0 line. The Q2′ and Q2 lines are also clearly seen in Figure 4.2(a). In the case of a laser power saturation the intensity is not distorted by the perturbation effects and is expected to be P2 : P1 : Q2 : Q1 : R0 : R1 : R2 = 0.17 : 0.50 : 0.22 :1 : 0.83 : 1.24 : 0.25, respectively, as given by the ratio of the degeneracy in the upper and lower states (2J′ + 1)/(2J′′ + 2J′ + 2) multiplied by the population of the rotational levels in the vibrational ground state of 5 : 9 : 2 for J′′ = 0 (A 1 ), 1 (F 2 ), 2 (E), respectively. 29 44 The ratio of the peak line intensities in the spectrum Figure 4.2(a) which is close to saturation was found to be P2 : P1 : Q2′ : Q1 : Q2: R0 : R1′ : R1 = 0.15 : 0.4 : 0.22 : 1 : 0.22 : 1.0 : 1.15 : 1.30. The saturated intensities of the Q2 and Q2′ lines and of the R1 and R1′ lines are the same within the experimental error as calculated for the Q2 and R1 lines, respectively, confirming the assignment of the lines to J′ = 2 ← J′′ = 2, and J′ = 2 ← J′′ = 1 transitions, respectively. Spectrum (a) at high laser pulse energy also shows a broad band (10 cm -1 ) having maximum around 2195-2200 cm -1 and shaded towards high frequency. Similar feature was previously observed in the spectrum of CO 2 in helium droplets, where it was assigned to the side band due to excitation of the molecular rotation coupled to some excitation in the helium surrounding. 24 5. Discussion Appearance of the R1′ - R1 and Q2′ - Q2 doublets of lines with similar intensity indicates that the J=2 level of the ν 3 vibrational state is strongly perturbed. Because the P1, Q1 and R0 lines do not have any satellites, the perturbation is a not pure vibrational one, but involves the rotational degrees of freedom. Silane has close laying ν 3 (F) and ν 1 (A) vibrational states, with the gas phase origins at 2189.187 and 2186.867 cm -1 , respectively. 22,23 Therefore, we assigned the perturbation to the vibration-rotation interaction of the ν 3 and ν 1 states. The absence of any perturbations in the spectra of isomorphic CH 4 , CD 4 , and SiD 4 molecules in He 45 droplets 5,17,30 is consistent with the large separation of the ν 3 and ν 1 states in those molecules of about 103, 151, and 15 cm -1 , respectively. Figure 4.3 shows low laying rotational levels of the ν 3 and ν 1 states in free SiH 4 . In free SiH 4 molecule the coupling between the 1 ν and 3 ν states is very weak. Due to the tetrahedral T d symmetry of the SiH 4 both the pure vibrational interaction and the Coriolis interaction between the ν 3 and ν 1 states is forbidden, and the interaction derives from the change of the rotational constants upon the vibrational 2180 2185 2190 2195 2200 2205 2210 2215 0.0 0.2 0.4 Wavenumbers, cm -1 0.0 0.4 0.8 1.2 Depletion, a.u. 0 1 2 3 Q1 R1' Q2' R0 R1 Q2 P1 c) E = 65μJ b) E = 400μJ a) E = 1mJ P2 Figure 4.2. Spectrum of silane in He droplets measured at different laser pulse energies of 1mJ (a), 400 μJ (b), and 65 μJ (c) and at the same pickup pressure corresponding to capture of about 0.5 molecules per droplet. 46 excitation. 22,23 The strength of the interaction scales as 2 13 J d ⋅ with d 13 =0.01747 cm -1 . In the gas phase NDME for J=0,1 vanish. For J=2 the NDME amount to 〈 ν 1 J=2, E|V| ν 3 J=2, F (0) , E〉 = 13 ) 2 / 3 ( d ⋅ = 0.037 cm -1 , (1) 〈 ν 1 J=2, F 2 |V| ν 3 J=2, F (-) , F 2 〉 = 13 ) 10 / 3 ( d ⋅ = 0.0096 cm -1 , (2) 〈 ν 1 J=2, F 2 |V| ν 3 J=2, F (+) , F 2 〉 = 13 ) 5 / 6 ( d ⋅ = 0.047 cm -1 . (3) Figure 4.3. Schematic diagram of the rotational energy levels of the ν 1 and ν 3 vibrational states of silane. Rotational levels of the ν 3 state are sorted according to the vibrational angular momentum sublevels F (-) , F (0) , and F (+) . 29 Circles show the upper levels of the observed lines. The arrows show the upper levels of the Q2 and R1 lines. F (-) F (o) F (+) 2.32 cm -1 A 1 EF 2 F 1 A 2 F 2 E F 1 F 2 F 2 F 2 F 1 F 1 E A 1 ν 1 (A 1 ) ν 3 (F 2 ) J=2 J=1 J=0 J=2 J=1 J=0 R1 Q2 47 Obviously the interaction in the free-molecule is too weak to explain the same intensity of the R1 and R1′ lines which are separated by about 2.3 cm -1 . Inspection of the diagram of energy levels in Figure 4.3 shows that the upper levels of the perturbed R1 and Q2 lines belong to the F 2 and E symmetry species of J=2 (F (+) ) and J=2 (F (0) ) rotational levels of the ν 3 state, respectively. It is seen that the J = 2 level of the ν 1 state also has the F 2 and E components and thus the interaction is allowed in the framework of T d symmetry group of SiH 4 . The diagram also shows that in the case of J = 1 and J = 0 rotational levels the ν 1 and ν 3 states have no counter partners of the same symmetry. This analysis confirms that the selection rules for the interaction implied by the T d symmetry of SiH 4 are preserved, when molecule is immersed into helium droplet. In order to quantify the strength of interaction we have applied the two-level interaction model. The de-perturbation analysis based on the measured intensity ratio and frequencies of the two components of the R1 line gives the NDME of about 1.13±0.15 cm -1 and places the energy of the unperturbed rotational levels of the ν 1 state and ν 3 state in close resonance of ΔE = 0.12±0.06 cm -1 . Similar results have been obtained from the analysis of the Q2 and Q2′ lines, although with lower accuracy. Thus, it is seen that the interaction with helium induces a strong vibration- rotation interaction between the J=2 levels of the ν 1 and ν 3 states. The obtained zero order position of the ν 3 , J=2 level of SiH 4 in helium is 1.15±0.2 cm -1 lower than predicted with the rigid rotor approximation. This suggests the strong centrifugal distortion of the ν 3 state which magnitude is estimated to be about D=0.03 cm -1 as 48 compared to D=2.8·10 -5 cm -1 in free molecules. This large value of D reveals the strong increase of the ro-vibrational coupling in He. The frequency of the ν 1 state in He was obtained from the deperturbation analysis and energy levels in Figure 4.3 to be ν = 2190.4 cm -1 . Thus the frequency of the ν 1 vibration increases in helium by about 3.5 cm -1 as compared to the increase by 1.2 cm -1 in the case of the ν 3 state. In search for an explanation of the great increase of the strength of the NDME in He we assumed that the rotation of SiH 4 interacts strongly with some excited states of helium environment. This interaction also manifests itself in the increase of the effective B constant and appearance of the side band in the spectrum of Figure 4.2(a). From the last, the characteristic energy of the local rotational- vibrational helium excitations ) (He E can be estimated to be about 5 cm -1 which corresponds well with the roton excitations in liquid He. Therefore, the rigid rotor energy terms are strictly no longer valid and should be replaced those coming from solution of a coupled system. The interaction having strength of about 2.3 cm -1 between the He excitations and the J=2 sublevel of the 3 ν state can induce, in the first order of the perturbation theory, (i) large increase of the B constant, (ii) a significant centrifugal distortion of the rotational levels and (iii) the increase of the effective interaction between the 1 ν and 3 ν vibrational states of silane molecule in helium droplet up to about 1 cm -1 . The peculiar feature of the helium excitations is that they do not imply their own symmetry such as in the case of a molecule in a crystal field, but adopt the symmetry of the embedded molecule. 49 An additional insight into the coupling mechanism is provided by the absence of any line due to excitation of the F 2 , J=2 (F (+) ) level. If the interaction strength in He had the same partition as in free molecule, which is given by eqs. (2) and (3), one would expect observing a triplet rather than doublet originating from the R1 line. The lack of the third line in the spectrum may help to identify the origin of the He excitations, which are coupled to molecular rotation. Observation of the rotational structure in the spectrum shows that the excitation in helium, which mediates the coupling E(He), is coherent with the molecular rotation. Therefore the combination states 1 ν + ) ( 1 He E and 3 ν+) ( 3 He E , which mediate the interaction between the 1 ν and 3 ν states, can be characterized by the rotational quantum number of the total angular momentum of the coupled system J. It implies that the side band spectrum in Figure 4.2(a) may contain contributions from different rotational lines. Additional experimental and theoretical investigations are necessary in order to figure out the nature of the excited states of He and the detailed interaction mechanism. To clarify the role of the interaction with the 1 ν state, it would be desirable to investigate the spectra of the isotopomers of silane 29 SiH 4 and 30 SiH 4 which have different splitting of the 1 ν and 3 ν states. Unfortunately such isotopes are not commercially available. 50 6. Chapter IV References (1) Toennies, J. P.; Vilesov, A. F. Ann. Rev. Phys. Chem. 1998, 49, 1. (2) Callegari, C.; Lehmann, K. K.; Schmied, R.; Scoles, G. J. Chem. Phys. 2001, 115, 10090. (3) Toennies, J. P.; Vilesov, A. F. Angew. Chem. Int. Ed. 2004, 43, 2622. (4) Stienkemeier, F.; Vilesov, A. F. The Journal of Chemical Physics 2001, 115, 10119. (5) Choi, M. Y.; Douberly, G. E.; Falconer, T. M.; Lewis, W. K.; Lindsay, C. M.; Merritt, J. M.; Stiles, P. L.; Miller, R. E. Int. Rev. Phys. Chem. 2006, 25, 15. (6) Stienkemeier, F.; Lehmann, K. K. J. Phys. B: At. Mol. Opt. Phys. 2006, 39, 127. (7) McKellar, A. R. W. Journal of Molecular Structure 2006, 795, 98. (8) Kwon, Y.; Huang, P.; Patel, M. V.; Blume, D.; Whaley, K. B. The Journal of Chemical Physics 2000, 113, 6469. (9) Paesani, F.; Whaley, K. B. The Journal of Chemical Physics 2004, 121, 5293. (10) Paesani, F.; Whaley, K. B. The Journal of Chemical Physics 2004, 121, 4180. (11) Tang, J.; McKellar, A. R. W.; Mezzacapo, F.; Moroni, S. Physical Review Letters 2004, 92, 145503. (12) Patel, M. V.; Viel, A.; Paesani, F.; Huang, P.; Whaley, K. B. The Journal of Chemical Physics 2003, 118, 5011. (13) Zillich, R. E.; Whaley, K. B. Physical Review B (Condensed Matter and Materials Physics) 2004, 69, 104517. (14) Zillich, R. E.; Kwon, Y.; Whaley, K. B. Physical Review Letters 2004, 93, 250401. (15) Grebenev, S.; Hartmann, M.; Havenith, M.; Sartakov, B.; Toennies, J. P.; Vilesov, A. F. J. Chem. Phys. 2000, 112, 4485. (16) Hartmann, M.; Portner, N.; Sartakov, B.; Toennies, J. P.; Vilesov, A. F. J. Chem. Phys. 1999, 110, 5109. (17) Nauta, K.; Miller, R. E. Chem. Phys. Lett. 2001, 350, 225. 51 (18) Nauta, K.; Miller, R. E. J. Chem. Phys. 2001, 115, 8384. (19) Slipchenko, M. N.; Vilesov, A. F. Chem. Phys. Lett. 2005, 412, 176. (20) Kuyanov, K. E.; Slipchenko, M. N.; Vilesov, A. F. Chem. Phys. Lett. 2006, 427, 5. (21) Nauta, K.; Miller, R. E. J. Chem. Phys. 2001, 115, 10254. (22) Susskind, J. J. Chem. Phys. 1972, 56, 5152. (23) Briss, F. W. Mol. Phys. 1976, 31, 491. (24) Hoshina, H.; Lucrezi, J.; Slipchenko, M. N.; Kuyanov, K. E.; Vilesov, A. F. Physical Review Letters 2005, 94, 195301. (25) Slipchenko, M.; Kuyanov, K.; Sartakov, B.; Vilesov, A. F. J. Chem. Phys. 2006, 124, 241101. (26) Rothman, L. S.; Jacquemart, D.; Barbe, A.; Benner, D. C.; Birk, M.; Brown, L. R.; Carleer, M. R.; Chackerian, C.; Chance, K.; Coudert, L. H.; Dana, V.; Devi, V. M.; Flaud, J. M.; Gamache, R. R.; Goldman, A.; Hartmann, J. M.; Jucks, K. W.; Maki, A. G.; Mandin, J. Y.; Massie, S. T.; Orphal, J.; Perrin, A.; Rinsland, C. P.; Smith, M. A. H.; Tennyson, J.; Tolchenov, R. N.; Toth, R. A.; Vander Auwera, J.; Varanasi, P.; Wagner, G. Journal of Quantitative Spectroscopy & Radiative Transfer 2005, 96, 139. (27) Hartmann, M.; Miller, R. E.; Toennies, J. P.; Vilesov, A. Phys. Rev. Lett. 1995, 75, 1566. (28) Willetts, D. V.; Jones, W. J.; Robiette, A. G. J. Mol. Spectr. 1975, 55, 200. (29) Herzberg, G. Molecular spectra and molecular structure, II Infrared and Raman spectra of polyatomic molecules; Van Nostrand: Princeton, New Jersey, London, 1968. (30) Hoshina, H.; Skvortsov, D.; Marinov, D.; Sartakov, B.; Vilesov, A. F. to be published. 52 Chapter V: Study of HCl Clusters in Helium Nanodroplets: Experiments and Ab Initio Calculations as Stepping Stones from Gas Phase to Bulk 1. Introduction Hydrogen chloride (HCl) is a simple textbook example of hydrogen bonding molecules. The HCl dimer is found to be a very floppy and weakly bound complex having dissociation energy of about D 0 = 5.25 kJ/mol. 1 The vibrationally averaged structure of the dimer is L-shape planar with an external angle (H···Cl-H) of about 95º. 2-4 Small HCl clusters up to tetramers have been studied via spectroscopy in gas- phase, 5-10 liquid, 11 matrix, 12-15 in large Ar clusters 16 as well as theoretical calculations. 2,17-21 It is well established that the most stable structures of the HCl trimer and tetramer are cyclic. 3,7,10,20 However, much less is known on the structures of larger HCl clusters. The central questions of this work are: how the planar cyclic structure, a characteristic for small clusters, transforms into the three dimensional structure for larger clusters and whether or not the cyclic structure prevails in larger clusters or is replaced by a branched one where the chlorine atoms serve as double acceptors. In this chapter, we report the results of a joint theoretical and infrared laser spectroscopic study of the hydrogen chloride clusters formed in helium nanodroplets. 22-25 The H-Cl stretching bands of the dimers, trimers, and tetramers show a large increase in the infrared intensity and low frequency shift with respect to 53 that in a single HCl molecule. The average frequency of the bands for clusters of <n> = 4-500 remains approximately constant at about 2770 cm -1 , which correlates well with the onset of the folded cyclic structure and with the full development of hydrogen bonding in larger clusters. We have identified absorption bands of clusters up to hexamers. Both calculations and experiments indicate that pentamers have an envelope like structure, while a folded chain geometry resembling a bi-pyramid is identified for hexamers. 2. Experimental Technique In this work, helium nanodroplets having an average size of about 4 × 10 3 , 1.6 × 10 4 , and 2.5 × 10 6 atoms are formed by supersonic expansion of high purity helium (99.9999%) gas at the source pressure of P 0 = 20 bar into vacuum through a 5 μm nozzle at a temperature of T 0 = 15, 11, and 9 K, respectively. The droplet beam passes through a 1.5 mm diameter skimmer and captures the HCl molecules in the 12 cm long pick-up chamber. The spectra were obtained by using an infrared pulsed laser (Laser Vision, 7 ns duration, 20 Hz repetition rate, 1 mJ pulse energy) having a line width of about 1 and 0.08 cm -1 with the injector seeder of the pump Nd:YAG laser (Continuum Powerlite 8020) off and on, respectively. The total flux of the droplet beam is detected by a quadrupole mass filter, which is adjusted to transmit all masses larger than 6 u. 54 3. Results 3.1. Ab Initio Calculations In spite of the numerous previous theoretical calculations of the structures and vibrational frequencies of small HCl clusters, 2,17-20 there have been very few studies of large HCl clusters beyond the pentamer. 3 Therefore, we have carried out calculations of the structures and vibrational frequencies of HCl clusters up to hexamer using the Møller-Plesset perturbation theory at the 2 nd order (MP2) level. The geometries of all molecules have been fully optimized with the Dunning’s correlation consistent polarized valence double zeta basis set augmented with diffuse functions (aug-cc-pVDZ) basis set, the Pople’s triple-zeta basis set (6-311++G**) with p polarization functions on hydrogen and d polarization functions on all other atoms plus diffuse functions and the 6-311++G(3df,3pd) basis set using Gaussian 03. 26 The local minimum structures are verified by observing that no negative vibrational frequencies were obtained with the optimized structures. Figure 5.1 shows the global minimum geometries of the (HCl) n (n = 2-6) clusters, which are found to be cyclic. We have found that the structure of the tetramer is twisted cyclic. The pentamer is also cyclic with one HCl molecule sitting almost upright with respect to the tetramer ring. The structure of the hexamer resembles a bi-pyramid. The results, including structures, frequencies, and infrared intensities from the ab initio calculations are presented in the Supporting Information in Figure 5.S1 and in Tables 5.S1-5.S5. 55 The structures and relative energies of local minimum isomers of HCl pentamer and hexamer are presented in the Supporting Information (see Figure 5.S2). Some of the low lying isomers have energies of only few kJ/mol higher than that for the global minimum isomers in Figure 5.1. This small energy difference may be comparable with the error of the calculations. Therefore, calculations alone are not sufficient to determine the isomers of clusters occurring in He droplets. However, as will be discussed in Section 4.3 the observed spectra strongly support predominant formation of the global minimum isomers in He droplets. n=2 n=3 n=6 n=4 n=5 Figure 5.1. The global minimum structures of (HCl) n (n = 2-6) clusters calculated at the MP2 level with an 6-311++G(3df,3pd) basis set using Gaussian 03. 56 3.2. Spectra of (HCl) n in He Droplets Figure 5.2 shows the spectra of HCl clusters as measured at different pressures of HCl in the pick-up cell and in He droplets of different average size. The numbers in brackets show the average number of HCl molecules captured by the helium nanodroplets, which is proportional to the pick-up pressure and droplets’ capture cross-section. The proportionality coefficient in small droplets of about 4000 He atoms has been obtained by fitting the intensity of the cluster bands as a function of pick-up pressure to Poisson functions (see Figure 5.S3 in the Supporting Information). In the case of larger droplets the numbers are estimated assuming geometrical capture cross-section. At the lowest HCl pick-up pressure, <n> = 0.25, the R(0) line of the monomer at 2905.4 cm -1 and free (v 1 ), and bonded (v 2 ), bands of HCl dimer at 2888.0 cm -1 and 2851.9 cm -1 , respectively, are seen in the spectrum. An additional weak band at 2715.0 cm -1 , marked with an asterisk, is assigned to the H 2 O-HCl complexes. Water molecules are captured from the rest gas in spite of the low residual pressure in the vacuum chambers of less than 10 -7 mbar. At higher pick-up pressure, the bands due to trimer through hexamer appear in the spectra at lower frequency. We were not able to identify free H-Cl stretches for the trimer and larger clusters, which indicates that these clusters have a cyclic structure, in agreement with the results of ab initio calculations. The frequencies of the observed bands of small clusters are listed in Table 5.1. Table 5.1 also contains the measured intensities of dimers, trimers and tetramers obtained from the spectra as described in details elsewhere. 27 The spectra of very large (HCl) n clusters of about <n> = 20 and <n> = 500 in Figure 5.2 (f and g) have a broad structureless band 57 around 2780 and 2775 cm -1 , respectively, with a FWHM of about 30 cm -1 . The broad band is a convolution of the spectra due to the bonded H-Cl stretching vibration in clusters of different sizes according to Poisson distribution, which cannot be resolved. Figure 5.3 (a) shows the measured IR spectrum of the HCl clusters having average size of <n> = 2 solvated in helium nanodroplets. According to the Poison pick-up statistics, 23,24,27 the droplets have an appreciable population of clusters of up to tetramers. The most intense peak in the spectrum at 2807.7 cm -1 is assigned to the cyclic trimer based on the pick-up cell pressure dependence experiments (see Figure 5.S3 in the Supporting Information). It is also in good agreement with results of previous experiments in the gas-phase, 5,9,10,28,29 which are listed in Table 5.1. Similarly, the strong peak at 2772.3 cm -1 is assigned to the cyclic tetramers. Figure 5.3 (b) shows the calculated spectra for the clusters up to tetramer [monomer (down triangle), dimer (square), trimer (triangle), and tetramer (circle)]. It is seen that the scaled (0.960 in order to account for anharmonicity) calculated frequencies are in good agreement with the experimental results. 58 2650 2700 2750 2800 2850 2900 2950 <500> <20> <0.25> <1.0> <2.0> <4.0> Depletion signal Wavenumber, cm -1 <8.0> * * * (e) (g) (d) (f) (c) (b) (a) 1 2 3 4 5 5 1 2 3 4 5 5 6 6 Figure 5.2. Spectra of HCl molecules and clusters in He droplets of 4000 atoms measured at different pressures of HCl in the pickup cell, (a) 2.1 × 10 -6 ; (b) 8.5 × 10 -6 ; (c) 1.7 × 10 -5 ; (d) 3.4 × 10 -5 ; (e) 6.8 × 10 -5 ; (f) 4.7 × 10 -5 ; (g) 1.0 × 10 -4 mbar. The numbers in brackets show the average number of molecules captured by the He droplets. The band marked with an asterisk is assigned to H 2 O-HCl complexes. The upper spectra (f) and (g) with <n> = 20 and <n> = 500 have been measured in larger He droplets of 1.6 × 10 4 and 2.5 × 10 6 atoms, respectively. 59 A high resolution spectrum of the clusters having an average number of four HCl molecules is shown in Figure 5.4 (a). The pick-up pressure dependence experiments were used to assign the experimental vibrational bands of pentamers and hexamers indicated in Figure 5.4. The relative intensities of the hexamer bands are smaller as compared to pentamer bands due to a factor of 2/3 smaller abundance of the former in the droplets at the used experimental conditions. The results of the ab initio calculations for the cyclic pentamer and hexamer of HCl clusters are shown in 2720 2760 2800 2840 2880 2920 Wavenumber, cm -1 (a) (b) <2> 2 2 3 4 1 Figure 5.3. (a) A spectrum of (HCl) n clusters in He droplets for the average cluster size of <n> = 2. (b) The scaled ab initio frequencies for the monomers, dimers, trimers, and tetramers are shown by down triangle, square, triangle, and circle, respectively. 60 Figure 5.4 (c) and (b), respectively. Finally, the spectrum in Figure 5.4 (a) also has a contribution from larger clusters of n > 6, which are responsible for the broad underlying band having a width of about 20 cm -1 (FWHM). This band is more obvious in the spectra of larger clusters in Figure 5.2 (e-g). 2700 2720 2740 2760 2780 2800 2820 2840 2860 2880 Wavenumber, cm -1 (a) (b) <4> 3 4 (c) (d) (HCl) 6 (HCl) 5 (HCl) 4+1 5 6 5 5 6 6 Figure 5.4. (a) A high resolution (δν = 0.08 cm -1 ) spectrum of (HCl) n clusters in He droplets; <n> = 4. The stick spectra are the results of calculations for the cyclic hexamers (b) and pentamers (c) using the MP2/aug-cc-pVDZ level of theory. Panel (d) shows the spectrum of the tail (4+1) isomer of the pentamer calculated with the same basis set. 61 4. Discussion 4.1. Monomer We have assigned the 2905.4 cm -1 peak to the R(0) ro-vibrational line of the single HCl molecules. The R(0) line is shifted toward lower frequency by about 0.9 cm -1 as compared to the gas-phase value of 2906.25 cm -1 . 30 Somewhat larger shift of 2.2 cm -1 has been previously observed in the case of HF molecules in He droplets. 31,32 Because the rotational constants of the light molecules in He droplets were found to be very similar to those in the gas-phase, 27,31,33-36 the measured shift should be very similar to that of the vibrational band origin in He droplets, which can be estimated to be at 2885.3 cm -1 by using the rotational constant of the free HCl molecules of 10.14 cm -1 . 30 It is known that the relaxation time of the vibrationally excited HF molecules is much longer than the flight time of the droplets. Based on the similarity with HF molecules, we expected a similar long relaxation time of the vibrationally excited HCl. In order to estimate the lifetime, we have compared the time resolved depletion signal originating from the laser excitation of monomers and trimers, in which the latter are expected to have a short relaxation time. From the ratio of the two signals, the lifetime of the vibrationally excited HCl molecules was estimated to be about 0.6 ms. This time, although long, is shorter than the time of flight of the molecules from the pick-up cell to the mass spectrometer of about 3 ms. Therefore, most of the excited molecules have sufficient time to relax, and on average only an estimated 10 % of the molecules remain in the vibrationally excited state upon reaching of the 62 detector. Thus, the relaxation time of the HCl is shorter than that in HF, which correlates well with about 1000 cm -1 smaller vibrational quantum in the former. Table 5.1. Frequency of (HCl) n (n = 1-6) clusters in He droplets and in the gas- phase. The frequencies are in wavenumbers (cm -1 ). The gas-phase frequencies are for H 35 Cl molecules and corresponding clusters. (HCl) n This Work Relative n Frequency a IR intensity b Nozzle beam Ragout jet c 1 d 2905.4 1 2906.2 e 2, ν 1 f 2888.0 2.5 2890.8 g 2890.0 2, ν 2 h 2851.9 2.5 2857.2 g 2856.9 3 2807.7 11 2809.8 i 2809.7 4 2772.3 22 2774 - 2778 i 2776.6 5 2786.4 5 2789.6 2791.6 ? 5 2767.6 2770.5 ? 6 2800.1 6 2795.4 6 2762 a. Error limits ±0.2 cm -1 . b. The infrared intensity relative to that of the fundamental band in free HCl molecules of 25 km/mol. 37,38 The error limits are estimated to be 20, 30 and 40 % for the dimers, trimers and tetramers, respectively. c. From reference. 9 d. R(0) line. e. From reference. 30 f. K'=1 ← K''=0 sub-band. g. From reference. 5 h. K'=0 ← K''=0 sub-band. i. From reference. 10 63 4.2. Dimer The frequencies of the two dimer bands are in good agreement with the previous measurements in the gas-phase, see Table 5.1. (HCl) 2 is a prolate nearly symmetric top, having rotational constants of A = 11.0 cm -1 , (B+C)/2 = 0.065 cm - 1 . 5,39 The band at 2888.0 cm -1 is assigned to the free H-Cl stretch mode ( ν 1 ), which is predominantly a perpendicular band. Thus, the observed transition in He droplets at T = 0.38 K should be assigned to the K'=1 ← K''=0 sub-band. The measured frequency compares well with that of the K'=1 ← K''=0 sub-band in the gas-phase at 2890.8 cm -1 . 5 The band at 2851.9 cm -1 is assigned to the bonded H-Cl stretching vibration ( ν 2 ), which is a predominantly parallel band. The free ( ν 1 ) and bonded (v 2 ) H-Cl stretching bands of the dimers in He droplets are shifted toward lower frequency by ~3 cm -1 and ~5 cm -1 , respectively, as compared to corresponding bands in the gas-phase. The frequency difference between the v 1 and v 2 stretches of 36 cm -1 is very close to the calculated value of 40 cm -1 . However, calculations, which were done in this work at geometry close to equilibrium, gave an intensity ratio for the v 2 and v 1 bands of about 4:1, i.e. showing a large expected increase in the intensity of the bonded stretch. On the other hand, the experimental results indicate the integrated intensity ratio of the bands to be close to 1:1. Each of the bands is enhanced by about a factor of 2.5 with respect to the monomer band as shown in Table 5.1. This large discrepancy between the results of calculations and experiment could be attributed to the intensity sharing due to the extensive mixing of the v 2 and v 1 states in the cause of the rapid interchange tunneling in the HCl dimers. 5 Higher resolution 64 spectra of the monomer and dimer as well as the magnitude of the interchange- tunneling splitting of the (HCl) 2 in helium droplets will be discussed elsewhere. 40 4.3. (HCl) n , n = 3-6, Clusters We begin this discussion by reviewing a number of related results from the previous helium nanodroplet studies of other H-bonded linear molecules, such as HCN 24,41 and HF. 24,42 (HCN) n clusters obtained in He droplets were found to grow as a linear chain up to n = 7 subunits long. The formation mechanism includes the guidance of the incoming molecules by the electric field of the previously formed cluster and the stabilization of the cluster in a linear configuration which corresponds to a local potential energy minimum. The size of the linear clusters was assumed to be limited by the size of the host He droplet. On the other hand, (HF) n complexes in He droplets are cyclic up to n = 4, whereas the spectrum of (HF) 5 was assigned to a cyclic tetramer with an additional molecule in the tail arrangement. 24,42 The preference of the cyclic structure is related to a large quadrupole moment of the HF molecules. Another factor is the large rotational constant of the HF molecules, which must facilitate the attainment of the global minimum structure via tunneling. In particular, the tunneling is presumably responsible for the insertion of the fourth HF molecule into the pre-formed cyclic trimer. Observation of the branched (HF) 5 complexes in He droplets shows that the fifth dangling HF molecule can not overcome the insertion barrier into the cyclic tetramer which has almost twice larger total binding energy than that of the cyclic trimer due to a smaller ring strain. 3,31 65 In contrast, calculations predict that the global minimum structures are cyclic for (HF) n (n = 3-10). 3 The binding in (HCl) 2 of 5.25 kJ/mol is more than a factor of two weaker than that in (HF) 2 of about 12.4 kJ/mol. 1,43,44 An even larger difference is found in the B3LYP/auc-cc-pVDZ calculations of binding energy of tetramers of HCl and HF of 20.8 and 91.5 kJ/mol, 3 respectively. Therefore, the HCl dimers are much floppier than HF dimers, 2,4,5,19,45 and the HCl molecules in clusters must experience a larger amplitude motion as compared to their HF counterpartners. 5 This is consistent with the results of this work that an incoming HCl molecule is able to insert itself into the larger pre-formed cyclic clusters at low temperature of He droplets to form larger cyclic complexes, at least up to hexamer. Single absorption line in the spectra of trimers and tetramers suggests a nearly planar ring structures in agreement with calculations. Splitting of the lines in the pentamers and hexamers spectra is consistent with non-planar geometry. The comparison of the measured and calculated band patterns shows that pentamers and hexamers have envelope and bi- pyramidal structures, respectively. Figure 5.4 (d) shows the stick spectrum of a branched pentamer, which has an HCl molecule attached to the cyclic tetramer, (HCl) 4+1 . It is seen that the band pattern in the panel (d) is very different from the observed experimental spectrum (a). Therefore, the HCl pentamer formed in helium droplets should be assigned to a cyclic isomer, which has been calculated to be a global minimum structure. The calculated spectra of the low energy isomers of hexamer are compared with the experimental spectrum in the Supporting Information (see Figure 5.S4). 66 This comparison supports our assignment of the hexamer to a cyclic bi-piramidal structure as shown in Figure 5.1. Figure 5.5 shows frequency shift, ∆v, of the average frequency of the cluster bands with respect to the band origin of the monomer, which was obtained in experiment and calculations. The last are unscaled harmonic frequencies. The measured infrared intensities of the clusters are shown in Table 5.1. The overall infrared intensity for dimers increases about a factor of five with respect to single HCl molecules, which is consistent with the formation of the hydrogen bond. 23 4 5 6 0 50 100 150 200 250 Exp. MP2/aug-cc-pVDZ MP2/6-311++G(d,p) MP2/6-311++G(3df,3pd) Δv (cm -1 ) n Figure 5.5. An average frequency shift of the bonded HCl vibration with respect to the band origin of the single HCl molecules vs. cluster size n. The squares with solid line are the experimental results of this work. Filled circles, up triangles and down triangles are results of the MP2 level of theory with aug-cc-pVDZ, 6- 311++G(d,p) and 6-311++G(3df,3pd) basis sets. 67 In trimers, in spite of the presence of three hydrogen bonds, the infrared intensity increases only by a factor of about two as compared to dimers, which is probably related to the strained structure of the trimer. Finally, in tetramers, the intensity is a factor of about four larger than in dimers, which correlates well with the four hydrogen bonds and an approximate 90° angle between HCl molecules in tetramer as seen in the crystals. 46,47 With respect to the monomer, the infrared intensity per hydrogen bond increases in the tetramer by about a factor of five. In comparison, in HCl crystal 48 the transition dipole moment per molecule has been found to be about 190 km/mol (with dielectric correction), which is a factor of about 7.5 larger than that in gas-phase of about 25 km/mol. 37,38 4.4. Large (HCl) n Clusters We observed that the structure of hexamers closely resembles a bi-pyramidal geometry for minimal energy configuration with only singly hydrogen bonded atoms and close packing. It would be interesting to see if this trend continues in larger clusters. The spectra for larger clusters of <n> = 20 and <n> = 500 are shown in Figure 5.2 (f), and (g), respectively. The spectra of large clusters are structureless rather symmetric bands having frequency (bandwidth) of 2780 (30) cm -1 and 2775 (30) cm -1 , respectively. It is remarkable that band centers of the large clusters are very close to the average frequency of pentamers and hexamers of 2777 and 2781 cm -1 , respectively. About 5 cm -1 smaller frequency in <n> = 500, as compared to <n> = 20, is probably a finite size effect. Moreover, the band breadth correlates nicely with the spread of the bands in pentamers and hexamers of about 30 cm -1 . The 68 spectra of the large clusters in Figure 5.2 (f and g) show no free H-Cl stretching bands at around 2886 cm -1 . This is consistent with the two different structures of the cluster. One is the branched structure, in which all HCl molecules on the surface of the clusters are hydrogen bonded to the chlorine atoms of the inner HCl clusters. In such a cluster, the hexamers provide the most efficient hydrogen bonding sites (chlorine pointing out) for additional approaching HCl molecules, which makes the Cl atoms of the molecules in the ring function as double acceptors. The vibrational frequency of the double acceptor HCl molecules in pentamers and hexamers is expected to be about 2709 and 2707 cm -1 and of the donor tail molecules about 2872 and 2858 cm -1 , respectively, as suggested by results of the calculations for the 4+1 and 5+1 clusters in Figure 5.4 (d) and Figure 5.S4 (d), respectively. The large spread of the absorption bands in the branched clusters is in disagreement with rather narrow measured band in large clusters of about 30 cm -1 . Another structure, which is in agreement with the present observations, is the folded cyclic structure that extends to much larger clusters. X-ray diffraction studies show that the HCl crystal structure is face-centered orthorhombic with respect to the chlorine atoms, having planar zigzag chains with the HCl molecules serving each as a single hydrogen bond donor and acceptor with angles between the molecular axis of about 90 degrees. 46,47 Figure 5.1 shows that the similar structure, but folded, is found for the tetramers, pentamers, and hexamers. Therefore, we can speculate that the singly connected hydrogen bonded cyclic structure may proliferate to larger HCl clusters. The spectrum of the large clusters deviates from the spectra in HCl low temperature crystals. 48,49 The latter have two bands at 2708 and 2749 cm -1 (δν ~ 20 69 cm -1 ), which were assigned to the Davidov type doublet due to exciton interaction between the molecules arranged in parallel zigzag chains. 50 The parallel zigzag chain pattern is not expected to be found in clusters, because such structures are energetically unfavorable due to the large number of unsaturated H-bonds on the surface. The spectrum of large clusters resembles that of a metastable low temperature phase or a high temperature disordered phase having absorption bands centered around ν = 2780 cm -1 and ν = 2768 cm -1 , respectively. 49,51 5. Conclusion In this work we report the infrared spectra of the HCl clusters in He droplets. Structure and spectra of clusters up to hexamer have also been calculated at the MP2 level with various basis sets. We obtained that clusters up to hexamer formed in helium nanodroplets have cyclic structure which corresponds to the global energy minimum. This finding indicates that an incoming HCl molecule is able to insert into the pre-formed cyclic clusters at an extremely low temperature of T = 0.38 K. The results indicate a non-planar twisted structure for tetramers, an envelope-like structure for pentamers and a pseudo bi-pyramid for hexamers. The absence of the bands due to free H-Cl stretches in the spectrum of large (HCl) n clusters (n > 20) is consistent with either branched structures with the surface HCl molecules oriented with the hydrogen atoms toward the cluster center or a cluster consisted of a folded chain of HCl molecules. 70 6. Supporting Information Figure 5.S1 shows the structure of (HCl) n (n = 4-6) clusters calculated at the MP2 level of theory with various basis sets. For the structures of tetramer, pentamer and hexamer, the MP2 calculations with a 6-311++G(d,p) (a) and 6- 311++G(3df,3pd) (b) basis sets are used. These calculations gave the structure of tetramer which varied upon the use of the different basis set. In particular, the tetramer in (a) is planar, however, in (b) it is twisted. The structure of pentamer and hexamer obtained from calculations with different basis sets appear to be very similar. The optimized geometries of the (HCl) n (n = 2-6) in Cartesian coordinates (Å) at the MP2 level of theory with an aug-cc-pVDZ, 6-311++G(d,p) and 6- 311++G(3df,3pd) basis set are shown in Tables 5.S1, 5.S2 and 5.S3, respectively. Calculated frequencies and infrared intensities of the (HCl) n (n = 2-6) clusters are shown in Tables 5.S4 and 5.S5. Figure 5.S2 shows the ab initio optimized structures and relative energies of the low-lying energy isomers of HCl hexamers based upon calculations at the MP2 level with an aug-cc-pVDZ basis set. For pentamer the two lowest energy isomers have very similar energy. For hexamer, the three lowest isomers have rather similar energy, with other isomers at much higher energy. The values in the brackets give the energies relative to the global minimum in kJ/mol with/without a harmonic zero point energy correction. Figure 5.S3 shows the Poisson pressure dependencies of the bands from the monomer to trimer shown in Figure 5.2. 71 Figure 5.S4 shows a spectrum of HCl clusters in He droplets and the stick spectra of the various isomers of HCl hexamer calculated using the MP2/aug-cc- pVDZ level of theory. The stick spectrum of the global minimum isomer (b) is in excellent agreement with the experimental spectrum of hexamer, whereas the other three isomers show very different frequency patterns. n=6 n=4 n=5 (b) (a) Figure 5.S1. The optimized global minimum structures of (HCl) n (n = 4-6) clusters, calculated at the MP2 level of theory with a 6-311++G(d,p) (a), and 6- 311++G(3df,3pd) (b) basis set using Gaussian 03. 72 Table 5.S1. Optimized geometries of the (HCl) n (n = 2-6) at the MP2 level of theory with an aug-cc-pVDZ basis set. (HCl) 2 Coordinates (Angstroms) (HCl) 5 Coordinates (Angstroms) Atom X Y Z Atom X Y Z Cl 1.911684 1.219495 0.000010 Cl 0.665766 2.719835 0.567137 H -1.944764 0.006753 0.000026 H -0.512403 2.203854 0.379895 Cl -0.662578 -0.153448 0.000004 Cl -2.665167 1.274909 0.023438 (HCl) 3 X Y Z H -2.323317 0.043833 -0.214681 Cl -1.621485 -1.403703 0.000076 Cl 2.396506 0.145323 -1.362346 H -1.533108 -0.110063 -0.000960 H 1.825796 1.147272 -0.762316 Cl -0.406427 2.104519 -0.000065 Cl 1.294363 -1.936314 1.429256 H 0.674336 1.387546 0.001912 H 1.836227 -1.248838 0.468552 Cl 2.027341 -0.700522 -0.000006 Cl -1.701107 -2.200617 -0.657205 H 0.868476 -1.282481 -0.001031 H -0.662427 -2.199433 0.123800 (HCl) 4 X Y Z (HCl) 6 X Y Z Cl 2.504250 -0.074863 -0.486847 Cl 0.257348 1.924565 -1.762181 H 1.725292 0.909154 -0.149908 H 1.285108 1.261937 -1.322203 Cl 0.074775 2.503303 0.486942 Cl 3.059499 0.334836 -0.013606 H -0.909420 1.724820 0.149409 H -2.302662 0.406178 0.739134 Cl -0.075007 -2.503160 0.487011 Cl -3.051462 0.340447 -0.020586 H 0.909951 -1.726401 0.147767 H 0.792942 1.969610 1.722998 Cl -2.504024 0.074821 -0.487015 Cl 2.302241 0.427709 0.712253 H -1.725707 -0.909276 -0.148804 H 0.378267 2.198286 0.513322 Cl -0.244631 1.987949 -1.708431 H -1.271961 1.306501 -1.297296 Cl -0.771822 1.900606 1.786124 H -0.370943 2.175411 0.581397 73 Table 5.S2. Optimized geometries of the (HCl) n (n = 2-6) at the MP2 level of theory with a 6-311++G(d,p) basis set. (HCl) 2 Coordinates (Angstroms) (HCl) 5 Coordinates (Angstroms) Atom X Y Z Atom X Y Z Cl 1.924446 -0.071925 -0.000039 Cl -0.186837 2.960421 0.535926 H 2.230767 1.165058 0.000115 H -1.188906 2.176073 0.401448 Cl -2.01205 0.009406 -0.000066 Cl -3.065398 0.531787 0.069349 H -0.741497 -0.102245 0.001673 H -2.476169 -0.575531 -0.184003 (HCl) 3 X Y Z Cl 2.52372 0.971678 -1.188386 Cl 1.691941 -1.446366 -0.000033 H 1.63104 1.75795 -0.717375 H 1.68919 -0.16878 0.001293 Cl 1.901388 -1.798864 1.297236 Cl 0.407918 2.187147 -0.000063 H 2.294647 -0.852625 0.53113 H 0.699918 1.550828 0.000631 Cl -1.181845 -2.665538 -0.713699 Cl 2.09909 -0.74001 0.000034 H -0.108085 -2.497106 -0.038459 H 1.002355 -1.395171 -0.000872 (HCl) 6 X Y Z (HCl) 4 X Y Z Cl -0.591841 1.790525 1.946215 Cl -2.691123 0.13258 -0.009327 H -1.440568 0.88387 1.642644 H -1.948285 -0.908865 -0.00388 Cl -2.952087 -0.393108 -0.064163 Cl -0.13273 -2.69081 0.009361 H -2.039888 -0.867193 -0.825257 H 0.909724 -1.949397 0.003358 Cl 2.945858 0.397252 -0.057268 Cl 0.132532 2.690899 0.009375 H -0.01546 2.0937 -1.776362 H -0.90894 1.948104 0.003121 Cl 2.030469 0.914434 -0.785725 Cl 2.691272 -0.132588 -0.009323 H -0.413459 2.400401 -0.601496 H 1.948327 0.908786 -0.004059 Cl 0.60887 -1.918401 1.832865 H 1.446363 -0.985274 1.583218 Cl 0.005035 -1.969545 -1.89692 H 0.410726 -2.353436 -0.747621 74 Table 5.S3. Optimized geometries of the (HCl) n (n = 2-6) at the MP2 level of theory with a 6-311++G(3df,3pd) basis set. (HCl) 2 Coordinates (Angstroms) (HCl) 5 Coordinates (Angstroms) Atom X Y Z Atom X Y Z Cl 1.852241 -0.070365-0.000036 Cl 0.07006 2.70819 0.48498 H 1.936091 1.200474 0.000086 H -0.96507 1.96328 0.33329 Cl -1.927598 0.005148 -0.00006 Cl -2.84520 0.59483 0.02774 H -0.655029 -0.091779 0.001539 H -2.22358 -0.49823 -0.23332 (HCl) 3 X Y Z Cl 2.20260 0.51634 -1.43509 Cl -1.48855 -1.514252-0.000003 H 1.46048 1.39883 -0.87000 H -1.493759 -0.233386 0.000048 Cl 1.58319 -1.35755 1.59256 Cl -0.567555 2.045831 0.000002 H 1.99055 -0.70263 0.56637 H 0.545721 1.412399 -0.000071 Cl -1.01975 -2.46061 -0.66938 Cl 2.055889 -0.531485 0.000001 H -0.10764 -2.18152 0.18996 H 0.951715 -1.180602 0.000032 (HCl) 6 X Y Z (HCl) 4 X Y Z Cl 0.54569 -1.82923 1.79456 Cl -2.364611 -0.621374 -0.560236 H 1.37209 -0.94049 1.37737 H 0.621568 -2.362296 0.560563 Cl 2.82181 0.32580 -0.03705 Cl 2.364376 0.620782 -0.560713 H 1.88769 0.81653 -0.76734 H -0.621599 2.362784 0.560519 Cl -2.82247 -0.32564 -0.03626 Cl -1.367993 -1.330232 -0.169536 H -0.04889 -1.94637 -1.76937 H 1.332538 -1.367196 0.169724 Cl -1.88890 -0.81230 -0.76996 Cl -1.330323 1.36905 0.16216 H 0.26437 -2.18328 -0.54854 H 1.370296 1.330157 -0.164621 Cl -0.54368 1.82104 1.80181 H -1.37091 0.93388 1.38296 Cl 0.04760 1.95440 -1.76160 H -0.26556 2.18563 -0.53964 75 Table 5.S4. A summary of the calculated harmonic vibrational frequencies (cm -1 ) and intensities (km/mol) for (HCl) n (n = 2-6) using the MP2 level of theory with various basis sets [aug-cc-pVDZ, 6-311++G(d,p) and 6-311++G(3df,3pd)]. (HCl) n MP2 n aug-cc-pVDZ 6-311++G(d,p) 6-311++G(3df,3pd) harmonic intensity harmonic intensity harmonic intensity freq (cm -1 ) a (km/mol) freq (cm -1 ) (km/mol) freq (cm -1 ) (km/mol) 1 3023.0 42.7 3087.1 34.9 3058.7 54.7 2 3008.0 52.2 3078.3 41.6 3043.2 63.0 2 2965.5 246.7 3059.3 140.0 2992.7 285.8 ∆v b 57.5 27.8 66.0 3 2924.0 392.8 3043.3 187.6 2953.3 436.3 3 2922.8 389.1 3042.6 192.5 2953.0 438.4 3 2889.6 0.4 3028.1 0.5 2916.8 0.1 ∆v 99.6 44.1 105.6 4 2894.5 92.3 3023.6 0.0 2920.8 138.0 4 2876.6 815.3 3014.2 454.0 2901.9 856.8 4 2876.5 815.8 3014.1 454.3 2901.3 859.0 4 2836.3 0.0 2994.7 0.0 2859.3 0.0 ∆v 146.4 72.9 157.1 5 2890.7 452.4 3018.9 181.7 2920.4 557.0 5 2887.0 38.3 3016.9 21.9 2912.4 37.0 5 2863.4 882.2 3004.4 518.9 2889.5 857.2 5 2862.8 887.5 3004.0 531.5 2888.6 884.6 5 2830.2 0.2 2987.6 4.9 2855.1 9.3 ∆v 159.9 82.9 169.7 6 2897.7 260.7 3037.7 328.8 2935.3 274.5 6 2895.3 864.7 3037.1 78.1 2933.9 869.0 6 2885.4 1.7 3027.0 7.1 2919.5 0.1 6 2863.8 570.5 3024.9 229.8 2902.2 448.6 6 2860.4 526.6 3011.8 284.2 2896.3 479.3 6 2839.6 1.3 3007.8 27.8 2878.5 6.2 ∆v 160.9 68.7 159.5 a. The harmonic frequencies are not scaled. b. The frequency shift ( ∆v) for each cluster is defined as the difference between the frequency of the monomer and the average bonded H-Cl stretches of the clusters. 76 Table 5.S5. A summary of the calculated harmonic vibrational frequencies (cm -1 ) and intensities (km/mol) for (HCl) n (n = 2-6) using the B3LYP level of theory with various basis sets [aug-cc-pVDZ, 6-311++G(d,p) and 6-311++G(3df,3pd)]. (HCl) n DFT (B3LYP) n aug-cc-pVDZ 6-311++G(d,p) 6-311++G(3df,3pd) harmonic intensity harmonic intensity harmonic intensity freq (cm -1 ) a (km/mol) freq (cm -1 ) (km/mol) freq (cm -1 ) (km/mol) 1 2912.5 37.8 2927.1 31.7 2943.5 44.9 2 2899.4 46.2 2915.8 41.9 2932.8 52.9 2 2827.1 293.1 2860.1 201.7 2861.8 287.5 ∆v b 85.5 67.0 81.7 3 2774.4 503.7 2832.7 316.5 2817.5 478.7 3 2772.6 505.1 2829.0 323.7 2817.0 476.3 3 2732.7 0.5 2805.4 5.1 2780.8 0.1 ∆v 139.0 96.3 126.3 4 2720.8 2.7 2783.9 18.9 2769.2 33.1 4 2700.1 1237.8 2767.6 845.0 2750.5 1087.6 4 2699.3 1245.5 2767.1 847.0 2750.3 1088.6 4 2642.4 0.6 2729.3 7.2 2701.8 0.0 ∆v 212.8 159.8 193.1 5 2710.9 150.6 2771.5 136.1 2756.5 44.5 5 2709.3 213.5 2770.4 134.1 2754.1 358.4 5 2680.2 1524.4 2747.2 1111.7 2728.0 1312.8 5 2678.5 1520.2 2746.6 1120.9 2727.3 1324.7 5 2630.7 5.1 2712.7 2.3 2685.9 12.1 ∆v 233.2 180.2 215.9 6 2712.2 138.4 2768.3 138.5 2761.3 183.6 6 2706.1 873.4 2762.4 337.9 2754.6 783.5 6 2700.3 0.5 2758.4 307.3 2752.1 44.7 6 2670.4 1750.4 2735.6 1083.9 2723.4 1345.7 6 2666.5 1342.3 2731.1 1247.9 2721.8 1314.4 6 2629.5 1.1 2705.2 1.0 2689.4 0.1 ∆v 244.0 193.8 221.0 a. The harmonic frequencies are not scaled. b. The frequency shift ( ∆v) for each cluster is defined as the difference between the frequency of the monomer and the average bonded H-Cl stretches of the clusters. 77 (0.3 / 1.9) (1.8 / 2.8) (8.6 / 11.1) (0 / 0) Energy (0 / 0) (2.5 / 1.1) Pentamer Hexamer Figure 5.S2. The optimized structures and relative energies of the low-lying energy isomers of HCl pentamer and hexamer from calculations at the MP2 level with an aug-cc-pVDZ basis set. The values in the brackets are energies relative to the global minimum in kJ/mol with/without a harmonic zero point energy correction. 78 01234 5 Monomer Dimer: ν 2 Dimer: ν 1 Trimer Normalized signal Pressure, 10 -5 mbar Figure 5.S3: Pick-up cell pressure dependencies of the bands of monomer through trimer. The intensity represents the maxima of the corresponding cluster bands. 79 2700 2750 2800 2850 2900 2950 Wavenumber (cm -1 ) (0.3 / 1.9) (1.8 / 2.8) (8.6 / 11.1) (0 / 0) (b) (a) (d) (c) (e) 1 2 2 3 4 5 6 5 6 Figure 5.S4. (a) A spectrum of (HCl) n clusters in He droplets; <n> = 4. The stick spectra are the results of calculations using the MP2/aug-cc-pVDZ level of theory. Panel (b) shows the spectrum of the global minimum cyclic hexamer. Panels (c-e) show the spectra of the low-lying energy isomers. The values in brackets give the energies relative to the global minimum in kJ/mol with/without a harmonic zero point energy correction. 80 7. Chapter V References (1) Ni, H.; Serafin, J. M.; Valentini, J. J. Journal of Chemical Physics 2000, 113, 3055. (2) Karpfen, A.; Bunker, P. R.; Jensen, P. Chemical Physics 1991, 149, 299. (3) Guedes, R. C.; do Couto, P. C.; Costa Cabral, B. J. Journal of Chemical Physics 2003, 118, 1272. (4) Vissers, G. W. M.; Oudejans, L.; Miller, R. E.; Groenenboom, G. C.; van der Avoird, A. Journal of Chemical Physics 2004, 120, 9487. (5) Schuder, M. D.; Lovejoy, C. M.; Lascola, R.; Nesbitt, D. J. Journal of Chemical Physics 1993, 99, 4346. (6) Furlan, A.; Wulfert, S.; Leutwyler, S. Chemical Physics Letters 1988, 153, 291. (7) Farnik, M.; Nesbitt, D. J. Journal of Chemical Physics 2004, 121, 12386. (8) Hartz, C.; Wofford, B. A.; Meads, R. F.; Lucchese, R. R.; Bevan, J. W. Review of Scientific Instruments 1995, 66, 4375. (9) Haber, T.; Schmitt, U.; Suhm, M. A. Physical Chemistry Chemical Physics 1999, 1, 5573. (10) Farnik, M.; Davis, S.; Nesbitt, D. J. Faraday Discussions 2001, 118, 63. (11) Vanderveken, B. J.; Demunck, F. R. Journal of Chemical Physics 1992, 97, 3060. (12) Barnes, A. J.; Hallam, H. E.; Scrimsha.Gf. Transactions of the Faraday Society 1969, 65, 3150. (13) Engdahl, A.; Nelander, B. Journal of Physical Chemistry 1990, 94, 8777. (14) Bohn, R. B.; Hunt, R. D.; Andrews, L. Journal of Physical Chemistry 1989, 93, 3979. 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Journal of Physics B-Atomic Molecular and Optical Physics 2006, 39, R127. (26) M. J. Frisch, G. W. T., H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople. Gaussian 03, Revision C.02 Wallingford CT, 2004. (27) Slipchenko, M.; Kuyanov, K.; Sartakov, B.; Vilesov, A. F. J. Chem. Phys. 2006, 124, 241101. (28) Meads, R. F.; McIntosh, A. L.; Arno, J. I.; Hartz, C. L.; Lucchese, R. R.; Bevan, J. W. Journal of Chemical Physics 1994, 101, 4593. 82 (29) Han, J.; Wang, Z. C.; McIntosh, A. L.; Lucchese, R. R.; Bevan, J. W. Journal of Chemical Physics 1994, 100, 7101. (30) Leblanc, R. B.; White, J. B.; Bernath, P. F. Journal of Molecular Spectroscopy 1994, 164, 574. (31) Nauta, K.; Miller, R. E. J. Chem. Phys. 2000, 113, 9466. (32) Lindsay, C. M.; Lewis, W. K.; Miller, R. E. The Journal of Chemical Physics 2004, 121, 6095. (33) Kuyanov, K. E.; Slipchenko, M. N.; Vilesov, A. F. Chem. Phys. Lett. 2006, 427, 5. (34) Moore, D. T.; Miller, R. E. J. Phys. Chem. A 2004, 108, 1930. (35) Nauta, K.; Miller, R. E. The Journal of Chemical Physics 2000, 113, 10158. (36) Nauta, K.; Miller, R. E. J. Chem. Phys. 2001, 115, 4508. (37) Lin, C. L.; Niple, E.; Shaw, J. H.; Uselman, W. M.; Calvert, J. G. J. Quant. Spectr. Rad. Trans. 1978, 20, 581. (38) Toth, R. A.; Hunt, R. H.; Plyer, E. K. J. Mol. Spectr. 1970, 35, 110. (39) Blake, G. A.; Busarow, K. L.; Cohen, R. C.; Laughlin, K. B.; Lee, Y. T.; Saykally, R. J. Journal of Chemical Physics 1988, 89, 6577. (40) Skvotsov, D. C., M. Y.; Vilesov, A. F. In Preparation 2007. (41) Nauta, K.; Miller, R. E. Science 1999, 283, 1895. (42) Douberly, G. E.; Miller, R. E. Journal of Physical Chemistry B 2003, 107, 4500. (43) Pine, A. S.; Howard, B. J. Journal of Chemical Physics 1986, 84, 590. (44) Bohac, E. J.; Marshall, M. D.; Miller, R. E. Journal of Chemical Physics 1992, 96, 6681. (45) Moazzenahmadi, N.; McKellar, A. R. W.; Johns, J. W. C. Journal of Molecular Spectroscopy 1989, 138, 282. (46) Grout, P. J.; Leech, J. W. Journal of Physics C-Solid State Physics 1974, 7, 3245. (47) Sandor, E.; Farrow, R. F. C. Nature 1967, 213, 171. 83 (48) Friedrich, B. H.; Person, W. B. J. Chem. Phys. 1963, 36, 811. (49) Savoie, R.; Anderson, A. J. Chem. Phys. 1966, 44, 548. (50) Ghosh, P. N. J. Phys. C 1976, 9, 2673. (51) Lee, E.; Sutherland, G. B. B. M.; Wu, C.-K. Proc. Roy. Soc. London 1940, A176, 493. 84 Chapter VI: Interchange-Tunneling Splitting in HCl Dimer in Helium Nanodroplets 1. Introduction In the past decade, infrared spectra of molecules in helium droplets at 0.38 K have been extensively studied. 1-6 The spectra show well resolved rotational structure which have been fitted using ro-vibrational Hamiltonians of free molecules. The effective rotational constants of molecules in liquid helium were found to decrease by about a factor of three for heavy molecules such as OCS and SF 6 . Conversely, little or no decrease in rotational constant is found for light molecules, such as HF, CH 4 , NH 3 , and H 2 O. 1-6 In spite of the considerable theoretical activity (see Ref. 7-10 and references therein), the details of the coupling of molecular rotation with liquid helium are still not fully understood. Therefore, it is of interest to study some other systems characterized by large amplitude molecular motion such as internal rotation or interchange tunneling. For example, it was obtained that the inversion splitting of ammonia molecules in He droplets remains the same as in free molecules. 1-6 On the other hand, however, a study of Ar-H 2 O complexes indicated a larger impairment of the H 2 O internal rotation in He droplets as compared to free complexes. 7 Nauta and Miller 1-6 reported that the interchange-tunneling (IT) splitting in (HF) 2 is reduced in He droplets by about 40% in both the ground and vibrationally excited states. Diffusion Monte Carlo (DMC) calculations showed that the IT splitting of the 85 ground state in HF dimers is quenched by about 30% upon addition of only four helium atoms. 1-6 However, the calculated splitting in HCl dimers with up to 14 attached He atoms remained the same as in the gas-phase. 1-6 Because of the close similarity between (HF) 2 and (HCl) 2, this result is unexpected. Therefore, the present work is to study the IT splitting of the HCl dimers in He droplets. Due to the rather weak intermolecular bonding in (HCl) 2 , D 0 = 5.15 kJ/mol, 8 and in (HF) 2 , D 0 = 12.4 kJ/mol, 8 and large rotational constants of HCl (10.1 cm -1 ) and HF (19.8 cm -1 ), 9 the molecules in dimers take part in large amplitude IT motion. 8,10-27 The IT splitting, Δν, of the gas-phase (HCl) 2 and (HF) 2 dimers in the ground vibrational state have been measured at 15.5 and 0.66 cm -1 , respectively, and about a factor of four and three, respectively, smaller in the vibrationally excited v 1 and v 2 states. 14,20 Besides that complete quenching of IT motion has been observed in the 2v 2 vibrational region for HCl heterodimer, since the energy separation between different dimers is much larger that the tunneling matrix element. 28 Figure 6.1 shows the energy level diagram for the (HCl) 2 ground state and v 1 and v 2 states corresponding to excitation of the stretching vibration of the free and bonded H-Cl, respectively. Each vibrational level has two IT components of (+) and (-) parity. Solid lines show the allowed infrared transitions. 29,30 Due to the lack of inversion symmetry, the so-called “broken symmetry” transitions, (+) – (+) and (-) – (-), are allowed in (H 35 Cl - H 37 Cl) heterodimers. 20,29,30 86 2. Experimental Details The helium nanodroplet technique has been described in detail elsewhere. 2,3,5,6 In this work, helium droplets having an average size of about 4000 atoms are formed by supersonic expansion of high purity helium (99.9999%) gas at the source pressure of P 0 = 20 bar into vacuum through a 5 μm nozzle at a temperature of T 0 = 15 K. The droplet beam is collimated by a 1.5 mm diameter skimmer and doped by HCl molecules in a 12 cm long pick-up chamber. The total flux of the droplet beam is detected by a quadrupole mass filter, which is adjusted to transmit all masses larger than 6 u. The transient decrease of the mass spectrometer Energy v 2 v 1 0 20 40 2870 2900 2880 2850 v 2 + v 2 - v 1 + v 1 - (+) (-) (+) (-) (+) (-) ~ 15.46 cm -1 ~ 3.73 cm -1 ~ 3.93 cm -1 v 1 v 2 Figure 6.1. The energy level diagram of the (H 35 Cl-H 37 Cl) heterodimers. 20 Solid and dotted lines show the fully allowed and “broken symmetry” transitions, respectively. The insert shows the equilibrium geometry of the HCl dimer. Transitions observed in this work are marked with filled circles. 87 signal upon the laser pulse is enhanced by a lock-in amplifier. The spectra were calibrated via opto-acoustic spectra of HCl gas. 3. Results and Discussion Figure 6.2 (a) shows the survey spectrum of monomer and dimer bands with spectral resolution of 1 cm -1 measured upon the capture of an average of two HCl molecules (<n> = 2) by helium nanodroplets. Bands of larger clusters were found at lower frequency, which is beyond the range of Figure 6.2 and are discussed elsewhere. 31 The upper panels of Figure 6.2 show the higher resolution scans of each of the spectral peaks which were obtained with nominal resolution of 0.08 cm -1 . 3.1. Monomer Figure 6.2 (b) shows the high resolution scans of the HCl monomer. The spectral peaks at 2905.4 and 2903.2 cm -1 were assigned to the R(0) line of single H 35 Cl and H 37 Cl molecules, respectively. The peaks have an intensity ratio of about 3:1, which corresponds well with the natural abundance ratio of the 35 Cl and 37 Cl isotopes of 75.5 and 24.5%, respectively. In He droplets, both lines are shifted towards lower frequency by about 0.9 cm -1 as compared to the corresponding gas- phase values of 2906.25 and 2904.11 cm -1 , respectively. 9 Because the rotational constants of light molecules in He droplets have been found to be very similar to those in the gas-phase, 1-6 the measured shifts in He should be comparable to those of the vibrational band origins for free HCl, which can be estimated to have a value of 2885.1 and 2883.9 cm -1 for H 37 Cl and H 35 Cl isotopomers, respectively. 88 Each observed R(0) line has a width of about 1.3 cm -1 (FWHM), which corresponds to the fast rotational relaxation time of about τ = 4 ps in He. The vibrational relaxation time of the HCl molecules in He was estimated to be about 0.6 ms by comparing the time resolved profiles of the laser depletion signal of the monomers and trimers. 31 The width of the R(0) line of the HCl molecules is larger than that of the previously measured HF molecules of 0.43 cm -1 , 32 which correlates well with the larger rotational constant of the latter. 2840 2850 2860 2870 2880 2890 2900 2910 2920 Wavenumber, cm -1 2848 2850 2852 2854 2900 2905 2910 2880 2885 2890 2895 v 2 , (HCl) 2 v 1 , (HCl) 2 R(0) , HCl (a) (37 –37) (35 –37) (37) (35) (b) (c) (d) (35 –37) (35 –35) Figure 6.2. (a) A survey spectrum of the HCl molecules and dimers in He droplets for the average cluster size of <n> = 2 with spectral resolution of 1 cm -1 . The higher resolution scans (0.08 cm -1 ) of the monomer, and dimer v 1 and v 2 bands are shown in panels (b), (c) and (d), respectively. 89 3.2. Dimer Figures 6.2 (c-d) show the high resolution scans for the v 1 and v 2 bands, respectively, of the HCl dimer in He. The frequencies of the v 1 and v 2 bands are compared with the corresponding values in the gas-phase in Table 6.1. Free (HCl) 2 is a prolate nearly symmetric top, having rotational constants of A = 11.0 cm -1 , (B+C)/2 = 0.065 cm -1 . 14,20 Thus, the ν 1 and ν 2 bands have predominant perpendicular and parallel character, respectively. The ν 1 band in He droplets at T = 0.38 K should consist of only one K' = 1 ← K'' = 0 sub-band. The central frequency of the ν 1 band in He droplets at 2888.0 cm -1 has a relatively small shift with respect to the frequencies of the K' = 1 ← K'' = 0 sub-bands of the (H 35 Cl) 2 , (H 35 Cl - H 37 Cl) and (H 37 Cl) 2 isotopomers in the gas-phase of 2890.8, 2889.4 and 2888.6 cm -1 , respectively, 20 which remain unresolved in He droplets. The observed line width of the ν 1 band is about 5 cm -1 , indicating the extensive lifetime broadening. The most probable relaxation mechanism includes the transition from the K' =1 to the K'' = 0 state within the ν 1 state with an energy release of about 11 cm -1 . The large breadth of the v 1 band of HF dimers in He droplets of about 2.2 cm -1 was previously assigned to the fast rotational relaxation. 32 A similar mechanism is responsible for the broadening of the rotational levels of other light rotor molecules such as NH 3 , 33 H 2 O, 33 and CH 4 . 34 In addition to the rotational relaxation, the vibrational relaxation from the ν 1 into the ν 2 is another viable relaxation channel given the close proximity of the states (36 cm -1 ). 90 Figure 6.2 (a) shows that the ν 2 band has a broad, rather weak but reproducible shoulder in the range of 2855 to 2865 cm -1 . The assignment of this feature to a K' = 1 ← K'' = 0 sub-band of the ν 2 band can probably be rejected since it was found in the gas-phase to have about a factor of 200 lower intensity as compared to the K' = 0 ← K'' = 0 sub-band. 20 The assignment as a combination band is also questionable because the frequencies of the intermolecular vibrational modes in (HCl) 2 have been found to be larger than about 30 cm -1 . 35 Therefore, we have tentatively assigned this broad spectral feature to a satellite band due to the creation of some excitations in He environment. Such satellite bands, which are ubiquitous in Table 6.1. Frequencies (cm -1 ) of the HCl dimer v 1 and v 2 bands, in helium and in gas-phase. Error limits (1σ) for frequencies in He are ± 0.1 cm -1 and ± 0.5 cm -1 for v 2 and v 1 bands, respectively. (H 35 Cl) 2 (H 35 Cl-H 37 Cl) (H 37 Cl) 2 in He 2888.0 a v 1 gas-phase b 2890.8 2889.4 2888.6 in He - - - broken symmetry, v 1 gas-phase b - 2893.3 - in He 2852.4 2851.7 2850.2 v 2 gas-phase c 2857.2 2856.4 2855.1 in He - 2849.0 - broken symmetry, v 2 gas-phase c - 2852.7 - a. The center of the unresolved v 1 band. b. From references 27 and 28. c. Frequency of the K' = 1 ← K'' = 0 sub-band. 91 the spectra of electronic excitation of molecules in helium, 3,36 are rarely observed in vibrational spectra because of the small change of the molecule – He interaction upon vibrational excitation. 37 In the case of (HCl) 2 , the interaction may be promoted by the large amplitude of the IT motion. The strong interaction of the IT state in (HCl) 2 with the He environment is also in agreement with the large decrease of the magnitude of the IT splitting in He as will be discussed below. At higher resolution, the ν 2 band consists of four components, see Figure 6.2 (d). The bands at 2852.4, 2851.7 and 2850.2 cm -1 are assigned to the allowed (-) ← (+) transitions of the (H 35 Cl) 2 , (H 35 Cl - H 37 Cl) and (H 37 Cl) 2 dimers, respectively (see Figure 6.1). The ν 2 bands of isotopomers in helium have an average shift of about 5 cm -1 from their corresponding gas-phase values (Table 6.1). We were not able to identify any transitions originating from the upper (-) IT component of the ground state, see Figure 6.1, showing that it is not populated at the temperature of 0.38 K in He droplets. The intensities of the bands due to the three isotopomers, (H 35 Cl) 2 : (H 35 Cl - H 37 Cl) : (H 37 Cl) 2 , were found in the ratio of 9.1 : 6.6 : 1, respectively, in good agreement with the intensity ratio of 9.4 : 6.1 :1, 11,20,38 calculated from the natural abundance of the chlorine isotopes. In the case of H 35 Cl - H 37 Cl, the intensity is a sum of the (+) – (-) and (+) – (+) bands, see Figures 6.1 and 7.2. The weak band at 2850.2 cm -1 , due to the (H 37 Cl) 2 complexes, is more clearly seen in the spectrum measured at higher laser pulse energy which is not shown here. It is seen that each band consists of two peaks, which were identified as the unresolved rotational P- and R-branches of the bands. The rotational constant for the end-over-end rotation, B He , of the dimer in He as well as the band 92 origins in Table 6.1 were obtained from the fit of the waveform of the bands to the linear rotor spectrum at T = 0.38 K and using nominal spectral resolution of 0.08 cm -1 . The frequencies of the band origins are summarized in Table 6.1. The accuracy of the origins of the v 2 bands is estimated to be ± 0.1 cm -1 (1σ) which was obtained by averaging of different scans and includes the uncertainty from the fit. Reproducibility of the frequency from different scans was usually better than ± 0.02 cm -1 . The obtained B He constant of 0.025 ± 0.005 cm -1 is smaller by about a factor of 2.6 as compared to that in the gas-phase of 0.065 cm -1 . 14,20 This is consistent with the similar reduction factor of the rotational constants of heavy rotors in He. 1-6 In addition, a reduction factor of 2.2 was previously obtained for HF dimers in He droplets. 14,20 The band at 2849 cm -1 has been assigned to the (+) – (+) “broken symmetry” transition of the (H 35 Cl - H 37 Cl) heterodimer. The intensity of this nominally forbidden band in helium is about a factor of 3.8 lower than that of its fully allowed counterpart as compared to a factor of about 12 smaller intensity in the free jet experiments. 20 The frequency difference of the allowed and “broken” symmetry v 2 bands of the H 35 Cl - H 37 Cl heterodimer in He droplets gives the magnitude of the IT splitting of Δν = 2.7 ± 0.2 cm -1 in the v 2 excited state, which is smaller than Δν = 3.73 cm -1 in the gas-phase. 20 Schuder et. al (Ref. 28) has shown that the two level model gives a fair representation of the IT splitting in the ground and excited states of (HCl) 2 . According to this model, the ground state of the homodimers is represented by the two degenerate energy levels, corresponding to two interchange isomers which are 93 coupled by the off diagonal interaction matrix element of β = 7.74 cm -1 . In the vibrationally excited dimer, the interaction decreases to β = 1.59 cm -1 because of the additional requirement of the vibrational energy exchange between the two molecules. For the heterodimer, H 35 Cl - H 37 Cl, the zero order vibrational frequencies differ by 2.1 cm -1 , i.e., the shift between the vibrational origins of the H 35 Cl and H 37 Cl monomers. Assuming the same interaction for homodimers, the IT splitting in free heterodimers of Δν = 3.8 cm -1 and the intensity ratio of the “broken symmetry” and allowed bands of 11 were calculated both in good agreement with the experimental results for the free dimer. 20 As indicated by the two level model, the IT splitting of the ν 2 state of the dimer in helium of Δν = 2.7 ± 0.2 cm -1 can be explained by taking the same difference of the vibrational frequency of the H 35 Cl and H 37 Cl molecules as in the gas-phase, but smaller interaction of β = 0.85 ± 0.15 cm -1 . The two level analysis is supported by the calculation of the intensity ratio of the “broken symmetry” and allowed bands of 4.4, in agreement with the ratio of about 3.8 measured experimentally. Thus, we conclude that the interaction between the two IT levels in the vibrationally excited state of the (HCl) 2 in helium is almost a factor of two smaller than in the gas-phase. Previously, 14,20 the IT splitting, Δν, in the ground and v 2 vibrationally excited state of the HF dimers of 0.39 and 0.13 cm -1 , respectively, was measured in He droplets as compared to 0.66 and 0.23 cm -1 in the gas-phase. 14,20 The decrease of the IT splitting in (HF) 2 by about 40% in helium droplets was initially explained by the variation of the polarization energy of the helium solvent as the dipole moment of (HF) 2 changes along the minimum energy IT path, thereby contributing to the 94 increase of the potential barrier. 14,20 Note that the contribution of this mechanism should be smaller in HCl dimers as the HCl molecule has a smaller dipole moment of 1.1 D as compared to 1.8 D in HF. In Ref. 13, the change of the IT splitting of (HF) 2 in He was phenomenologically explained by an increase of the IT barrier along the minimum energy path from about 300 cm -1 in the gas-phase to about 400 cm -1 in He. In the case of (HCl) 2 , the tunneling splitting in the gas-phase is consistent with a barrier height at around 40 cm -1 . 20 Similar considerations show that a factor of two increase of the IT splitting would require an increase of the barrier in helium to about 70 cm -1 . The results of the DMC study 14,20 of small He n (HF) 2 clusters show that just four helium atoms, which reside in the equatorial belt around the transition state of the hydrogen-bond inter-conversion pathway of the HF dimer, account for 74 % of the reduction in the IT splitting, which has been measured in droplets of about 2000 He atoms. A more recent DMC study 14,20 showed that the IT splitting in the ground vibrational state of (HCl) 2 in He clusters remains the same as in the gas-phase over the cluster size range of n = 1 - 14, in spite of the similar equatorial donut ring of He atoms as in the case of (HF) 2 . The difference between the (HF) 2 and (HCl) 2 was rationalized by the smaller radius of the He donut ring of about 3.6 Å in the former as compared to about 4 Å in the latter. In this work, the value of β = 0.85 ± 0.15 cm - 1 was found for the magnitude of the IT interaction in the vibrationally excited v 2 state of the H 35 Cl - H 37 Cl heterodimer of in He droplets as compared to β = 1.59 cm -1 in the gas-phase. 14,20 Thus, we predict Δν = 1.7 ± 0.2 cm -1 for the corresponding splitting in the homodimers as compared to Δν = 3.07 cm -1 in the gas-phase. Assuming that the ratio of the off-diagonal coupling matrix element in the ground 95 and excited states of the HCl dimers in He is similar to the ratio in the gas-phase, as indicated for HF dimers, an estimate of the IT splitting of the ground state of HCl homodimers in He of Δν = 8.3 cm -1 was obtained. This result is at variance with the prediction in Ref. 15 that the solvation in He droplets has only a very slight effect, if any, on the IT splitting of the HCl dimer. We note, however, that the theoretical results are based on the solvation of up to 14 He atoms instead of ~4000 He atoms in this study. Therefore, one explanation would be that much more than 14 He atoms are required to achieve the nano-droplet limit. The motion of the molecules along the minimal energy path closely resembles a rotational motion. On the other hand, the rotational energy of light molecules in helium are known to be very similar to those in free molecules. 1-6 In particular in HF molecules, the rotational constant in helium 32 was found to be 19.48 cm -1 as compared to 19.79 cm -1 in the gas-phase. Therefore, the strong decrease of the IT splitting in both (HF) 2 and (HCl) 2 , is surprising. So far, the discussion of the quenching of the IT splitting in He was centered around the increase of the potential barrier on the minimum energy path. Here, we note that another contribution to the effect comes from the kinetic energy part of the Hamiltonian. The IT motion in the dimers is associated with some change of the He density as it is not exactly symmetric with respect to the center of mass of the dimer. This is equivalent to an increase of the effective mass of the tunneling particles which is another contribution to the quenching of the IT splitting. Finally, we comment on the similar intensity of the v 1 and v 2 bands, each having about a factor of 2.5 larger intensity with respect to that of the monomer. 31 96 In comparison, calculations of the v 2 bonded HCl stretch for the dimer in the equilibrium geometry gave about a factor of 4 larger intensity than that of the free HCl stretch (v 1 ). 31 Note, however, that the ground state wavefunction of (HCl) 2 is delocalized to a large extent 20 so that the probability density to find the system in the transition state is only about 20% smaller than that in the equilibrium configuration, which is shown in Figure 6.1. The v 2 state in dimers correlates with the symmetric stretch, which is not infrared active, in the C 2h transition state. Thus, we expect that the averaging over the tunneling coordinate will decrease the relative intensity of the v 2 band in agreement with the results of the measurements. Note that for (HF) 2 in the gas-phase, the intensity of the v 2 band was about a factor of two stronger as compared with the v 1 band 39 , which is in agreement with its more localized ground state wave function. 4. Conclusion We report the infrared spectra of the free and hydrogen bonded stretches of the HCl dimers solvated in He nanodroplets. In the case of the ν 2 vibration, the bands due to the isotopomers of the HCl dimers, (H 35 Cl) 2 , (H 35 Cl - H 37 Cl) and (H 37 Cl) 2 , have been resolved. Observation of the “broken symmetry” band in heterodimers allows the IT splitting of Δν = 2.7 ± 0.2 cm -1 in the ν 2 vibrationally excited state of the HCl dimers to be obtained, from which the IT matrix element of β = 0.85 ± 0.15 cm -1 was estimated. This coupling value is about a factor of two smaller than in the free dimers. In comparison, the results of the recent DMC calculations predict no splitting changes in (HCl) 2 in small He clusters of up to 14 97 atoms. The partial quenching of the IT splitting of the HCl dimers provides further information on the interaction of the large amplitude molecular motion with liquid helium. We hope this experimental result will initiate more calculations on the IT splitting of HCl dimers in He, which will be extended to the excited state. 20 98 5. Chapter VI References (1) Toennies, J. P.; Vilesov, A. F. Ann. Rev. Phys. Chem. 1998, 49, 1. (2) Callegari, C.; Lehmann, K. K.; Schmied, R.; Scoles, G. J. Chem. Phys. 2001, 115, 10090. (3) Toennies, J. P.; Vilesov, A. F. Angew. Chem. Int. Ed. 2004, 43, 2622. (4) Stienkemeier, F.; Vilesov, A. F. The Journal of Chemical Physics 2001, 115, 10119. (5) Choi, M. Y.; Douberly, G. E.; Falconer, T. M.; Lewis, W. K.; Lindsay, C. M.; Merritt, J. M.; Stiles, P. L.; Miller, R. E. Int. Rev. Phys. Chem. 2006, 25, 15. (6) Stienkemeier, F.; Lehmann, K. K. Journal of Physics B-Atomic Molecular and Optical Physics 2006, 39, R127. (7) Kuma, S.; Slipchenko, M. N.; Momose, T.; Vilesov, A. F. to be submitted 2006. (8) Pine, A. S.; Howard, B. J. Journal of Chemical Physics 1986, 84, 590. (9) Leblanc, R. B.; White, J. B.; Bernath, P. F. Journal of Molecular Spectroscopy 1994, 164, 574. (10) Pine, A. S.; Lafferty, W. J. Journal of Chemical Physics 1983, 78, 2154. (11) Ohashi, N.; Pine, A. S. Journal of Chemical Physics 1984, 81, 73. (12) Lafferty, W. J.; Suenram, R. D.; Lovas, F. J. Journal of Molecular Spectroscopy 1987, 123, 434. (13) Furlan, A.; Wulfert, S.; Leutwyler, S. Chemical Physics Letters 1988, 153, 291. (14) Blake, G. A.; Busarow, K. L.; Cohen, R. C.; Laughlin, K. B.; Lee, Y. T.; Saykally, R. J. Journal of Chemical Physics 1988, 89, 6577. (15) Moazzenahmadi, N.; McKellar, A. R. W.; Johns, J. W. C. Journal of Molecular Spectroscopy 1989, 138, 282. (16) Bumgarner, R. E.; Suzuki, S.; Stockman, P. A.; Green, P. G.; Blake, G. A. Chemical Physics Letters 1991, 176, 123. (17) Karpfen, A.; Bunker, P. R.; Jensen, P. Chemical Physics 1991, 149, 299. 99 (18) Jensen, P.; Bunker, P. R.; Karpfen, A. Journal of Molecular Spectroscopy 1991, 148, 385. (19) Meads, R. F.; McIntosh, A. L.; Arno, J. I.; Hartz, C. L.; Lucchese, R. R.; Bevan, J. W. Journal of Chemical Physics 1994, 101, 4593. (20) Schuder, M. D.; Lovejoy, C. M.; Lascola, R.; Nesbitt, D. J. Journal of Chemical Physics 1993, 99, 4346. (21) Anderson, D. T.; Davis, S.; Nesbitt, D. J. Journal of Chemical Physics 1996, 104, 6225. (22) Elrod, M. J.; Saykally, R. J. Journal of Chemical Physics 1995, 103, 921. (23) Bacic, Z.; Miller, R. E. Journal of Physical Chemistry 1996, 100, 12945. (24) Qiu, Y. H.; Bacic, Z. Journal of Chemical Physics 1997, 106, 2158. (25) Sarsa, A.; Bacic, Z.; Moskowitz, J. W.; Schmidt, K. E. Physical Review Letters 2002, 88. (26) Vissers, G. W. M.; Oudejans, L.; Miller, R. E.; Groenenboom, G. C.; van der Avoird, A. Journal of Chemical Physics 2004, 120, 9487. (27) Jiang, H.; Sarsa, A.; Murdachaew, G.; Szalewicz, K.; Bacic, Z. Journal of Chemical Physics 2005, 123. (28) Liu, K.; Dulligan, M.; Bezel, I.; Kolessov, A.; Wittig, C. Journal of Chemical Physics 1998, 108, 9614. (29) Mills, I. M. Journal of Physical Chemistry 1984, 88, 532. (30) Hougen, J. T.; Ohashi, N. Journal of Molecular Spectroscopy 1985, 109, 134. (31) Skvotsov, D.; Choi, M. Y.; Vilesov, A. F. Submitted to J. Phys. Chem. A 2007. (32) Nauta, K.; Miller, R. E. J. Chem. Phys. 2000, 113, 9466. (33) Kuyanov, K. E.; Slipchenko, M. N.; Vilesov, A. F. Chem. Phys. Lett. 2006, 427, 5. (34) Nauta, K.; Miller, R. E. Chem. Phys. Lett. 2001, 350, 225. (35) Farnik, M.; Davis, S. R.; Nesbitt, D. J. Faraday Disc. 2001, 118, 63. 100 (36) Hartmann, M.; Mielke, F.; Toennies, J. P.; Vilesov, A. F.; Benedek, G. Physical Review Letters 1996, 76, 4560. (37) Hoshina, H.; Lucrezi, J.; Slipchenko, M. N.; Kuyanov, K. E.; Vilesov, A. F. Physical Review Letters 2005, 94, 195301. (38) Rank, D. H. S., P.; Glickman, W. A.; Wiggins, T. A. Journal of Chemical Physics 1963, 39, 2673. (39) Laush, C.; Lisy, J. M. J. Chem. Phys. 1994, 101, 7480. 101 Chapter VII: Measurement of the relative energy of the conformers in 2-chloroethanol in helium droplets 1. Abstract 2-chloroethanol molecules at temperature in the range of 300 – 600 K have been captured by helium droplets and studied via infrared spectroscopy in the range of O-H and C-H stretching bands. We found that the intensity ratio of the bands due to trans- and gauche- conformers follows the Arrhenius dependence, giving the enthalpy of interconversion, ΔH 0 = 1.12 ± 0.09 kcal/mol. We concluded that the relative abundance of the conformers, which is at equilibrium in the gas phase, remains frozen upon the rapid cooling of the molecules in helium droplets. These results suggest that helium droplet technique can be used for attaining of the energetics of conformers of larger organic molecules. 2. Introduction Organic molecules are characterized by ubiquity of conformers. Even in the case of small systems, such as amino acids, the potential energy surface landscape has large number of local minima. Often, some of these minima can be simultaneously populated at room temperature and low barriers allow for interconversion between different conformers. Free energy of interconversion, ΔH 0 , 102 can in principle be deduced from the abundance ratio of the conformers in equilibrium. However spectroscopic measurements of the abundance ratio are usually complicated by the insufficient resolution of infrared and electronic spectra at ambient temperature, as well as by the unknown absorption cross sections of the corresponding transitions. On the other hand, the usefulness of the NMR is often compromised by the rapid interconversion of the isomers and concomitant averaging effects in the spectra. Therefore a considerable effort has been directed over the past decades to the development of low temperature experimental techniques of interrogation of conformers. Most successful approaches include freezing of the ambient population of conformers via rapid cooling in an adiabatic nozzle beam expansion of molecules such as 3-methil cyclohexanone 1 or upon entrainment in a solid matrix, which has recently been applied to study of glycine. 2 Studies of conformers in molecular beams have so far been limited to molecules having convenient electronic excitation spectra. On the other hand, the infrared spectra in cryogenic matrices often have insufficient resolution and their analysis can be complicated by interconversion of the conformers during the time of the experiment. Recently, relative energies of the conformers of some molecules such as N- acetyltryptophan methyl amide, 3 have also been obtained by observing interconversion upon infrared excitation in the high pressure range of the nozzle beam expansion using IR - UV double resonance technique. At present, theoretical calculations are the main source of our information on the binding energies in conformers. However, in many cases energies of the conformers differ of about or less than few kcal/mol, which is comparable with the accuracy of the calculations. 103 In this work we explored the usefulness of the He droplet technique for obtaining energies of molecular conformers. Spectra in superfluid He droplets usually have at least an order of a magnitude better resolution as compared with solid matrices due to weak interaction with He atoms. 4 Electronic spectra of tryptophan and tyrosine molecules isolated in He droplets revealed a number of peaks assigned to different conformers, 5 thus confirming the arrest of the conformers' population in He droplets at T = 0.38 K. 6 Similar results have been obtained in study of nucleotides in He droplets by R. Miller et.al., 7,8 where the measured angles between the permanent and vibrational transition dipole moments have been used for the assignment of the conformers. Here we studied 2-chloroethanole (2-CLE), which is a simple gaseous molecule having three low energy conformers G g ’, T g and T t , see Figure 7.1. In order to obtain the enthalpy of interconversion of the conformers, ΔH, the molecules having different temperature in the range of 300 to 600 K were captured by He droplets. ΔH has been obtained from the analysis of the intensities of the OH- and CH- stretching bands of conformers using van't Hoff's equation. 3. Experimental Details The helium droplet beam apparatus, which has been described in details elsewhere. 4 Helium droplets, consisting of about 3000 atoms, were formed by an adiabatic expansion of helium gas from a 5 μm orifice at a stagnation pressure of 20 bar at a temperature of 17 K. Helium droplets were doped with 2-CLE (99.0 %, Sigma-Aldrich) molecules in a 4 cm long and 2 cm diameter pick-up cell made of 104 stainless steel. The cell was hosted in an experimental vacuum chamber, equipped with an ionization pressure gauge. The temperature of the cell could be set in the range 300-700 K by resistive heating and has been monitored by K-type thermocouple attached to the inner surface of the cell. The lower part of the cell was packed with a glass wool that facilitated equilibration of the conformers. The droplet beam was analyzed by a quadrupole mass filter equipped with an electron impact ionizer. During the measurements the mass filter was tuned to the mass 30u corresponding to CHOH + splitter ion, which was found to be the major fragmentation product upon ionization of single 2-CLE molecules in He droplets. Laser frequency was calibrated by the absorption lines of the water vapor and methane gas in an opto-acoustic cell. 4. Results Figure 7.1 shows the structure and relative energy of the conformers of 2- CLE molecules which were calculated using the PC GAMESS ab initio package. 9 The optimization of the structure and calculation of the harmonic frequencies has been done at the MP2 level of theory with cc-pVDZ basis set. Five conformers of 2- CLE have been found in agreement with previous studies. 10,11 The gauche conformer, G g ', with an internal hydrogen bond between the chlorine atom and the OH group has the lowest energy. The two higher energy trans- conformers T g and T t are different from each other by rotation of the OH group. The calculated conformational frequency shifts in all of the four CH 2 stretching bands were found 105 to be about or less than 10 cm -1 , which is comparable with the accuracy of the calculations. On the other hand, the calculated frequency of the OH stretch in the G g ' conformer was found to be about 55 cm -1 lower as compared with that in the T t and T g conformers, which is consistent with the formation of the internal hydrogen bond in the former. Figure 7.2 shows spectra of the 2-CLE molecule in the CH 2 stretch (a) and in the OH stretch (b) regions, which have been obtained at different temperature of the pickup cell. The temperature increases from 298 K in the upper spectrum to 598 K in the lower spectrum. The spectrum in the OH- range has a strong band at 3624.1 cm -1 and about a factor of ten weaker band at 3678.3 cm -1 , which are labeled as G g ' Figure 7.1. The structure of the conformers of 2-chloroethanol molecule calculated at the CCSD/cc-pVDZ level of theory. Numbers are relative energies in units of kcal/mol, which take into account different zero point energy of the conformers. 0.0 +1.6 +1.5 +2.4 +2.5 G g ’ T t T g G t G g 106 and T, respectively. Based upon the results of the calculations and previous works 10,12,13 , we assigned the bands to G g ' and T t /T g conformers, respectively. Apparently, the bands due to the T t and T g conformers are not resolved. In order to exclude the contribution to the spectra from dimers, during the measurements the pickup pressure of 2-CLE was kept at about a factor of 2.5 lower than that required for the maximum abundance of single molecules in helium droplets. At high pickup pressure an additional spectral peak due to dimers of 2-CLE appeared at 3615.7 cm -1 , which is however well resolved from both the G g ' and T peaks. Normalized depletion signal 3010 3020 3620 3640 3660 3680 Wavenumber, cm -1 // // // // // a) *CH 2 asym stretch b) OH stretch G g ’ G g ’ T t /T g T t /T g 298 K 298 K 405 K 433 K 518 K 518 K 598 K 598 K Figure 7.2. Spectra of the 2-CLE molecules in the *CH 2 asymmetric stretch of the CH 2 Cl group (a) and in the OH stretch region (b) measured at four different temperatures of the pickup cell as indicated in each panel. Spectral resolution is 0.08 cm -1 and 1 cm -1 in a) and b), respectively. 107 Figure 7.2 shows that the relative intensity of the peak T increases with temperature. In addition, at the constant flux of 2-CLE into the pickup cell, the increase of the temperature from 300 to 600 K caused the decrease of the absolute intensity of the peak G g ' by about a factor of two. This effect is partially related to increase of the population of the T conformers at higher temperatures. The second contribution comes from possible reduction of the capture probability of molecules by helium droplets and lower number density of the molecules in the pickup cell at higher temperature. Finally, more efficient scattering and larger decrease of the droplet size upon capturing of hot molecules must lead to lower efficiency of the mass-spectrometric detection. In order to compensate for these effects, the flux of the 2-CLE molecules, which was monitored via pressure rise in the experimental chamber, was gradually increased with temperature, being about 50% larger at T = 600 K. At the cell temperature of about 650 K we have observed a sudden increase of the pressure in the experimental chamber which was ascribed to decomposition of the 2-CLE molecules in agreement with previous observations. 14 In the spectral range of the CH- stretching vibrations we observed bands at 2885.4, 2935.5, 2971.8, and 3015.6 cm -1 which were assigned to CH 2 symmetric and anti- symmetric stretches of CH 2 OH and CH 2 Cl groups of the 2-CLE molecules. An additional band at 2957.6 cm -1 remained unassigned. Similar spectra have been previously observed in a gas phase and in cryogenic solutions. 10,13 Except for the *CH 2 anti-symmetric stretch of the CH 2 Cl group the CH bands do not reveal any splitting due to G g ' and T conformers, which bands must therefore have very similar frequencies. Thus only the spectra of the *CH 2 anti-symmetric stretch band at 108 different pickup temperatures are shown in Figure 7.2, where the stronger and weaker bands are assigned to G g ' and T conformers, respectively. Figure 7.3 shows semi-logarithmic plots of the ratio of the integrated intensities of the G g ' and T band vs. inverse temperature as obtained from the OH and *CH 2 bands, which are shown by solid squares and open circles, respectively. Error bars in the case of the *CH 2 band are somewhat larger than for OH band due to the inferior S/N ratio of the former spectra. Lines are linear fits of the corresponding results. It is seen that in both cases the dependences are linear bearing same slope. 0.0000 0.0008 0.0016 0.0024 0.0032 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 -ln(I G /I T ) 1/T, K -1 CH 2 - OH- Figure 7.3. Temperature dependence of the intensity ratio of the G g ' and T bands. Results for OH band and *CH 2 asymmetric stretching band of the CH 2 Cl group are shown by solid squares and open circles, respectively. Lines are the results of the least square fitting of the data. Dashed lines are asymptotic behavior at infinite temperature. 109 5. Discussion The analysis of the results is based on the van't Hoff's equation, similar as used previously. 1 The enthalpy of interconversion of the conformers, ΔH = H T - H G , can be obtained using the temperature dependence of the equilibrium constant: R S RT H T K Δ + Δ − = )) ( ln( , (1) where ΔS is the change of the entropy upon interconversion. Equation (1) assumes that both ΔH and ΔS=H T - H G are independent of temperature over the temperature range considered. The equilibrium constant can be expressed as: T G G T I I G T K σ σ = = ] [ ] [ , (2) where I T and I G and σ T and σ G are the integrated intensities and absorption cross sections of the infrared bands for conformers T and G, respectively. Thus eq. (1) can be rewritten as: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + Δ − Δ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ G T T G R S RT H I I σ σ ln ln (3) From the slope of the measured value of ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ T G I I ln vs. 1/T in Figure 7.3 the values of ΔH = 1.12 ± 0.09 kcal/mol and ΔH = (1.1 ± 0.1) kcal/mol, have been obtained from the measurements of the OH- and CH- bands, respectively. Thus the values of ΔH are the same within the error bars as expected. The ΔH values obtained in this work are the same within error bars as previously measured in liquid 110 Xe (1.2 kcal/mol), 10 in gas phase (1.2 kcal/mol), 15 and smaller than value calculated in this work (1.6 kcal/mol). According to Equation (3) the intercept in Figure 7.3 carries information on the change of the entropy and absorption cross section upon conformational change, which cannot be disentangled without further assumptions. If σ T and σ G were known ΔS of interconversion could be obtained or other way around. In 2-CLE ΔS = RΑln(2) can be estimated based on the fact that the vibrational frequencies of the conformers are very similar, and that the T bands contain unresolved contributions from T t and T g conformers, and thus have a factor of two larger statistical weight as compared to the G band. Thus the intercept equals to ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = T G Intercept σ σ 2 ln . (4) From Equation (4) we obtained the absorption cross section ratios σ G / σ T of 2.9 and 1.8 for the OH- and CH- bands respectively. The increase of the absorption cross section of the OH- band upon formation of the internal hydrogen bond by about a factor of three is in line with recent measurements in other hydrogen bonded complexes. 16,17 However, present work shows that the H-bond formation also has a large effect on the weak asymmetric stretch band of the hydrogen atoms of the CH 2 Cl group, which do not directly participate in the H-bond formation. 111 6. Conclusions In this work we report the spectroscopic study of the conformers of the 2- chloroethanol in He droplets. Infrared spectra of the molecule obtained in the regions of OH and CH 2 vibration at different temperatures (300 – 600 K) allows for determination of the relative energy of two dominant conformers (G g ' and T), which has been found to be ΔH 0 = 1.12 ± 0.09 kcal/mol. Here, He droplets played the crucial role in trapping the population distribution of conformers at different temperatures. Low temperature of the droplets (0.38K) does not allow for interconversion between conformers. The fact that line positions in the OH and CH 2 infrared absorption region are very close to the gas phase data confirm the minimal caging effects of the He droplet on the embedded 2-CLE molecule. Besides that, good fitting of the experimental data to the Arrhenius equation is in favor of fast vertical cooling of molecules once they trapped by He droplet. 112 7. Chapter VII References (1) Potts, A. R.; Baer, T. Journal of Chemical Physics 1996, 105, 7605. (2) Stepanian, S. G.; Reva, I. D.; Radchenko, E. D.; Rosado, M. T. S.; Duarte, M. L. T. S.; Fausto, R.; Adamowicz, L. Journal of Physical Chemistry A 1998, 102, 1041. (3) Zwier, T. S. Journal of Physical Chemistry A 2006, 110, 4133. (4) Toennies, J. P.; Vilesov, A. F. Angew. Chem. Int. Ed. 2004, 43, 2622. (5) Lindinger, A.; Toennies, J. P.; Vilesov, A. F. Journal of Chemical Physics 1999, 110, 1429. (6) Hartmann, M.; Miller, R. E.; Toennies, J. P.; Vilesov, A. Physical Review Letters 1995, 75, 1566. (7) Choi, M. Y.; Douberly, G. E.; Falconer, T. M.; Lewis, W. K.; Lindsay, C. M.; Merritt, J. M.; Stiles, P. L.; Miller, R. E. International Reviews in Physical Chemistry 2006, 25, 15. (8) Choi, M. Y.; Miller, R. E. Journal of the American Chemical Society 2006, 128, 7320. (9) Granovsky, A. A. PC GAMESS; Moscow State University, Moscow, Russia. (10) Durig, J. R.; Zhou, L.; Gounev, T. K.; Klaeboe, P.; Guirgis, G. A.; Wang, L. F. Journal of Molecular Structure 1996, 385, 7. (11) Tian, S. X.; Kishimoto, N.; Ohno, K. Journal of Physical Chemistry A 2003, 107, 53. (12) Kovacs, A.; Varga, Z. Coordination Chemistry Reviews 2006, 250, 710. (13) Perttila, M.; Murto, J.; Halonen, L. Spectrochimica Acta Part a-Molecular and Biomolecular Spectroscopy 1978, 34, 469. (14) Skingle, D. C.; Stimson, V. R. Australian Journal of Chemistry 1976, 29, 609. (15) Buckley, P.; Giguere, P. A.; Schneide.M. Canadian Journal of Chemistry 1969, 47, 901. 113 (16) Kuyanov, K. E.; Kuma, S.; Slipchenko, M. N.; Momose, T.; Vilesov, A. F. Abstracts of Papers of the American Chemical Society 2006, 231. (17) Slipchenko, M. N.; Kuyanov, K. E.; Sartakov, B. G.; Vilesov, A. F. Journal of Chemical Physics 2006, 124. 114 Chapter VIII: Rotation of CO 2 Isotopomers in Helium Droplets 1. Introduction Studies of the molecules inside helium droplets 1,2 have showed that the helium environment allows for the free rotation of the trapped molecules. It has been found that spectra of embedded molecules resemble their corresponding gas phase structure thus allowing the extraction of spectroscopic constants. For light rotors (rotational constant B > 1 cm -1 ) it has been shown that B constant does not change much upon solvation in superfluid helium. In contrast, the rotational constant of heavy rotors (B < 1 cm -1 ) changes significantly (up to five times). 3 Recent theoretical studies attribute the change of the rotational constant mostly to the anisotropy of the molecule-helium interaction potential. 4-7 On the other hand, this effect can be completely described if the energy states and interaction strength of both molecule and helium environment are known. In this work, we have tried to observe the effect on the rotational constant of a probe molecule (CO 2 ) as the function of the number of interaction energy levels. By studying the isotopic species of carbon dioxide ( 16 OC 16 O, 16 OC 18 O, 18 OC 18 O) in He droplets we can vary the number of interacting levels (symmetric CO 2 has odd J levels missing in the ground state) while keeping the anisotropy of the interaction potential almost unchanged. 115 2. Experimental Details The experimental setup used in this work has been discussed in detail previously 2,3 . Only brief a description is given here. The laser system allows a scanning range of 3500-3700 cm -1 with resolution ∼0.1 cm -1 and the output energy of ∼3-4 mJ. Several broadband filters were used to reduce the laser radiation energy inside the helium droplet machine in order to avoid effect of power line saturation. The photoacoustic cell filled with water at 100 mbar was used for absolute wavelength calibration. Since mixed carbon dioxide ( 16 OC 18 O) is not commercially available, we have performed our own sample preparation for this experiment. All isotopic species of CO 2 gas have been prepared by simple burning of normal C 16 O in the presence of 18 O 2 (2CO + O 2 → 2CO 2 ). For these purposes both gases have been premixed into one-liter stainless steel (SS) cylinder according to corresponding stoichiometric ratio (see Figure 8.1). The pressure inside was monitored by standard pressure gauge. The cylinder was heated by a propane torch to initiate reaction inside. The pressure in the SS cylinder gradually rose to the point where a sudden jump in the pressure occurred and the audible popping sound was detected. After cooling the cylinder to the room temperature the content was analyzed by a quadrupole mass spectrometer. The following relative concentrations of CO 2 isotopic species were detected 16 OC 16 O : 16 OC 18 O : 18 OC 18 O = 31 : 48 : 21. This mixture was then seeded to the pickup cell allowing the measurement of the spectra of all three isotopic species. 116 In order to separate the depletion signal from different CO 2 isotopic species, the quadrupole mass spectrometer was tuned to masses 44, 46, and 48 for normal, single, and doubly substituted carbon dioxide, respectively. 3. Results The recorded spectra of the 16 OC 16 O, 16 OC 18 O, and 18 OC 18 O molecules in He droplets are shown on Figure 8.2 in trace (a), (b), and (c), respectively. The Y-axis to Mass Spectrometer C 16 O 18 O 2 Propane + Oxygen Torch Stainless Steel Cylinder Figure 8.1. Schematic diagram of the experimental setup for the production of mixed ( 16 OC 18 O) carbon dioxide. The volume of the stainless cylinder is about 1 liter. The gases (CO and O 2 ) has been premixed according to the stoichiometric ratio of the reaction 2CO + O 2 → 2CO 2 . 117 on the Figure 8.2 is the total depletion signal in percent. Even though the pressure at which the spectra had been recorded was kept below that needed to pickup only monomers some spectroscopic signatures from CO 2 dimer were found in the spectra. The feature in the spectrum of normal carbon dioxide (Figure 8.3) around 3611.3 cm -1 was indeed the signal from CO 2 dimer as has been reported previously 8 . In the spectra (a) and (c) of the symmetric CO 2 molecules the transitions from the levels with odd rotational quantum numbers J in the ground vibrational state ν = 0 are missing, due to the nuclear spin of I=0 for both 16 O and 18 O atoms. 9 In this case only three lines P(2), R(0), and R(2) are observed. For the asymmetric 16 OC 18 O molecules, five lines P(2), P(1), R(0), R(1), and R(2) are present, as shown in Figure 8.2 (b). The linewidth in the measured spectra is approximately 0.15 cm -1 , which is limited by laser resolution of about 0.1 cm -1 and the data acquisition rate. 118 3524.0 3524.5 3525.0 3525.5 3526.0 0 4 8 12 3570.0 3570.5 3571.0 3571.5 0 4 8 12 16 3611.5 3612.0 3612.5 3613.0 3613.5 0 1 2 3 c) Wavenumber, cm -1 R(2) Dimer Depletion signal, % R(0) P(2) P(2) R(0) R(2) b) P(1) R(1) P(2) R(0) R(2) a) Figure 8.2. Spectra of 16 OC 16 O (a), 16 OC 18 O (b), and 18 OC 18 O (c) molecules embedded in helium droplets. Spectra were measured at pickup pressure of the mixed gas of 6⋅10 -6 mbar. 119 4. Discussion Carbon dioxide is a linear molecule having D ∞h and C ∞h symmetry in case of symmetric ( 16 OC 16 O and 18 OC 18 O) and asymmetric ( 16 OC 18 O) isotope substituted species, respectively. The molecule has three vibrational modes: symmetric stretch (ν 1 , Σ g + ), asymmetric stretch (ν 3 , Σ u + ), and doubly degenerate bend (ν 2 , Π u ). 9 In our experiment we have observed the ro-vibrational combination band from ground vibrational state (ν = 0) into the state 2ν 2 +ν 3 having Σ u + symmetry. This transition is a part of the Fermi diad (02 0 1)/(10 0 1). In the gas phase these transition have been 3610.5 3611.0 3611.5 3612.0 3612.5 3613.0 3613.5 0.00 0.02 0.04 0.06 Dimer P(2) R(2) Depletion signal, % Wavenumber, cm -1 R(0) Figure 8.3. Spectrum of 16 OC 16 O molecules embedded in helium droplets. Spectra were measured at pickup pressure of the mixed gas of 6⋅10 -6 mbar. Feature at 3611.0-3611.5 is a clear signature of CO 2 dimer 120 previously measured 10 and the band origins in the C 16 O 2 molecule have been located at 3612.84 cm -1 and 3714.78 cm -1 for 02 0 1 and 10 0 1 bands, respectively. The spectra of this Fermi diad in the C 16 O 2 molecule have previously been measured in He droplets in the group of R. Miller 8 . The frequency of the lines in Figure 8.2 have been used to obtain the band origin, averaged (ground and excited vibrational states) rotational constant B, and averaged centrifugal distortion constant D, which are listed in the Table 8.1. In the case of asymmetric CO 2 molecules, B and D constants in both ground and vibrational excited states can be obtained. For the purpose of the comparison of different isotopic species of CO 2 , we have also calculated averaged B and D values for the 16 OC 18 O molecules. Measurements and calculations for this experiment along with previous results in He droplets and in the gas phase are summarized in the Table 8.1. Table 8.1 also contains the spectroscopic constants obtained in the gas phase as well as constants for C 16 O 2 measured previously in He droplets. 8 121 As can be seen from the Table 8.1, the rotational constant B in case of all three molecules is reduced in helium environment by about a factor of 2.5. Similar behavior has been observed previously 1,12 for other heavy rotors (B < 1cm -1 ). Reduction in the rotational constant can be seen as if the CO 2 molecules rotate with some additional mass attached to them – surrounding helium atoms in this case. One Table 8.1. Comparison of the molecular constants of the CO 2 isotopes obtained in this work in He droplets and previous results in the gas phase. Error bar for absolute and relative frequency measurement are 0.2 cm -1 and 0.01 cm -1 . Molecule ν a , cm -1 B b , cm -1 D c , cm -1 I Eff , amu Å 2 ΔI HE d , amu Å 2 In He e 3612.4 0.158 1.3·10 -3 106.9 Gas f 3612.837 0.3875 1.57·10 -7 43.5 63.4 16 OC 16 O In He g 3612.42 0.154 1.1·10 -3 109 65.5 In He e 3570.7 0.145 0.9·10 -3 116.5 Gas f 3571.14 0.3653 1.37·10 -7 46.1 70.4 16 OC 18 O In He h 2331.77 0.144 - 117.2 71.1 In He e 3524.8 0.147 1.3·10 -3 114.5 18 OC 18 O Gas f 3525.20 0.3439 1.18·10 -7 49.0 65.5 a Band origin of the 02 0 1 vibrational band b Rotational constant averaged over ground and vibrationally excited states, error bars ±0.002 cm -1 c Centrifugal distortion constant averaged over ground and vibrationally excited states error bars ±0.1·10 -3 cm -1 d Increment of the effective moment of inertia of the molecules in helium droplets, error bars ±1.2 amu·Å 2 e This work f From reference 10 g From reference 8 h Measurements have been done in ν 3 region. 11 Rotational constant have been obtained from three lines P(1), R(0), and R(1) 122 can calculate an additional moment of inertia, ΔI HE , associated with the effect of the helium environment ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = Gas HE 2 HE B 1 B 1 c 8π h ΔI , which are included in the Table 8.1. It can be seen that obtained values of ΔI HE are significantly larger than the moment of inertia of the free CO 2 molecules. In the rigid rotor approximation it would mean that significant additional mass is attached to the parent molecule. Assuming the averaged Van-der-Waals distance for the He is 4 angstroms, it can be calculated that ΔI HE ~ 60 amu·Å 2 corresponds to the rotation of the one He atom rigidly attached to the CO 2 molecule. Overall, we can see that as the mass of the molecule increases so does the additional moment of inertia. Even though the interaction between CO 2 molecule and surrounding He atoms remains the same, these changes show the importance of the rotational dynamics when considering such complicated systems. In the case of light rotors the He atoms do not have enough time to adjust for the changes in the anisotropic potential and it can be assumed that He see almost isotropic potential. 13 For these rotors the rotational wavefunction does not change its value significantly. In the case of rotating heavy molecules, He surroundings have enough time to follow the changes in the anisotropic field.Here, the rotational function will mimic the potential surface created by the rotor. In the case of asymmetric CO 2 ( 16 OC 18 O) the small, but measurable (5 ± 3 amu Å 2 ), increase in the additional moment of inertia has been detected compared to that one, which could be expected due to the increase in the overall mass of the 123 molecule. This effect can be attributed to the enhancement in the coupling between He and the trapped molecule. As has been mentioned earlier symmetric isotopic species of CO 2 have their odd levels missing due to the spin statistics of the identical oxygen atoms. When the asymmetric CO 2 rotates in the He environment, missing rotational levels can contribute to the interaction with the He bath and increase the effective coupling. 5. Conclusions The effect of isotopic substitution on molecular rotations of CO 2 has been studied via infrared spectroscopy in helium droplets. In the spectral region of 2ν 2 + ν 3 (3500 - 3700 cm -1 ), rovibrational spectra of 16 OC 16 O, 16 OC 18 O, and 18 OC 18 O have been obtained showing significant participation of surrounding helium in rotations. Rotational constants and band origins for all species have been determined. Enhancement of coupling of molecular rotations with helium has been observed for the asymmetric CO 2 . This observation can be described in terms of the increasing number of interacting levels for 16 OC 18 O molecules as compared to symmetric CO 2 isotopic species, where, due to the bosonic statistics of oxygen atoms, odd rotational levels are missing. 124 6. Chapter VIII References (1) Grebenev, S.; Hartmann, M.; Havenith, M.; Sartakov, B.; Toennies, J. P.; Vilesov, A. F. J. Chem. Phys. 2000, 112, 4485. (2) Toennies, J. P.; Vilesov, A. F. Angew. Chem. Int. Ed. 2004, 43, 2622. (3) Choi, M. Y.; Douberly, G. E.; Falconer, T. M.; Lewis, W. K.; Lindsay, C. M.; Merritt, J. M.; Stiles, P. L.; Miller, R. E. Int. Rev. Phys. Chem. 2006, 25, 15. (4) Kwon, Y.; Whaley, K. B. Journal of Chemical Physics 2001, 115, 10146. (5) Kwon, Y.; Whaley, K. B. Journal of Physics and Chemistry of Solids 2005, 66, 1516. (6) Paesani, F.; Kwon, Y.; Whaley, K. B. Physical Review Letters 2005, 94. (7) Zillich, R. E.; Paesani, F.; Kwon, Y.; Whaley, K. B. Journal of Chemical Physics 2005, 123. (8) Nauta, K.; Miller, R. E. Journal of Chemical Physics 2001, 115, 10254. (9) Herzberg, G. Molecular spectra and molecular structure, II Infrared and Raman spectra of polyatomic molecules; Van Nostrand: Princeton, New Jersey, London, 1968. (10) Rothman, L. S.; Hawkins, R. L.; Wattson, R. B.; Gamache, R. R. Journal of Quantitative Spectroscopy & Radiative Transfer 1992, 48, 537. (11) Lehnig, R.; Jager, W. Chemical Physics Letters 2006, 424, 146. (12) Hartmann, M.; Portner, N.; Sartakov, B.; Toennies, J. P.; Vilesov, A. F. J. Chem. Phys. 1999, 110, 5109. (13) Yongkyung, K.; Francesco, P.; Whaley, K. B. Physical Review B (Condensed Matter and Materials Physics) 2006, 74, 174522. 125 Chapter IX: Conclusions and Future Work 1. Conclusions In this work we have studied several molecular systems in He droplets. Hydrogen bonded HCl clusters were studied via infrared spectroscopy. With the help of theory we were able to identify and assign spectroscopic features of the cyclic structures of HCl clusters up to hexamers. The effect of the solvation in liquid helium on the interchange-tunneling motion in HCl dimer has been studied. Infrared absorption spectra of spherical top molecules (methanes and silanes) are obtained in the asymmetric vibrational region. The effect of the superfluid helium on the rotation of these molecules was discussed. Unexpected large enhancement of the vibrational modes coupling was observed in silane. We have shown that He droplets can be used for study of the conformers of large molecules, since superfluid helium as host for matrix isolation spectroscopy has great advantage over other matrixes.. 2. Spherical Top Molecules Infrared spectroscopic study of germane (GeH 4 ) and stannane (SnH 4 ) will be a logical continuation of the work on spherical top molecules. There are five stable isotopes of germanium atom 70 Ge, 72 Ge, 73 Ge, 74 Ge, and 76 Ge with relatively high abundance of 21%, 27%, 8%, 36%, and 7%, respectively. We can expect to observe all five isotopomers in the ν 3 rovibrational spectra of germane. The gas phase rotational constant of germane is approximately 2.68 cm -1 which is smaller than in 126 silane (2.84 cm -1 ) and somewhat larger than in deuterated methane (2.62 cm -1 ). We have already observed that the change of the rotational constant upon solvation in liquid helium not only depends on the intrinsic moment of inertia but is also affected by the anisotropy of the helium-molecule interaction potential. We saw that the change in the rotational constant of silane is larger than that in deuterated methane even though the rotational constant of CD 4 is smaller. It will be interesting to observe another molecule with a similar rotational constant. In addition, ν 1 transition of germane is very close to the ν 3 transition (see reference 1 ).The shift between these two bands varies from one isotopomer to another from 1.7 cm -1 for 70 GeH 4 to almost zero in the case of 76 GeH 4 . One will be able to study the effect of the enhancement of the coupling between these two vibrational modes as a function of energy difference between states. This may result in a better understanding of the role of helium in the coupling mechanism. 3. Study of the Conformers of the Large Biomolecules We have shown that He droplets can be used as a perfect host for the matrix isolation spectroscopy and identification of the conformers of the molecules. Further study of more complicated species, such as amino acids and other important biomolecules, will provide not only much needed information about conformational landscape for biology, but will serve as a benchmark for testing theoretical computational chemistry methods. The experimental challenge here is the creation of a thermal distribution of the conformers other than that at room temperature without 127 decomposing the molecules. This will be a broad field for invention in engineering of temperature controlled pick-up cells. 4. Study of the HCl-(H 2 O) n Complexes The study of HCl clusters presented in this work is a part of a larger investigation of HCl – H 2 O complexes. The goal of the study is to observe dissociation of the HCl molecule upon solvation by water molecules. The helium droplet technique offers a controlled way of doping clusters with foreign species 2 , which will allow for studying all combinations of the (HCl) n – (H 2 O) m species for n, m = 1 - 6. The most interesting region for observing of the dissociation of HCl is the HCl stretch, which is why detailed investigation in that region and identification of the spectroscopic features due to the HCl clusters has been performed. Formation of the hydronium ion H 3 O + results in the sudden change in the spectrum and the appearance of a strong vibrational band in the 2800-2900 cm -1 region. It should be remarked, that large amplitude motion in the helium may result into the fast relaxation of these vibrations and significant broadening of the spectra. In this case, detailed study and simulations can be carried out in the OH vibrational region. 128 5. Chapter IX References (1) Lepage, P.; Champion, J. P.; Robiette, A. G. Journal of Molecular Spectroscopy 1981, 89, 440. 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Abstract (if available)

Abstract This thesis covers different aspects of the spectroscopy of molecules andmolecular clusters embedded in helium droplets. The interaction between the trappedmolecules and the host He clusters as well as the use of helium as a media for novelmatrix isolation spectroscopy experiments will be discussed.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Skvortsov, Dmitry S. (author)

Core Title Rovibrational spectroscopy in helium droplets

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Publication Date 07/24/2008

Defense Date 06/12/2008

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

Tag helium droplets,laser spectroscopy,OAI-PMH Harvest

Language English

Advisor Vilesov, Andrey F. (committee chair), Kresin, Vitaly V. (committee member), Reisler, Hannah (committee member)

Creator Email skvortso@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1402

Unique identifier UC1158906

Identifier etd-Skvortsov-20080724 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-195812 (legacy record id),usctheses-m1402 (legacy record id)

Legacy Identifier etd-Skvortsov-20080724.pdf

Dmrecord 195812

Document Type Dissertation

Rights Skvortsov, Dmitry S.

Type texts

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

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu