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Infrared spectroscopy and ab initio studies of carbon dioxide van der Waals complexes

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Infrared spectroscopy and ab initio studies of carbon dioxide van der Waals complexes

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Content INFRARED SPECTROSCOPY AND AB INITIO STUDIES OF CARBON DIOXIDE VAN DER WAALS COMPLEXES by Alex Sazonov A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF SCIENCE (Chemistry) December 1997 Copyright 1997 Alex Sazonov Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. U N IV E R S IT Y O F S O U T H E R N C A L IF O R N IA THE GRADUATE S C H O O L . U N IV ER SITY P A R K LOS A N G ELES. C A L IF O R N IA 8 0 0 0 7 This thesis, ‘ written by A lex Sazonov under the direction of h is Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillm ent of the requirements for the degree of MASTER OF SCIENCE Date 28 A u g u st 1997 THESIS COMMITTEE Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS I w ould like to thank my research advisor Bob Beaudet for giving me the opportunity not only to learn quantum mechanics, but also to feel it by my own hands doing experim ental w ork in the field of spectroscopy. I thank m y colleague Cathy D utton whom I worked w ith in a group and who taught me the m ost in the lab, Ross Lewis whose help in fixing electronics w as alw ays quick and radical, and Steve Bunte, whose com puter "Fight On!" w as solving my ab initio problem s successfully for about a year. I w ould also like to acknowledge C urt Wittig and H anna Reisler for organizing extrem ely helpful group sem inars and for teaching me their challenging Special Topics, Unim olecular Kinetics, and m uch more. My special thanks are in order to Misha Zyrianov and Ilya Bezel, since we spent a great deal of time together talking about diode lasers, spectroscopy, m olecular dynamics, driving cars, living in America, surviving in Los Angeles, and discussing even m ore serious and interesting things. Their moral support in doing and especially in finishing this w ork can be hardly overestim ated. Last b u t not least, I would like to acknowledge the D epartm ent of Chemistry for providing me a financial support through the M errit Fellowship. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS ACK NO W LEDG M ENTS...................................................................... ii LIST OF FIGURES..................................................................................iv LIST OF TABLES......................................................................................v CHAPTER 1 INTRODUCTION ..................................................................................... 1 1.1 References................................................................................................4 CHAPTER 2 SPECTRAL ANALYSIS AND AB INITIO STUDY OF C 02-N 20 .....5 2.1 Introduction......................................................................................... 5 2.2 Spectrum and Structure..................................................................... 7 2.3 Ab Initio ............................................................................................ 12 2.4 D iscussion............................................................................................ 19 2.5 References.............................................................................................20 CHAPTER 3 SPECTROSCOPIC AND AB INITIO STUDY OF C 0 2-Br2.............22 3.1 Introduction ........................................................................................22 3.2 Experimental ....................................................................................26 3.3 Spectral Analysis ...............................................................................28 3.4 Ab Initio ............................................................................................34 3.5 Discussion............................................................................................37 3.6 References ..........................................................................................44 CHAPTER 4 THE INFRARED SPECTRUM OF THE OPEN-SHELL C 0 2- 0 2 COMPLEX.................................................................................. 47 4.1 References............................................................................................ 50 iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES Figure 2.1 Experimentally determ ined (C02)2 and (N20)2 geometries. The center of mass distances are given....................................................................... 6 Figure 2.2 Band center of CO 2 -N 2 O spectrum depicting a parallel band of QQiCa(J) and two perpendicular bands pQi and RQo...............................8 Figure 2.3 The first assigned R branch transitions around 2353 cm '1............9 Figure 2.4 Two possible slipped parallel configurations of CO 2 -N 2 0 ........... 11 Figure 2.5 H F /6-3llg * energy m inima for five planar geometries of CO 2 -N 2 O. The intem uclear C-N distances and slipped parallel angles are given.................................................................................................................13 Figure 3.1 Schematic of the experimental apparatus...........................................25 Figure 3.2 A portion of the R branch of the C02-Br2 V 3 C0 2 = 0— > 1 spectrum . * indicates the peaks assigned to (CC>2)2 and ** peak is assigned to a monomeric CO 2 transition.................................................................... 27 Figure 3.3 Unassigned system in the C02-Br2 spectrum .....................................33 Figure 3.4 Ab initio calculated equilibrium geometries of the C02*Br2 complex and potential energies along the Rcm distances. Calculations were done at the MP2 level and corrected for BSSE. Dashed lines represent the quadrupole-quadrupole potential...........................35 Figure 3.5 The structure of CC> 2 -Br2 and definition of the coordinates.........39 Figure 3.6 Potential contours for the linear C C > 2 -Br2 as a function of 0CO2 and & B r2- Calculations were done at the MP2 level and corrected for BSSE. C ontour spacing is 20 cm '1. Zero corresponds to the energy of the equilibrium structure.................................................................42 Figure 4.1 A portion of the CO 2 -O 2 spectrum .......................................................49 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES Table 2.1 HF, MP2, and MP3 6-3llg * ab initio results for the planar slipped parallel geometries of C 02-N 20, (C02)2/ and (N20)2 dim ers.............. 15 Table 2.2 H F /6-3llg* van der Waals vibrational frequencies (cm '1) of CO 2 -N 2 O, (COz)2/ and (N20)2...................................................................................17 Table 2.3 Experimental m olecular constants of C 02-N 20, (CC>2)2/ and (N 2 0 ) 2 ..........................................................................................................................18 Table 3.1 Experimental and calculated transition frequencies of the CC> 2 -Br2 complex................................................................................................... 29 Table 3.2 Molecular constants of the C C > 2 -Br2 complex....................................31 Table 3.3 Molecular constants of the C02-Br2 isomers (ab initio results)................................................................................................................ 36 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1 INTRODUCTION Weakly bound van der Waals molecules (also called van der W aals complexes, associates, clusters) have fascinated scientists for many years. In part, it is a result of the prom ise they hold for bridging the gap, in a m ore or less continuous fashion, between the gaseous and condensed states of m atter. On the other hand, chem ical reactions, photodissociation dynamics, state-to- state energy transfer, gas-solid adsorption an d m any other processes are also subjects to the weak long-range intermolecular forces. There have been m ajor advances in experim ental m ethods for observing van der W aals complexes, mostly by spectroscopic means. The idea of detecting clusters by using infrared vibrational spectroscopy dates back to the 1930's. The frequency shifts in hydrogen stretching vibrational bands were found in many com pounds which form interm olecular hydrogen bonds in the liquid phase.1 In 1960’ s, the study was extended to the gas phase by using a long path gas cells.2'3 Although rotational structure was not resolved w ith the spectrom eters available at that time, the experim ental data provided basic knowledge of hydrogen-bonded complexes such as bonding forces. A remarkable breakthrough for spectroscopic study of van der W aals complexes was realized in 1970's when a supersonic expansion and m olecular beam techniques were introduced into this field. Since a rotational tem perature as low as IK can be produced in the free jet expansion, it became possible to study complexes bound with electrostatic and even very w eak 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dispersion interactions. The developm ent of laser light sources w as another driving force for rapid developm ent of the spectroscopy of w eakly bound complexes. The resulting rotationally resolved infrared spectra contain a great deal of detailed inform ation on interm olecular forces and have stim ulated corresponding advances in the theoretical m ethods used for calculating interm olecular potential energy surfaces and for handling the dynam ics of the complexes themselves. M ost of the ab initio calculations that have been perform ed on van der W aals complexes have been so-called superm olecule calculations: separate calculations are perform ed on the complex and on the individual monomers, and the interaction energy is evaluated by sim ply subtracting the m onom er energy from the complex energy. This has obvious num erical disadvantage, called basis set superposition error: the interaction energy is som ew hat overestim ated because the basis functions on one m onom er add flexibility to the basis set on the other. It is usual to correct this error by the counterpoise m ethod,4 in which m onom er energies are calculated in the full dim er basis. H ow ever, this m ethod gives only a rough estim ate of the "true" effect. O n the other hand, the calculations w ith very large basis sets are essentially free of superposition error and need no correction.5 Ab initio calculations at the self-consistent field level are straightforw ard and com putationally inexpensive. H ow ever, they fail to take into account the correlation effects. Since the dispersion energy w hich dom inates the attractive p art of the potential for m any sim ple system s, is itself a correlation effect, self-consistent field calculations alone are inadequate for 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. many purposes. Nevertheless, it is possible to make sem iempirical corrections to account for the correlation energy. There are also various m ethods that calculate correlation energy directly, for exam ple configuration interaction or perturbation theory calculations. They are m uch m ore expansive and, except for the very sm allest systems, have difficulty in recovering the w hole of the dispersion energy. The present w ork deals with both the infrared spectroscopy studies and ab initio calculations of some van der Waals complexes containing the carbon dioxide molecule. In Chapter 2, we present our assignm ent of the spectrum of the CO 2 - N 2 O. The experimental spectrum was obtained in collaboration w ith C. Dutton. Approxim ately 340 lines of parallel and perpendicular bands have been assigned and the spectroscopic constants for lower and upper states have been obtained. Ab initio calculations for several CO 2 -N 2 O equilibrium structures have been perform ed at the self-consistent field level using a 6- 31 lg* basis set. M oller-Plesset perturbation theory MP2 and MP3 calculations were carried out for the two slipped parallel configurations of the dimer. The planar slipped parallel geometry with the O atom of N 2 O nearest the CO 2 was found to be the m ost stable structure. For this configuration, the MP2 and MP3 calculated rotational constants were in the best agreem ent w ith the experimental ones. Shortly after the publication of our study, Leung6 reported a m icrowave spectroscopic study on CO 2 -N 2O. Her results confirmed our rotational constants for the ground state. 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3 is the infrared spectroscopy and ab initio study of CC> 2 -Br2 . The absorption spectrum has been observed by probing the asymmetric stretch of the CO 2 moiety near 2349 cm*1. The complex was formed by the supersonic expansion of a mixture of CO 2 and brom ine vapor with He as a carrier gas. CC> 2 -Br2 was found to have a linear structure with one Br atom close to the center of mass of the system. The isotopic mixture of the second Br provided the splitting of the observed peaks into two. The distances from the Br2 bond center to the C atom are determined to be 5.116 and 5.083 A for the ground and excited states, respectively, and the force constant of the van der Waals stretching mode was estimated to be 0.004 m d y n /A in both states. The experim ental values were compared to the results of ab initio calculations perform ed at the self-consistent field and MP2 levels. In Chapter 4, the infrared absorption spectrum of the CO 2 -O2 open- shell complex is reported. 1.1 References 1. Hilbert, G. E.; Wulf, O. R.; Hendricks, S. R.; Liddel, U. f. Am. Chem. Soc. 1936, 58, 548. 2. Rank, D. H.; Rao, B. S.; Wiggins, T. A.; J. Chem. Phys. 1962,37, 2511. 3. Berite, J. E.; Millen, D. J. J. Chem. Soc. 1965, 497. 4. Boys, S. F.; Bemardy, F. / Mol. Phys. 1970,19, 553. 5. Buckingham, A. D.; Fowler, P. W.; Hutson, J. M. Chem. Rev. 1988, 88, 963. 6. Leung, H. O. The 52nd Ohio State University International Symposium on Molecular Spectroscopy, 1997, Talk WI14. 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 2 SPECTRAL ANALYSIS AND AB INITIO STUDY OF C 0 2-N20 2.1 Introduction The homodimers (C 0 2 ) 2 and (N 2 0 ) 2 have been extensively studied over the last two decades, how ever the mixed C 0 2 -N 20 dim er has not been identified. For years the structure of (C 0 2 ) 2 underw ent m uch debate , 1 *5 but only m odem high resolution laser spectroscopy was able to give the correct answ er. Sub-Doppler resolution infrared spectroscopy of the vi + V 3 com bination m ode of C 0 2 studied by Jucks and co-w orkers 6 confirmed that the structure of (C 0 2 ) 2 is slipped parallel. Further sub-D oppler infrared spectroscopy studies by Jucks and co-workers7 in the 2.7 fim region of the Ferm i diad vi + V 3 / 2 v2° + V 3 unequivocally reveal that the complex is planar w ith C2/i symmetry. Walsh and co-workers8 obtained a rotationally resolved spectrum of supersonically cooled (C 0 2 ) 2 in the V 3 asym m etric stretching region of C 0 2 monomer. They observed both a- and b-type transitions and determ ined that the structure w as a slightly asym metric prolate top. The band center of the dimer is 1.61 cm * 1 blue-shifted from the C 0 2 m onom er (2349.16 cm*1). Since C 0 2 itself has no perm anent dipole but has a large quadrupole m om ent (-14.34 x 1 0 * 4 0 Cm2), bonding originates predom inantly from quadrupole-quadrupole interactions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.6023A o c o / 3.4206A 61.2 N N O Figure 2.1 Experimentally determ ined (CC> 2 ) 2 and (N 2 0 ) 2 geometries. The center of m ass distances are given. 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The N 2 O dim er also has been extensively studied and was determ ined to have a slipped parallel structure similar to (CC> 2 )2 - H uang and M iller9 obtained rotationally resolved infrared spectra for both (1 4 N 1 4 N 1 6 0 ) 2 and ( 1 5 N 1 4 N 1 6 0 ) 2 by exciting vi + V 3 vibrational m ode of N 2 0 . They were able to show unam biguously the structure that agreed best w ith their data w as the centrosymmetric slipped parallel structure show n in Figure 2.1 ("oxygen to oxygen"). The structure obtained by Ohshima and co-w orkers 1 0 by m easuring the infrared absorption spectrum of supersonically cooled (N 2 0 ) 2 in the vi region (-1280 cm-1) of the N 2 O monomer is consistent w ith that obtained by H uang and Miller. 2.2 Spectrum and Structure The CO 2 -N 2 O spectrum was first assigned by identifying b-type RR branches in the less congested high-frequency region near 2353 cm '1, (see Figure 2.2). The spacings between transitions within the RR branches are approxim ately B + C (-0.105 cm*1), while the spacing between two successive RR branch origins are roughly 2A (-0.590 cm-1). The m ost striking feature in the band center is the QQ branch (see Figure 2.3). This region also shows pQ(i) and RQ(0 ) branches. From this assignm ent, preliminary values for A and B + C were determ ined. By use of the planarity relationship betw een moments of inertia la + lb = Ic and by assum ing that the rotational constants are the same both for ground and the excited states, the three constants w ere estimated. After this point, a bootstrapping procedure was used: the assigned transitions w ere 7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o 00 v 0 in c o cs cr C N C O in a a. 00 Figure 2.2 Band center of CO 2 -N 2 O spectrum depicting a parallel band of QQKaG) and two perpendicular bands pQ i and RQo- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2348.4 2348.6 2348.8 2349.0 2349.2 2349.4 Frequency, c m 1 ^ C* 0 0 P H as U ♦ CO O \£ ) P* Q £ C N -O n -00 IN <j + C Q N O in Figure 2.3 The first assigned R branch transitions around 2353 cm-1. 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2,353.00 2,353.10 2,353.20 2,353.30 2,353.40 2,353.50 2,353.60 2,353.70 2,353.80 2,353.90 Frequency / cm'1 iteratively fed into a fitting program to predict som e other transitions, and so forth. A total of -340 a- and b-type transitions w ere assigned. The spectrum was fit to the Watson S-reduced rotational H am iltonian 1 1 the fit over the rigid rotor approxim ation. The spectral constants for CO 2 -N 2 O are com parable to those of the CO 2 and N 2 O homodimers. The distance between centers of mass of the m onom ers Rcm and the acute slipping angle 0 were determ ined using the following expressions: w here lo c o and Imno are the moments of inertia for the respective m onom ers, and M is the reduced m ass of the dimer. These equations assume the m onom er structures are unchanged upon complexation. The similarities in the spectral constants indicate that the structure of the heterodim er is sim ilar to that of the hom odim ers. However, the orientation of N 2 O w ith respect to CO 2 is not determ inable from these constants. Three degrees of freedom are required to orient the m onom ers in the plane w ith respect to each other. However, only two independent rotational constants can be determ ined from the rovibrational spectrum due to the planarity relationship. M oreover, even if w e assum e that the two Hro t = AJ2 + (£ + C)(J2 -Jl)/2 + ( B - C)(J2 + J :)/4 - D ,r - D]kJ 2Jl + D tra + 5y J2(J2 + j ! ) + Sk(Jt + Ji ) The addition of quartic centrifugal distortion term s significantly im proved 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. O N N N N O i / Rc m = 3.4701 A 0 = 60.1 ° o c o o c o Figure 2.4 Two possible slipped parallel configurations of CO 2 -N 2 O. 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m onom ers are perfectly parallel (which we actually did, deriving the expression for 6), there are still two ways to place the nonsymmetric N 2 O in the complex (see Figure 2.4). The only experim ental way to determ ine its orientation would be to obtain the spectra of CO 2 -N 2 O isotopomers. However, ab initio calculations also give some insight into the CO 2 -N 2 O structure. 2.3 Ab Initio High-level ab initio calculations have proven to be dependable for predicting geometries of small van der Waals complexes. 1 2 -1 3 The H artree- Fock self-consistent field (HF) theory and second and third orders of the Moller-Plesset m any body perturbation theory (MP2, MP3) were used to calculate the equilibrium structures of CO 2 -N 2 O dimer, thus determ ining the m ost probable orientation of the N 2 O moiety. All calculations were perform ed within a 6-311g* standard polarized basis set. 1 4 The d-polarization function exponents for C, N, and O atoms were equal to 0.626, 0.913, and 1.292, respectively. The Bemy optim ization algorithm 1 5 was used to search for the optim al geometry. The structure optimization criteria were set equal to 1 x 10* 5 hartree/bohr or radian for all energy gradients. The ab initio calculations w ere perform ed using the Gaussian-9216 and Gaussian-9417 program s for quantum chemistry. HF theory was first used to find the minim a on the potential energy surface (PES) of the CO 2 -N 2 O dimer. It reveals the possible existence of five planar equilibrium geom etries, three T-shaped and two slipped parallel. In 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. L T J rs i o o > » «N £ £ o K C > f) O o ja £ £ o )o !<J )o j-_tU3//iSu3UJ Figure 2.5 H F /6-3llg * energy minima for five planar geometries of CO 2 - N 2 O. The intem uclear C-N distances and slipped parallel angles are given. 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. all five cases, the eigenvalues of the Hessian were found to be positive, thus providing robust m inim a on the PES. The optim ized HF planar geometries, corresponding structural parameters, and van der W aals binding energies (determ ined as the difference between the energy of the complex and the energy of the two free monomers) are given in Figure 2.5. Among those five structures, the one slipped parallel structure having the lowest energy, and most likely observed in the experiment, has been chosen for further analysis. This structure does not change significantly at the MP2 and MP3 levels from the calculations perform ed on the HF level. The HF and MP2 van der W aals energies w ere corrected for basis set superposition error (BSSE) by Boys and Bem ardy point counterpoise m ethod . 1 8 Similar calculations were performed on the CO 2 -CO 2 and N 2 O -N 2 O isoelectronic slipped parallel structures . 7 ' 1 0 The results were com pared to the experim ental structural param eters existing in the literature to lend confidence in our ability to make reliable predictions on the CO2 -N 2 O geometry. It was found that (CChh and (N 2 0 )2 / originally having Cs geometries, reoriented to C2/1 geometry to satisfy the m inim a conditions. Similar behavior was observed in the case of CO 2 -N 2 O dimer; namely, the optim ized structure had the monomer sym m etry axes exactly parallel to each other w ithin 0.2° uncertainty. For (C02)2/ a stable T-shaped structure (with R cc of 4.28lA) was found at the HF level. Its w an der W aals bond energy is -300 cm*1, 70 cm ' 1 higher than the energy for the slipped parallel isomer, which is in good agreem ent with the sem iem pirical calculations done by Kiode and Kihara. 4 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. Table 2.1 HF, MP2 and MP3 6-311g* ab initio results for the planar slipped parallel geometries of C 0 2- N 2 0 , (C 0 2 ) 2 and (N2 0 ) 2 dimers. c o 2-n 2 o co2 -co2 n 2 o -n 2o HF MP2 MP3 HF MP2 MP3 HF MP2 MP3 A (cm"1) 0.3199 0.2916 0.3031 0.3325 0.2902 0.3051 0.3216 0.3023 0.3140 B (cm'1) 0.0535 0.0566 0.0580 0.0464 0.0540 0.0527 0.0583 0.0584 0.0605 C (cm'1) 0.0458 0.0474 0.0487 0.0408 0.0455 0.0449 0.0493 0.0499 0.0507 R a (A ) 3.664 3.537 3.499 3.879 3.584 3.625 3.556 3.512 3.467 e (deg) 59.28 59.17 58.76 55.15 58.90 57.90 57.30 58.16 57.89 Rco (A ) 1.135 1.169 1.153 1.135 1.169 1.154 — — — r n n ( A ) 1.084 1.162 1.116 — — — 1.084 1.162 1.116 r n o ( A ) 1.172 1.181 1.181 — — 1.172 1.180 1.180 E (cm'1) -494 -519 -604 -376 -549 -514 -603 -475 -663 Eb b (cm'1) -309 -164 ---- -208 -187 — -398 -134 — ui a. Distance between monomer's central atoms. b. Eb is the van der Waals bond energy including BSSE. The HF, MP2, and MP3 ab initio results for all three slipped parallel complexes, (C02)2/ ( ^ 0 )2 , and CO2 -N 2 O, are listed in Table 2.1. The MP2 and MP3 rotational constants are in very reasonable agreem ent w ith the experimental results and are in better agreem ent than the H F constants for all three isoelectronic complexes. According to the ab initio results, it can be concluded that the com plex observed in the experiment has the slipped parallel structure show n in Figure 2.4(a) being an analogue of the (CC> 2 ) 2 and (N 2 0 ) 2 studied by group previously described. It is difficult to interpret the energy results, since the HF, MP2, and MP3 van der Waals binding energy values alternate unpredictably, especially w hen BSSE is taken into account. The BSSE values calculated by the point counterpoise m ethod are too large to be a reasonable estim ate of the real basis set errors. Finally, the H F vibrational frequencies were calculated for each of the three isoelectronic complexes (the van der Waals normal m odes are listed in Table 2.2). In the case of (C02)2/ the intermolecular stretching and symmetric bending frequencies have been previously estim ated from the experimentally obtained centrifugal distortion constants. 7 The corresponding frequencies determined by ab initio (HF) are 35.0 and 93.3 cm-1, respectively. These are in good agreement w ith the experimental estimates of 32(2) and 90(1) cm*1. One could expect that the internal vibrational dynamics of small van der Waals complexes can be adequately reproduced even by HF theory. The HF calculations predict that the CO 2 asymmetric stretching frequency in the CO 2 - N 2 O complex is red-shifted by -1.6 cm-1, while the experim ental shift is -0.3 cm"1. 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2.2 H F /6-311g* van der Waals vibrational frequencies (cm'1) of (C02)2, CO2-N2O, and (N20)2- co2 -co2 c o 2-n 2o n 2o -n 2o V j (torsion) 24.99 (Au) 32.01 (A") 37.84 (Au ) V 2 (sym. bend) 13.98 (Bu ) 29.06 (A') 45.77 (Bu ) V 3 (stretch) 34.95 (Ag) 45.59 (A’ ) 59.27 (Ag) V 4 (asym. bend) 93.28 (Ag) 110.55 (A') 121.71 (Ag) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2.3. Experimental molecular constants of C02-N20, (C02)2/ and (N20)2- CO 2 -CO 2 N 20 -N 20 N 2 O-CO 2 Ref. [7] Ref. [8 ] Ref. [9] Ref. [10] Present w ork A 0.300281 0.30033 0.299559 0.29922 0.294924 B 0.053604 0.05326 0.059968 0.05999 0.058004 C 0.045337 0.04511 0.049867 0.04988 0.048400 Atot 1.205 1.05 0.611 0.62 0.509 D /x 1 0 7 2.831 2.26 2.30 — 5.03 Djk x 1 0 6 -2.393 -1.90 -0.71 — -3.92 Dk \ 105 1.343 1.38 0 . 6 6 — 1.26 SjK 1 0 8 5.79 — 7.0 — 0 . 2 1 8k * . 1 0 6 1.40 — 4.7 — 1.26 4v x I0 4a) 1 . 0 1.7 2 . 0 2 0 . 0 5.0 < T X 104b> 1 . 2 3.0 2.3 13.0 4.0 All constants are in cm-1 except for inertial defect A to t. which is in am u A2- a) The experim ental uncertainty of m easured frequencies. b) The root-mean-square deviation of the fit. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.4 Discussion The experimentally determ ined spectral constants for the CO 2 -N 2 O dim er are shown in Table 2.3. The constants closely resem ble those of the slipped parallel structures of the CO 2 and N2 O hom odim ers. The upper state geom etry of the dim er is virtually unchanged from the lower state geometry. The asym m etry param eter k for this complex is -0.92, indicating that it is a slightly asymmetric prolate rotor. The set of experim ental constants alone, however, is insufficient to distinguish between the tw o slipped parallel structures. The ab initio results indicate that the slipped parallel configuration as show n in Figure 2.4(a) is the m ost energetically favorable. They also indicate that m inim a exist for T- shaped dim ers, though they have not been observed experimentally. Of course, the kinetic stability of the higher energy isom ers depends on the height of the barrier along the lowest energy path on the PES between the isomers. We have not attem pted to investigate these paths. Given that there is no dipole moment in CO 2 and the dipole m om ent of N 2 O is extremely small, the bonding in the hybrid dim er CO 2 -N 2 O is predom inately due to quadrupole-quadrupole interaction. The effect of this interaction on the equilibrium structures of van der W aals complexes will be explained in details in C hapter 3. The experimental data and calculations used in conjunction w ith ab initio results show that the structure of the CO2 -N 2 O dim er is slipped parallel with the O of N 2 O above the C. 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.5 References 1. Mannik, L.; Stryland, J. C.; Welsh, H. L. Can. f. Phys. 1971, 49, 3056. 2 . Novick, S. E.; Davies, P. B.; Dyke, T. R.; Klem perer W. f. Amer. Chem. Soc. 1973, 95, 8547. 3. Fredin, L.; Nelander, B.; Ribbegard, G. J. Mol. Spec. 1974, 53, 410. 4. Koide, A.; Kihara, T. Chem. Phys. 1974, 5, 34. 5. Barton, A. E.; Chablo, A.; How ard, B.J. Chem. Phys. Lett. 1978, 60, 414. 6 . Jucks, K. W.; Huang, Z. S.; Dayton, D.; Miller, R. E. /. Chem. Phys. 1987, 86,4341. 7. jucks, K. W.; Huang, Z. S.; Miller. R. E.; Fraser, G. T.; Pine, A. S.; Lafferty, W. J. / . Chem. Phys. 1987, 88, 2185. 8 . Walsh, M.A.; England, T .H.; Dyke, T. R.; H ow ard, B.J. Chem. Phys. Lett. 1987,142, 265. 9. Huang, Z. S.; Miller, R. E. f. Chem. Phys. 1988, 89, 5408. 1 0 . Ohshima, Y.; Matsumoto, Y.; Takami, M.; Kuchitsu, K. Chem. Phys. Lett. 1988,152, 294. 1 1 . W atson, J. K. G. J. Chem. Phys. 1967, 46, 1935. 1 2 . Hobza, P.; Zahradnik, R. Intermolecular Complexes; pp30-96, Elsevier, New York 1988. 13. Chalasinski, G.; Gutowski, M. Chem. Rev. 1988, 88, 943. 14. Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72,5639. 15. Schlegel, H. B. f. Comp. Chem. 1982, 3, 214. 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 . Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; A ndres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; M artin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/D FT, Revision G.3; Gaussian, Inc., Pittsburgh, PA, 1993. 17 . Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Peterson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; H ead- Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Revision B.l; Gaussian, Inc., Pittsburgh, PA, 1995. 18. Boys, S. F.; Bemardy, F. / Mol. Phys. 1970,19, 553. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 3 SPECTROSCOPIC AND AB INITIO STUDIES OF CO2-BR2 3.1 Introduction Diode laser IR spectroscopy has proven to be an effective method for studying w eakly bound complexes, 1 and carbon dioxide complexes are a natural choice for such studies. The asymmetric stretch norm al mode has one of the largest transition dipole m om ents. Also, since CO 2 has been used in a num ber of oriented-reactants experim ents, it is desirable to characterize the weakly bound precursors as fully as possible . 2 -3 To date, high resolution rovibrational spectroscopy has provided the structures and vibrational dynam ics of a wide variety of CO 2 weakly bound complexes. Here we will only review those that are pertinent to our study. The following trends have been observed in C0 2 -Rg series of complexes (Rg = He-Xe): (i) the distance between C and the rare gas atom increases monotonically while the m ean value of the angle betw een the C-Rg and CO 2 axes approaches 9 0 ° in going from N e to Xe; (ii) the V3 CO 2 asymmetric stretch band origin shifts to lower frequencies.4 However, as it was shown later, 5 in the C 0 2 -He complex, the intem uclear distance R(He-C) = 3 .5 8 A is surprisingly greater than R(Ne-C) = 3 .3 0 A in C 0 2 -Ne- Such an exception can be caused by two factors. First, since He atom has only two electrons, van der Waals attraction between the species should be extremely weak and repulsive forces m ay start to contribute significantly at longer separations. Second, due 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to its small mass and weak binding He atom can undergo large am plitude zero point m otions leading to an observed distance which does not reflect the m inim um of the potential well even approxim ately. The CC > 2 -H(D)X ( X = F, Cl, Br) complexes have also been extensively studied by rotational and rovibrational spectroscopy. Linear equilibrium geometries were observed for HF, HC1 and the corresponding deuterides . 6 ' 1 0 For HF and H C1, the CO 2 asymmetric stretch band origins, V3 , w ere blue- shifted by 9.9 and 3.9 cm*1, respectively, and deuteration resulted in larger blue shifts of 10.6 and 4.7 cm '1, respectively. O n the other hand, the CO 2 - H(D)Br structure w as found to be inertially T-shaped (Rcm = 3.58 A), with essentially parallel HBr and CO2 axes. The V3 rovibrational band origin was red-shifted by 0.94 and 0.87 cm ' 1 for HBr and DBr, respectively . 1 1 The microwave spectra of eight HBr-C0 2 isotopom ers 1 2 are consistent w ith a T- shaped Br-C0 2 geom etry giving, however, an equilibrium CBrH angle of = 103° (vs. 8 6 ° as obtained in [11]). Only a few studies on Br2 complexes have been reported. Fluorescence excitation spectra associated with the Br2 (B < — X) bands in He-Br2 1 3 and Ne- B r2 l4 ,l5 have been recorded and their rotational structure has been resolved. Both complexes have a T-shaped geom etry w ith the separation betw een noble gas atom and the Br2 bond center of RC m - 3.7 and 3.65 A for He and Ne, respectively. Bloemink and Legon 1 6 investigated the ground states of four isotopomers of the prereactive interm ediate H 3 N — Br2 w ith Fourier-transform microwave spectroscopy. Chemical reaction betw een the m onom ers was avoided by using a fast-mixing nozzle. The symmetric-top spectra were 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. analyzed to determine rotational constants, the centrifugal distortion constants Dj and Djk, the Br-nuclear quadrupole coupling constants for both brom ine atoms, and the Br-nuclear spin-rotation coupling constants. The distances r (N— Br inner) = 2.72(2) A and r (Br-Br) = 2.335(10) A in the complex w ere obtained from the rotational constants while the intermolecular stretching force constant ka = 18.5(5) N n r 1 was estimated from D/. High resolution rovibrational absorption spectrum of the OC-Br2 1 7 have been recorded in the region of the CO stretching mode near 2143 cm-1. Four progressions originating from different brom ine isotopic species w ere consistent with a linear complex. The distances from the Br2 bond center to the CO center of mass were determined to be 4.884 and 4.893 A for the ground and excited states, respectively. The orientation of the CO was presum ed to be the sam e as in CO-CI2 . In Bunte's studies of the CO-CI2 complex a good agreem ent between ab initio calculated 1 8 and experimentally m easured 1 9 spectroscopic constants has been obtained. The ab initio results suggested that the equilibrium structure of that complex is OC-CI2 . The later m icrowave study of seven isotopic species of OC-CI2 2 0 has show n the same result. Based on the sim ple analogy and supported by the Lewis acid-base model of the binding for the carbonyl group in complexes, the OC-Br2 structure was proposed; however, neither ab initio calculations nor microwave studies of this molecule have been perform ed yet. In this work, we report the rovibrational absorption spectrum of the CC> 2 -Br2 weakly bound complex observed by pulsed-nozzle, diode laser IR spectroscopy. 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Mode-selection monochromator Confocal Etalon Diode To Vacuum System Gas Mixture Focus Lens i i Pulsed Slit Nozzle Figure 3.1 Schematic of the experim ental apparatus. 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2 Experimental. The detailed experim ental setup (see Figure 3.1) has been described previously , 2 1 and only a few aspects relevant to this particular study are presented below. A m ixture of = 0.2% CO 2 and = 0.8% Br2 (M allinckrodt, 99.7% of bromine) in helium was expanded through a pulsed slit nozzle at a rate of 3 Hz from a stagnation pressure of = 2 atm. Background pressure in the cham ber was about 10 mTorr during the expansion. Each gas pulse lasted 1.5 ms. A single m ode from a tunable IR diode laser (operating near 2349 cm"1, which corresponds to the asymmetric stretching m ode of CO 2 ) w as selected by a 0.5 m monochrom ator. Two small fractions of the diode pow er w ere sent through a CO 2 reference gas cell and a confocal etalon (FSR = 0.099 cm '1) in order to calibrate the frequency scale. Most of the laser radiation entered the vacuum chamber and m ade a double pass through the gas expansion space. All three IR absorption signals were taken sim ultaneously by rapidly scanning the laser frequency during a stable period of the gas pulse. The supersonic jet absorption signal was filtered through a band pass filter which cut off the frequencies outside the range of 10 kHz to 100 kHz. The diode laser was scanned about 0.35 cm " 1 during each gas pulse and usually 100 scans were averaged. The absorption features presum ably belonging to the CC> 2 -Br2 complex were recorded between 2347.5 and 2351.5 cm*1. These absorptions were not present w hen either of the two com ponents (CO 2 , Br2 ) was absent. How ever, some peaks belonging to the CO 2 dim er were observed. The gas 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.2 A portion of the R branch of the C C > 2 -Br2 \'3C02 = 0— >1 spectrum . * indicates the peaks assigned to (CC> 2 ) 2 and ** peak is assigned to a m onom eric CO 2 transition. 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2350.10 2350.20 2350.30 2350.40 2350.50 2350.60 2350.70 2350.80 Frequency / c m 1 concentrations were adjusted to obtain the strongest spectrum m inim izing the (C 0 2 ) 2 resonances. 3.3 Spectral Analysis The observed spectrum can be divided into two portions. Figure 3.2 displays the high-frequency region. Some peaks here were identified to belong to the V 3 = (1 < — 0) rovibrational band of (C02)2- However, the m ost prom inent feature of this spectrum is a progression of lines equally separated by = 0.034 cm '1, degraded to the higher frequencies, and split into doublets of equal intensity. Since no other series with similar spacing was found, it w as concluded that the complex m ust have linear or quasilinear geometry, and the observed splittings m ust be attributed to the presence of different isotopically substituted species w ith the inner Br atom situated very close to the center of mass of the complex. These species w ere called CC> 2 -7 9 Br2 and C 0 2 -8 1 Br2 where the superscript denotes the mass num ber of the outer Br. H ence the experimental intensity ratio is consistent w ith the natural abundances of 79Br and 81Br (50.54% and 49.46%, respectively). The measured transition frequencies of the tw o isotopomers were fit to the sem irigid linear rotor m odel, V = V0 + B T ( f + \) - D ( T ( f +1))2 - + ) ) 2 w here all terms have their usual meanings. The experimental and calculated frequencies are listed in Table 3.1 (blended lines w ere not included into the fit and are not reported). The spectroscopic constants are given in Table 3.2. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. Table 3.1 Experimental and calculated transition frequencies of the C02-Br2 Complex. Transition (C02-79Br2) (C02-81Br2) Transition (C02-79Br2) (C02-81Br2) P(3) 2349.6888(-0) 2349.6895(4-1) P(4) 2349.6603(+0) 2349.6610(-2) P(5) 2349.6328(46) 2349.6332(-2) P(6 ) 2349.6043(-l) 2349.6057(-l) P(7) 2349.5768(-l) 2349.5784(-l) P(8 ) 2349.5496(+l) 2349.5513(-1) P(9) 2349.5228(42) 2349.5247(+0) P(10) 2349.4956(-3) 2349.4984(+l) P(H) 2349.4695(-1) 2349.4721(-1) P(12) 2349.4436(-0) 2349.4462(-2) P(13) 2349.4176(+2) 2349.4211 (+2) P( 14) 2349.3923(-l) 2349.3956(-l) P(15) 2349.3677(45) 2349.3705(-2) P(16) 2349.3417(-7) 2349.3457(-4) P( 17) 2349.3177(-1) 2349.3217(-2) P( 18) 2349.2936(-0) 2349.2975(-3) P( 19) 2349.2696(-l) 2349.2747(+6) P(20) 2349.2461(-0) 2349.2503(-4) P(21) 2349.2221 (-7) 2349.2281 (+6 ) R(l) 2349.8353(-l) R(2) 2349.8659(+3) 2349.8647(-0) R(3) 2349.8966(+6) 2349.8948( 1) R(5) 2349.9578(-l) 2349.9561(40) R(6 ) 2349.9889(-3) 2349.9874(42) R(7) 2350.0204(-3) 2350.0189(44) R(8 ) 2350.0522(-4) 2350.0503(42) R(9) 2350.0848(+l) 2350.0816(-4) R(10) 2350.1171(-1) 2350.1146(44) R(ll) 2350.1499(+0) 2350.1467(41) R( 1 2 ) 2350.1830(+2) 2350.1791 (-2) R(I3) 2350.2167(4-7) 2350.2124(43) R(14) 2350.2498(43) 2350.2457(43) R(15) 2350.2836(44) 2350.2790(43) R(16) 2350.3171(-1 ) 2350.3124(-0) R(17) 2350.3510(-2) 2350.3463(-2) R(18) 2350.3856(-3) 2350.3807(42) R(19) 2350.4203(-3) 2350.4151(-0) R(20) 2350.4555(-l) 2350.4496(-l) Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. Table 3.1 (continued). Transition (C0 2 -7 9 Br2 ) (C0 2 -8 lBr2 ) Transition (C0 2 -7 9 Br2 ) (C0 2 -8 lBr2 ) P(22) 2349.1998(+1) 2349.2049(+2) R(21) 2350.4906(-2) 2350.4845(-l) P(23) 2349.1769(-1) 2349.1824(42) R(22) 2350.5260(-2) 2350.5190(-7) P(24) 2349.1548(+3) 2349.1605(44) R(23) 2350.5615(-4) 2350.5550(-2) P(25) 2349.1328(45) 2349.1385(+4) R(24) 2350.5973(-4) 2350.5903(-5) P(26) 2349.1101(-5) 2349.1165(-0) R(25) 2350.6264(-2) P(27) 2349.0896(47) 2349.0948(-4) R(26) 2350.6706(44) 2350.6627(41) P(28) 2349.0680(+3) 2349.0737(-4) R(27) 2350.7071 (+4) 2350.6994(46) P(29) 2349.0470(+2) 2349.0533(-l) R(28) 2350.7438(+3) 2350.7354(41) P(30) 2349.0263(+2) 2349.0331 (+2) R(29) 2350.7807(42) P(31) 2349.0057(-l) 2349.0134(+6) R(30) 2350.8178(42) 2350.8088(40) P(32) 2348.9857(-l) 2348.9927(-2) R(31) 2350.8548(-2) 2350.8461(41) P(33) 2348.9659(41) 2348.9730(-3) R(32) 2350.8921(-5) 2350.8830(-2) P(34) 2348.9461 (-2) R(33) 2350.9305(42) 2350.9209(42) P(36) 2348.9079(-3) Residuals in parentheses are from least-squares fit and are (observed-calculated)xlO’4; a = 0.0003 cm-1 C O o Table 3.2 Molecular constants of the C C > 2-Br2 complex. C 0 2 -7 9 Br2 C 0 2 -8 1 Br2 Vo (cm-1) 2349.775866(89) 2349.775770(95) B "(cn r 1) 0.0146591(26) 0.0145321(28) B' (cm-1) 0.0148044(26) 0.0146763(27) D" (cm-1) 6.01(16)xl0-8 6.04(19)xl0-8 D ' (cm-1) 6.43(17)xl0'8 6.42(18)xl0"8 Ro" (A) 5.1161(6) 5.1160(6) Ro'(A) 5.0830(6) 5.0828(6) c q " (cm’1) 14.5(2) 14.3(2) co' (cm*1) 14.2(2) 14.0(2) R ob/ ’ (A) 2.8122(6) 2.8121(6) RO Br (A) 2.7748(6) 2.7746(6) k 0 " (m dyn/A ) 0.0043(1) 0.0042(1) k G' (m dyn/A ) 0.0041(1) 0.0040(1) U ncertainties are in the last two digits and are one standard deviation of least- squares fit. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Because the addition of higher order centrifugal distortion terms did not improve the fit, they were om itted. After the sim ulation of the entire spectrum , the rotational tem perature of the formed complex was estim ated to be 7 ± 1 K. Since no Q branch was observed, this spectrum must be that of a £ - I transition. A ssum ing that the intem uclear distances in CO 2 and Br2 rem ain constant upon complexation, the distance between centers of mass of the m onomers can be expressed as where I's are the corresponding moments of inertia and f i is the reduced mass of the binary complex. Mass of the inner bromine was set equal to 79 or 81 a.m.u. for both experim entally distinguished isotopomers. Thus, the four values of Ran were calculated. The isotopic shift of the center of mass position in Br2 , was then taken into account and the isotopically invariant distance betw een geometric centers of the m onom ers R q =Rcm +AR was eventually calculated. Within the experim ental error, the Ro values were not affected by the m ass of the inner Br. W ith the use of the pseudo-diatomic approximation, van der W aals stretching vibrational frequencies were obtained as2 2 complex AR = R outer inner ^ d i n n e r + ™ ,m er ) 4 B 3 6) = J - — w hereupon the force constants for both states, 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C v 00 * co C M o in o o c o C M o 00* C O C M Figure 3.3 Unassigned system in the C0 2 -Br2 spectrum . 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ka =HGT , w ere evaluated. The molecular constants are given in Table 3.2. In Figure 3.3, the low-frequency portion of the experimental spectrum is shown. In contrast to the region shown in Figure 3.1, this absorption intensity profile bears no resemblance to a canonical I - I band. The progressions of lines separated by = 0.025 cm ' 1 were found on each side of the strong m aximum near 2348.64 cm-1. In OCO-HF and SCO-HF, 6 the principal band has been accompanied by a slightly red-shifted doublet-type subsidiary bands that can be interpreted as a hot band of low frequency bending vibrations or K = 1 subbands of bent molecules. In either case, a Q branch show s up in the middle of a satellite band. How ever, attempts at fitting those equally spaced peaks to the model described in [6 ] have not been successful. A nother possibility to explain this spectral feature will be discussed later on. 3.4 Ab Initio The Hartree-Fock self-consistent field (HF) technique along w ith the M oller-Plesset many body second order perturbation theory (MP2) were used to calculate the van der W aals potential energy surface (PES) for the CO 2 - Br2 system. Commonly employed 6-31+g* basis sets 2 3 (£< / = 0.8) were used for carbon and oxygen. To describe bromine, a com pact valence double-zeta gaussian-type basis set developed by Andzelm et al.,2 4 : augmented with two sets of d-polarization functions (Q = 0.562, 0.176), was used because it 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.4 Ab initio calculated equilibrium geom etries of the CC> 2 -Br2 complex and potential energies along the RC m distances. Calculations were done at the MP2 level and corrected for BSSE. Dashed lines represent the quadrupole-quadrupole potential 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission Table 3.3 Molecular constants of the C0 2 -Br2 isomers (ab initio results). HF MP2 HF MP2 HF MP2 Rcm (A ) 5.4931 5.2272 4.1926 3.6532 3.9439 3.3271 0CO2 (°) 0 0 90 90 90 90 eB n n 0 0 90 90 90 90 < M ° ) - - 0 0 90 90 Rco (A )a 1.1433(+0) 1.1817(4-9) 1.1435(4-2) 1.1820(4-12) 1.1435(4-2) 1.1819(4-11) RtirBr (A ) a 2.2919(+10) 2.3186(4-33) 2.2920(4-11) 2.3184(4-31) 2.2930(4-21) 2.3176(4-23) EvdW(c m’1) -577 -845 -191 -437 -169 -277 V3(C02) (cm*1) b 2572.71(+8.1U) 2569.21(4-4.60) 2569.75(4-5.14) V1(C02) (cm4 ) b 1513.51(+2.38) 1511.41(4-0.28) 1511.40(4-0.27) V2(C02) (cm4 ) b' c 753.75(+4.42) 753.57(4-4.24) 752.14(4-2.81) - 751.81(4-2.48) 750.37(4-1.04) V(Br2) (cm4 ) b 337.18(+0.74) 336.13(-0.31) 334.93(-1.51) WlvdW (cm*1) d 54.74 (n) 24.57 (Ai) 22.44 (Ai) 0>2vdw (cm-1) d 49.16 (I) 24.39 (B2) 21.04 (B2) 0)3vdW (cm '1) d 20.29 (n) 7.22 (A2) 8.85 (Bi) G^wiwCcm-1) d - 5.36 (B2) 4.43 (A2) a Change with respect to free monomer [e.g., r(complex)-r(free), in AxlO'4] is in parentheses, w b Shift with respect to free monomer [e.g., v(complex)-v(free), in cm-1] is in parentheses. c V2(C02) is split in the nonlinear isomers. d Symmetry is in parentheses. reproduces the m olecular properties of Br2 - For equilibrium structures both van der Waals and intramolecular param eters were optimized. Basis set superposition error (BSSE) was accounted for by utilizing the counterpoise m ethod . 2 5 The calculations were perform ed using Gaussian-92.26 The three distinct minima: linear, parallel, and nonplanar X-shaped were found on the C 0 2 -Br2 PES when either level of theory was used. In Figure 3.4 the MP2 energies for all three equilibrium structures are plotted as a function of RC m ■ The calculated molecular param eters of those isom ers are listed in Table 3.3. In all three cases, adding MP2 correction shorten the equilibrium Rcm suggesting a significant contribution of electron correlation to the van der W aals bond energy. The MP2 calculated Rcm for the linear isomer (5.227 A) agrees with the experimental value (5.116 A). The small discrepancy can arise out of the underestim ation of a total configuration interaction by MP2. The HF calculation of vibrational frequencies leads to an incorrect large value for Avs(co2) (8.1 cm - 1 instead of 0.6 cm*1) and to an overestimated van der Waals stretch frequency (49 cm - 1 by ab initio vs. 14 cm ' 1 estimated from the centrifugal distortion constant). Because of lim ited com puter resources, the MP2 vibrational frequencies have not been calculated. 3.5 Discussion As show n in the previous section, the experimentally observed linear C 0 2 -Br2 is predicted to have the lowest energy among all its isomers. Neither the parallel nor the X-shaped structures have been observed. Since the height 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the barriers between linear and nonlinear structures have not been determ ined, there is no reason to believe that these other forms actually exist. Also, because of the low tem perature created by supersonic expansion, the concentration of the higher energy forms should be small if an equilibrium is attained. A lthough ab initio calculations can, in principle, explain the structures of the CC> 2 -Br2 (in terms of molecular orbitals), it is intuitively more m eaningful to apply a simple electrostatic model. The first nonvanishing term in the m ultipole expansion for C C> 2 -Br2 is the quadrupole-quadrupole interaction j j ^ ^ ■ / - 5c o s ~ 6c02 - 5cos~QB r 2 + 17cos~6c02cos~6B r 2 + 2sin2 8C O 2 sin2 0B r 2 cos2 ( f > — 16sin 0C O 2 sin 0B r2 cos dC O 2 cos0B r 2 cos< p where Q c02 and Qfir2 are the perm anent quadrupole m om ents of the monomers, and the definition of coordinates is given in Figure 3.5. 2 7 We will now only consider angular coordinates while Rcm rem ains constant. In general, the shape of the quadrupole-quadrupole potential is determ ined by the signs of the quadrupole moments of the partners. For two quadrupoles of the same sign it has two minima, corresponding to two T- shaped structures, isoenergetic at the sam e Rcm • A saddle point of first order corresponds to a slipped parallel geometry with the slipping angle about 50°. The analysis of the potential for the case of two quadrupoles of opposite sign leads to two m inim a corresponding to the linear and the parallel isomers. A saddle point of first order occurs for the X-shaped geometry. The ratio between the energies of those three structures (at constant Rcm ) is 8:3:1, the most stable one is linear and the least stable one is X-shaped. t / _ 3QcQ2QBr2 V Q Q ~ 4Rs cm 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o Br Br2 C02 Br cm Figure 3.5 The structure of C 0 2 -Br2 and definition of the coordinates. 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The estim ated quadrupole-quadrupole contributions for C0 2 -Br2 are represented by dashed lines in Figure 3.4 (the experim ental value of Qco2 = -14.34xlO-40 Cm 2 was taken from [28] and ab initio calculated value of Q bt2 = 3 0 .5 2 X 1 0 " 40 Cm 2 from [2 9 ]; the experimental QBr2 has not been reported). In com parison to the ab initio results, they reflect the sam e trend in energy. Based on this, the absolute and relative stabilities of the linear and parallel isom ers have prim arily an electrostatic origin. In the case of an X-shaped isom er the repulsion betw een O and Br atoms should be much smaller than in the parallel isomer case. This allows the m onom ers to approach closer, so close that the forces other than quadrupole-quadrupole provide a m inim um w ith respect to < j ) angle. A stable X-shaped structure is now found for the CO 2 - CS2 van der Waals com plex . 3 0 A similar m echanism is probably responsible also for slipped parallel equilibrium geometries of the homomolecular dim ers (CC> 2 )2 3 1 and (N 2 0 )2 , 3 2 and heteromolecular dim er CO 2-N 2 O . 2 1 The spectroscopic study of the linear CC> 2 -Br2 suggests a significant (about 0 .0 3 3 A ) contraction of the van der Waals bond with vibrational excitation of CO2 . An analogous effect has been observed in a number of IR studies of weakly bound c o m p le x e s .6'10 For example, in C 0 2 -H(D)F such a contraction takes place w hen either the H(D)F stretch or CO 2 asymmetric stretch vibrations are excited. It is known that the rco distance in the V 3 = 1 CO 2 is lengthened by -0.0022 A with respect to one in the ground state3 3 (it was taken into account w hen we calculated R 'cm)- This change is expected to increase the value of Qc02 and, consequently, the attraction between the m onom ers. Moreover, both molecules m ust induce a sm all dipole moments in partners which give rise to intermolecular attraction and those moments 4 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. are also dependent on rco• Finally, an additional com puter experiment has been performed: the CO distances in the linear complex w ere raised by 0.0022 The result of an optimization done by this expedient on the HF level was the Surprisingly, the intermolecular stretch force constant is not affected by the excitation of CO 2 , only a little softening of this mode (within the experimental error for both isotopomers) can be obtained. In contrast to the present study, drastic decreases in ka were observed in C0 2 -H(D)F, SCO-HF and other linear complexes. It is interesting to note that in such systems the softening of van der Waals stretching is accompanied by the decrease of van der Waals molecular radii mentioned above, and the conclusions about stabilization or destabilization of the intermolecular bonds on excitation are then ambiguous. There is no escape from the fact that the experimentally determ ined stretching force constants of CC> 2 -Br2 are anomalously weak even for van der Waals bond. Up to this point we have considered a real C C> 2 -Br2 system in terms of a rigid distortable molecule. It is also w orth turning to the alternative model of a floppy linear rotor3 4 extensively used in microwave studies . 1 6 ' 3 5 Here the contribution of intermolecular bending vibrations to the zero-point motion of the complex is described by the oscillating angles Qcoi, 9Br2 and < p (see Figure 3.5), so that the m om ent of inertia of the complex is given by A and kept fixed while other param eters (Rcm and rgrBr) were allowed to vary. decrease of Rcm by 0.05 A, which supports our interpretation of the effect. 1 + cos 2 QB r 2 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3.6 Potential contours for the linear CC > 2 -Br2 as a function of Q qoz and 6bt2• Calculations were done at the MP2 level and corrected for BSSE. Contour spacing is 20 cm-1. Zero corresponds to the energy of the equilibrium structure. 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where the angular brackets indicate the average over the zero-point motion. One can see if <cos29c02> a n d /o r <cos29sr2> differ from 1, the <Rcm> is som ewhat longer than that determ ined for a rigid rotor. As it w as calculated ab initio, the interm olecular potential (Figure 3.6) does not allow monomers to oscillate about the equilibrium point with a large am plitude. Unfortunately, there is no w ay to obtain all three values of interest from only two experim entally m easured rotational constants of isotopom ers without additional assum ptions. The only thing one must keep in m ind is that the experimental values of Rcm reported in this work are actually lower limits of the corresponding molecular param eters. In the unassigned spectrum show n in Figure 3.3, the equal spacing found betw een lines is inconsistent w ith the C0 2 -Br2 dim er since it provides very low values of B + C. Even under an assum ption that B = C the corresponding distance betw een centers of mass is -5.8 A, w hich is too large for a bound complex. Nevertheless, this spectral feature has been observed repetitively and only if Br2 is present in the gas mixture. The probability of a higher order clustering in a supersonic jet can not be neglected, especially in the case of such complexants as CO 2 and bromine. We have not been able to infer the com position of this complex from the observed spectrum . The complex could also involve an im purity from the gas handling system. In sum m ary, we have obtained and assigned the V 3 band of C 0 2 -Br2 in terms of a sem irigid linear rotor Hamiltonian. The structure in the ground and excited vibrational states has been accurately determ ined. The linear equilibrium geom etry and a sm all shift of the vibrational frequency in the 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. chrom ophore imply that the van der Waals binding mechanism in the CO 2 - Br2 complex is predom inantly electrostatic. 3.6 References 1. Miller, R. E; in: Atomic and Molecular Beam Methods, vol. 2, ed. Scoles, G.; Oxford Univ. Press: New York, 1992; pp 192-212. 2. Buelow, S.; Noble, M.; Radhakrishnan, G.; Reisler, H.; Wittig, C.; Hancock, G.; f. Phys. Chem., 1986, 90, 1015. 3. Buelow, S.; Radhakrishnan, G.; Wittig, C.; /. Phys. Chem., 1987, 91, 5409. 4. Randall, R. W.; W alsh, M. A.; H ow ard, B. J.; Faraday Discuss. Chem. Soc., 1988, 85, 13. 5. Weida, M. J.; Sperhac, J. M.; Nesbitt, D. J.; f. Chem. Phys., 1994,101, 8351. 6 . Fraser, G. T.; Pine, A. S.; Suenram, R. D.; Dayton, D. C.; Miller, R. E.; J. Chem. Phys., 1989, 90, 1330. 7. Lovejoy, C. M.; Schuder, M. D.; Nesbitt, D. J.; J. Chem. Phys., 1987, 86, 5337. 8 . Baiocchi, F. A.; Dixon, T. A.; Joyner, C. H.; Klemperer, W.; f. Chem. Phys., 1981, 74, 6544. 9. Altman, R. S.; Marshall, M. D.; Klemperer, W.; f. Chem. Phys., 1982, 77, 4344. 10. Sharpe, S. W.; Zeng, Y. P.; Wittig, C.; Beaudet, R. A.; /. Chem. Phys., 1990,92, 943. 11. Zeng, Y. P.; Sharpe, S. W.; Shin, S. K.; W ittig, C.; Beaudet, R. A.; J. Chem. Phys., 1992, 97, 5392. 12. Rice, J. K.; Lovas, F. J.; Fraser, G. T.; Suenram , R. D.; f. Chem. Phys., 1995,103,3877. 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13. van de Burgt, L. J.; Nicolai, J-P.; Heaven, M. C ; J. Chem. Phys., 1984, 81,5514. 14. Swartz, B. A.; Brinza, D. E.; W estern, C. M.; Janda, K. C.; f. Phys. Chem., 1984,8 8 ,6272. 15. Thom m en, F.; Eward, D. D.; Janda, K. C.; J. Chem. Phys., 1985, 82, 5295. 16. Bloemink, H. I.; Legon, A. C.; J. Chem. Phys., 1995,103, 876. 17. Lin, Y.; Beaudet, R. A.; J. Phys. Chem., 1994, 98, 8310. 18. Bunte, S. W.; Chabalowski, C. F.; Wittig, C.; Beaudet, R. A.; /. Chem. Phys., 1993, 97, 5864. 19. Bunte, S. W.; Miller, J. B.; H uang, Z. S.; Verdasco, J. E.; Wittig, C.; Beaudet, R. A.; f. Chem. Phys, 1992, 96, 4140. 20. Jager, W.; Xu, Y.; Gerry, M. C. L.; f. Phys. Chem., 1993, 97, 3685. 21. Dutton, C.; Sazonov, A.; Beaudet, R. A.; J. Phys. Chem., 1996, 100, 17772. 22. Kroto, H. W. Molecular Rotational Spectra; Dover: N ew York, 1992; p 118. 23. Hehre, W. J.; Ditchfield, R.; Pople, J. A.; /. Chem. Phys., 1972,56, 2257. 24. A ndzelm , J.; Klobukowski, M.; Radzio-Andzelm, E.; /. Comp. Chem., 1984,5,146. 25. Boys, S. F.; Bemardy, F.; J. Mol. Phys, 1970,19, 553. 26. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; W ong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92fDPT, Revision G.3; Gaussian, Inc., Pittsburgh, PA, 1993. 27. Hobza, P.; Zahradnik, R. Intermolecular Complexes; Elsevier: New York, 1988; p 6 6 . 28. Stogryn, D. E.; Stogryn, A. P.; Mol. Phys., 1966,11, 371. 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29. Archibong, E. F.Thakkar, A. J.; Chem. Phys. Lett., 1993, 201, 485. 30. Dutton, C.; Beaudet, R. A. To be published. 31. Jucks, K. W.; Huang, Z. S.; Miller, R. E.; Fraser, G. T.; Pine, A. S.; Laffrety, W. J.; /. Chem. Phys., 1987, 88, 2185. 32. Huang, Z. S.; Miller, R. E.; f. Chem. Phys., 1988, 89, 5408. 33. Herzberg, G.; Molecular Spectra and Molecular Structure II; Van Nostrand-Reinhold: New York, 1991; p 394. 34. Fraser, G. T.; Leopold, K. R.; Klemperer, W.; J. Chem. Phys., 1984, 80, 1423. 35. Hinds, K.; Legon, A. C.; Chem. Phys. Lett., 1995,240, 467. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4 THE INFRARED SPECTRUM OF THE OPEN-SHELL C 0 2- 0 2 COMPLEX A lthough there has been an ever growing num ber of van der Waals complexes reported in the literature, there have been only a few studies of open-shell van der Waals species. These species are of particular interest in that the m onitoring of the unpaired electron distribution via hyperfine effects perm its an investigation of electron redistribution on complex formation. Mills et a/ . 1 reported the microwave and radio-frequency spectra of the open-shell Ar-NO van der Waals complex. Their results show a near T-shaped molecule w ith a vibrationally averaged center of mass distance of 3.7lA. A new H am iltonian has been derived for the analysis of the spectrum , where both fine structure and hyperfine effects are considered . 2 W ithin the complex the orbital angular momentum of NO is largely unquenched, but the barrier to free orbital m otion exhibits a m inim um with the ^-electron out of plane of the dim er. N itrogen hyperfine param eters are derived for the complex and are* show n to be slightly perturbed from those of the monomer. However, the overall results are consistent with little electron rearrangem ent on the complex form ation. The four pure rotational transitions of the open-shell complex A r-N 0 2 have been observed by Low and co-workers using a Fourier-transform m icrowave spectrom eter. 3 The spectrum showed fine, magnetic hyperfine and electric quadrupole structure. The data have been fitted to a sem irigid 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ham iltonian to determ ine molecular param eters for the Kt4 = 0 state. The spectral analysis suggested that there is a little or no perturbation of the electronic structure of NO 2 by the Ar atom , at least near the 14N nucleus. The structure of the complex was found to be a m ore or less T-shaped, with large angular zero am plitudes for Ar atom m otions. The van der W aals bond length defined as a distance between Ar and the N O 2 center of m ass is 3.485 A. Bunte et al. presented an infrared study of the N 2 O -O 2 open shell com plex . 4 Symmetrical spectral features w ere observed in the region of V 3 asym metric stretch of N 2 O, b-type transitions dom inated the spectrum . It was concluded that the complex must be nonlinear, probably slipped parallel. Four Q, one P, and one R branches were assigned to bands of Ka : 1 — >0 and 0 — > 1 , however the inconsistency was found in the fitting of Ka ■ 2— > 1 and 1 — *2 transitions. The prelim inary analysis show ed that the distance between centers of mass of the m onomers in this complex is about 3.4 - 3.5 A. The band origin of the complex is slightly blue-shifted from that of free N 2 O. The electron spin of O 2 is not totally quenched in N 2 O-O 2 . In this Chapter, we report a high-resolution infrared spectrum of the CO 2 -O 2 open-shell complex, isoelectronic w ith N 2 O-O 2 . The spectrum was taken within 2345.5 - 2354.0 cm" 1 region by probing the V3 asym m etric stretching m ode of CO 2 . The experimental procedure used in this study is basically described in Chapter 3. Only m inor differences concerning the concentration ratio of clustering gases is im portant: a m ixture of 0.3% of CO 2 and 30% of O 2 in He was used to prevent clustering of carbon dioxide with itself. The backing pressure was between 1.5 and 2 atm. 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.1 A portion of the CO 2 -O 2 spectrum. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IMAGE EVALUATION TEST TARGET (Q A -3 ) 1 . 0 l.l 1.25 U i » 2.8 Li _ Ui I b I: 14 2.2 2.0 1 . 4 1 . 8 1 . 6 150mm IIVUGE . in c 1653 East Main Street Rochester. NY 14609 USA Phone: 716/482-0300 Fax: 716/288-5989 O 1993. Applied Image. Inc.. 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Asset Metadata

Creator Sazonov, Alex (author)

Core Title Infrared spectroscopy and ab initio studies of carbon dioxide van der Waals complexes

School Graduate School

Degree Master of Science

Degree Program Chemistry

Degree Conferral Date 1997-12

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

Tag chemistry, physical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Beaudet, Robert (committee chair), [illegible] (committee member), Flood, Thomas (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-19420

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