10100
J. Phys. Chem. 1996, 100, 10100-10110
Ab Initio Calculations on Fluoroethanes: Geometries, Dipole Moments, Vibrational Frequencies, and Infrared Intensities Stella Papasavva, Karl H. Illinger, and Jonathan E. Kenny* Department of Chemistry, Tufts UniVersity, Medford, Massachusetts 02155 ReceiVed: January 2, 1996; In Final Form: March 20, 1996X
Ab initio calculations have been performed at the MP2/6-31G** level for the series of fluorinated ethanes, C2HnF6-n, n ) 0-5. The resulting geometries, dipole moments, vibrational frequencies, and absolute infrared intensities are reported for stable conformers of the series, including both anti and gauche species, together with their energy differences, for 1,2-difluoroethane, 1,1,2-trifluoroethane, and 1,1,2,2-tetrafluoroethane. The results are compared to available experimental data. In particular, because of the importance of members of this series as potential CFC substitutes, the accuracy of the computational results for infrared frequencies and intensities is discussed, including the dependence on basis set, for calculations at the MP2 level of the theory.
Introduction International efforts have targeted the phase-out of chlorofluorocarbons (CFC) at the end of 1995 in order to avoid further stratospheric ozone depletion. Temporary replacements have been proposed, and some have already been introduced. These include hydrofluorocarbons (HFC) and hydrochlorofluorocarbons (HCFC). The ozone depletion potentials1 of the former are zero and those of HCFCs are more than 90% lower than those of CFCs. Even though HFCs do not deplete the ozone layer, they still pose a threat to the environment because they potentially contribute to enhanced global warming. A salient measure of this contribution is the total absolute infrared intensity in the atmospheric window to the terrestrial blackbody radiation, Awin, in the frequency range 700-1500 cm-1. Our goal is to determine whether ab initio computational methods for infrared spectroscopic properties give results that are in good agreement with experiment. To the extent to which they do, they may then be used in cases where experimental data are not available; in addition they will permit examination of trends in the absolute infrared intensity of molecular systems, and hence the trends in Awin. In this study, we address the series of fluorinated ethanes, C2HnF6-n (n ) 0-5), which includes a number of proposed CFC substitutes, including one of the most widely used, HFC-134a. While the literature contains a number of ab initio studies that investigate the structural parameters of the molecules addressed here, either the reported results are at a lower level of theory2-4 or results obtained at a higher level5 are not based on frequency calculations that provide energy minima with certainty. The geometry optimizations reported here are always coupled with frequency calculations, and we report potential energy minima for each molecule. We present calculations for equilibrium geometries, dipole moment components, vibrational frequencies, and absolute infrared intensities for individual vibrational fundamentals, using the GAUSSIAN92 software.6 Furthermore, we provide extensive comparison between theory and available experimental data. Computational Methods The accuracy of the ab initio methods is related to the choice of basis sets. Minimal basis sets, such as STO-3G, use fixedsize atomic orbitals and often give unrealistic results. Basis sets without polarization functions compute molecular paramX
Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(96)00017-2 CCC: $12.00
eters that deviate considerably from the experimental values.7 When polarization functions, which are expressed as d-type orbitals and denoted as *, are introduced into all first-row elements, the results improve significantly. Basis sets that include polarization functions on all atoms, including p-type functions for hydrogen, and denoted as **, do not change the results significantly. We have performed calculations with Møller-Plesset secondorder perturbation theory (MP2), using double-split (6-31G**) and triple-split (6-311G**) basis sets. While we have also examined the accuracy of the HF level of theory with various basis sets, only the more accurate MP2/6-31G** results are reported here. They appear to be a viable compromise between accuracy of method and the limitations on the size of the molecular systems that can be efficiently computed. Results and Discussion I. Equilibrium Geometries. In this paper, we utilize the modifier, clustered, for those isomers of the fluoroethanes which have a maximum number of fluorines on one of the two carbon atoms; their more symmetrically substituted counterparts are referred to as unclustered. For the clustered fluoroethanes, we have performed unconstrained geometry optimizations, which result in the staggered conformations. The symmetry point group of all but CF3CH3 and CF3CF3 in their staggered conformations is Cs, whereas that of trifluoroethane is C3V and that of perfluoroethane is D3d. For the unclustered fluoroethanes, calculations were performed for both anti and gauche conformations. For 1,2difluoro- and 1,1,2,2-tetrafluoroethane, the anti conformations are more symmetrical than the gauche conformations. The former belong to the C2h symmetry point group, with the unique atoms on each of the methyl groups defining a 180° torsional angle about the C-C bond. The gauche conformations belong to the C2 point group, with the unique atoms oriented at a 60° torsional angle. For 1,1,2-trifluoroethane, the anti conformation has C1 symmetry, whereas the gauche conformation, with the unique atoms on each methyl group defining a 180° torsional angle, has Cs symmetry. We compare our results to those determined in previous experimental and theoretical studies in Tables 1 and 2. Not infrequently, structures determined from experimental quantities are based inter alia on assumptions concerning © 1996 American Chemical Society
Ab Initio Calculations on Fluoroethanes
J. Phys. Chem., Vol. 100, No. 24, 1996 10101
TABLE 1: Equilibrium Geometries of Clustered Fluoroethanes
experiment EDa C1C2 C1H1 C2H4 C1F1 C2H3 ∠C2C1H1 ∠C1C2H4 ∠C1C2H3 ∠F1C1H1 ∠C2C1F1 ∠H1C1H2 ∠H4C2H5
MWb
1.502 1.097 1.097 1.397 1.097 113.6 113.6 113.6 109.4 110.4 100.0 105.0
1.505 1.095 1.090 1.398 1.091 112.9 109.7 106.1 109.7 108.8 108.9
experiment MP2/6-31G**m 1.509 1.091 1.088 1.398 1.089 111.5 110.3 110.3 107.9 109.3 108.6 108.6
EDc C1C2 C1H1 C2H2 C1F1 ∠C2C1H1 ∠C1C2H2 ∠C1C2H4 ∠F1C1H1 ∠C2C1F1 ∠H3C2H4 ∠F1C1F2
experiment
MWd
1.498 1.081 1.081 1.364 111.0 111.0 111.0 108.5 110.7 107.9 107.4
MP2/6-31G**m
1.540 1.100 1.100 1.345 109.5 109.5 109.5
1.499 1.090 1.087 1.373 114.2 108.7 110.0 107.7 109.7 109.4 107.5
109.3 110.1 109.8
EDe C1C2 C2H2 C1F1 ∠C1C2H2 ∠C2C1F1 ∠H2C2H3 ∠F2C1F3
1.494 1.081 1.340 112.0 111.9
MWf 1.492 1.078 1.348 109.4 112.1 109.3 106.4
MP2/6-31G**m 1.497 1.086 1.354 109.2 111.6 109.7 107.2
Rotational Constants exp A (MHz) B (MHz) C (MHz)
36070.30 9364.54 8199.74
exp 36104 9420 8239
9491.95 8962.65 5040.0
experiment ED C1C2 C1F1 C1F2 C2F4 C2H1 ∠C2C1F1 ∠C2C1F2 ∠C1C2F4 ∠C1C2H1 ∠F2C1F3 ∠F1C1F2 ∠H1C2H2 ∠H1C2F4
g
1.501 1.334 1.334 1.389 1.077 110.4 110.4 112.3 106.1 108.6 108.6 109.4 111.4
MWh 1.525 1.336 1.336 1.345 1.090 108.9 112.1 109.7 112.9 107.8 108.9 106.1
exp 5510.89l 5185.36 5185.36
9331 9043 5152
experiment MP2/6-31G**m 1.508 1.353 1.346 1.382 1.088 109.1 111.6 108.7 108.9 108.0 108.2 110.3 109.9
EDi C1C2 C1F1 C1F3 C2F4 C2H1 ∠C2C1F1 ∠C2C1F2 ∠C1C2F4 ∠C1C2H1 ∠F3C1F2 ∠F3C1F1 ∠F4C2F5 ∠H1C2F4
1.525 1.327 1.327 1.347 1.09 110.0 110.0 110.0 109.0 109.0 109.0 108.0 109.9
MWj 1.520 1.335 1.335 1.345 1.10 109.6 110.0 108.1 108.1 109.1
5405 5164 5164
experiment MP2/6-31G**m 1.521 1.339 1.345 1.358 1.088 111.1 108.3 109.6 111.3 108.6 109.0 109.3 109.8
C1C2 C1F1 ∠C1C2F4 ∠F2C1F3
EDk
MP2/6-31G**m
1.545 1.326 109.7 109.1
1.530 1.339 109.7 109.2
Rotational Constants exp A (MHz) B (MHz) C (MHz) a
j
5355.63 2799.24 2759.45
exp 5286 2794 2760
3691.01 2419.70 2005.99
3623 2433 2004
2786 1847 1847
Reference 11. b Reference 9. c Reference 12. d Reference 13. e Reference 16. f Reference 17. g Reference 18. h Reference 19. i Reference 11. Reference 21. k Reference 22. l Reference 43. m Present study. The experimental rotational constants are from the MW studies.
10102 J. Phys. Chem., Vol. 100, No. 24, 1996
Papasavva et al.
TABLE 2: Equilibrium Geometries of Unclustered Fluoroethanes
MP2/6-31G** (our work) C1C2 C1F1 C2H4 C2H3 ∠C1C2H4 ∠C2C1H2 ∠F1C1C2 ∠H2C1H1 ∠H1C1F1 ∠H3C2F2 τFCCF
1.512 1.394 1.089 1.089 110.6 110.6 107.8 109.4 109.2 109.2 180.0
C1C2 C1F1 C2H4 C2H3 ∠C1C2H4 ∠C2C1H2 ∠F1C1C2 ∠H2C1H1 ∠H4C2F2 ∠H3C2F2 τFCCF
ED29
MW30
MP2/6-31G** (our work)
1.503 1.389 1.103 1.103 110.0 110.0 110.3 108.5 109.0 109.0 71.3
1.493 1.390 1.099 1.093 108.4 111.3 110.6 109.1 109.6 107.8 71.0
1.502 1.391 1.090 1.092 110.2 110.0 109.7 109.5 108.6 108.8 68.7
Rotational Constants experimental A (MHz) B (MHz) C (MHz)
31950 3873 3612
ref 44
ref 30
17322.42 5013.11 4382.78
17322.39 5013.15 4382.72
MP2/6-31G** (our work) C1C2 C1H1 C2H3 C2H2 C1F1 C1F2 C2F3 ∠C2C1F2 ∠C2C1F1 ∠C1C2F3 ∠C2C1H1 ∠C1C2H2 ∠C1C2H3 ∠F3C2H3 ∠H2C2H3 ∠F2C1F1
1.505 1.092 1.090 1.090 1.367 1.367 1.383 109.7 109.7 109.2 112.1 109.5 109.5 109.4 109.8 108.0
τ(F3C2C1H2)
180.0
A (MHz) B (MHz) C (MHz)
7290 4264 3477
ED15 C1C2 C1H1 C2H3 C2H2 C1F1 C1F2 C2F3 ∠C2C1F1 ∠C2C1F2 ∠C1C2F3 ∠C2C1H1 ∠C1C2H2 ∠C1C2H3 ∠F3C2H2 ∠H1C1F2 ∠H1C1F1 ∠H2C2H3 ∠F2C1F1 τ(H2C2C1H1)
1.500 1.088 1.088 1.088 1.353 1.353 1.387 109.0 109.0 109.0 108.9 108.9 108.9
120.9 106.8 160.0
16904 5130 4437
MP2/6-31G** (our work) 1.506 1.089 1.089 1.089 1.371 1.365 1.388 107.8 109.6 108.4 113.4 108.9 109.9 109.8 108.5 109.1 110.1 108.4 174.8
Rotational Constants (Our Work) 9024 3659 2809
Ab Initio Calculations on Fluoroethanes
J. Phys. Chem., Vol. 100, No. 24, 1996 10103
TABLE 2 (Continued)
ED14 C1C2 C1H1 C1F1 C2F3 ∠C1C2F4 ∠C2C1F2 ∠C2C1H1 ∠H1C1F1 ∠F1C1F2 τ(H1C1C2H2) A (MHz) B (MHz) C (MHz)
1.518 1.098 1.350 1.350 108.2 108.2 110.3 107.3
MP2/6-31G** (our work)
MP2/6-31G** (our work)
1.513 1.089 1.363 1.363 108.3 108.3 112.0 109.7 108.8 180.0
C1C2 C1H1 C1F1 C2F3 ∠C1C2F4 ∠C2C1F2 ∠C2C1H1 ∠H1C1F1 ∠F3C2F4 τ(F1C1C2H2)
Rotational Constants (Our Work) 5026 3179 2062
selected geometrical parameters, in order to permit the complete analysis of the data. For this reason, in some cases the experimental results give unrealistic values for certain geometrical structural features. This needs to be taken into account when the theoretical values are compared with those experimentally determined. In particular, we found that there is considerable discrepancy in the attribution of C-C bond lengths for these systems in the microwave and electron diffraction experimental values in the literature. For this reason, the correctness of our computed geometries was also checked by comparing the computed rotational constants with those determined from microwave spectroscopy (Tables 1 and 2). The computed results agree with the experimental to within 1% for the unclustered molecules. In those cases where there is disagreement between the calculated results for individual structural features and the values assumed in the experimental analysis, in spite of the correct ab initio prediction of the experimental data, e.g., rotational constants, there is good reason to believe that the assumed values are at fault. This suggests that ab initio calculations, at a sufficiently high level of theory, should be employed as a guide in choosing assumed values for structural parameters required in the experimental analysis. Clustered Fluoroethanes C2HnF6-n (n ) 0-5). (i) n ) 3, 4, and 5. We initially examine the trends of the geometrical parameters for the first three compounds of the series CH2FCH3, CHF2CH3, and CF3CH3. This is done because trends in the series are not strictly monotonic but are modulated when the fourth F atom is introduced. This observation is in agreement with calculations2 performed both at a lower level of theory, HF/6-31G*, as well as with the MP2/6-31G* method5 using Gaussian-90. These results are in very good agreement with our calculations, to within 1%. The general observation has been made that geminal interactions play a key role in the equilibrium geometries of all the clustered fluoroethanes.7 Such interactions lead to a significant shortening of the C-F bond lengths as more fluorines are added to a given carbon atom. Speis and Buss8 investigated the geometry of CHF2CH3 at both the HF and MP2 level with Gaussian-90 using a variety
1.515 1.089 1.359 1.365 109.2 108.1 112.0 109.3 109.0 173.2 5178 2867 2512
of basis sets. Our computed geometrical parameters for comparable basis sets are in agreement to within 1%. The results of our calculations performed at the MP2/6-31G** level predict that the C-C, C-H, and C-F bond lengths decrease as more F atoms replace H atoms on a given C atom. The ∠C2C1H1 bond angle increases by about 3° when a second H is substituted by F. The ∠CCH bond angles involving the equivalent H atoms of the -CH3 group do not change substantially, while those involving the inequivalent H atoms of the -CH3 group decrease by 1.6°. The ∠HC2H bond angles involving equivalent H atoms increase as the number of F atoms bonded to the first C atom increases. The ∠C2C1F bond angle remains almost unchanged in the first two molecules, whereas it increases beyond tetrahedral by 2° in CF3CH3. The ∠FC1H bond angles are not appreciably affected by the increase in the number of F atoms. The ∠FC1F angles are calculated to be smaller than tetrahedral by 2°. CH2FCH3. The structural parameters of fluoroethane have been investigated by both microwave spectroscopy and electron diffraction. One study9 analyzes previous microwave experimental work10 and provides a more realistic value for the C-C bond length, which had previously been overestimated. Our computational results and this reanalysis are consistent in pointing out the differences in ∠CCH angles, which electron diffraction constrained to be equal at 113.6°. This constraint also forced a value of 100° on the ∠HCH angle of the -CH2F group, which is inconsistent with the microwave and ab initio calculated results, which are in good agreement. The electron diffraction study assumes all C-H bond lengths to be equal, whereas those obtained from the microwave experiment are different and are in better agreement with our computed values. The computed rotational constants agree with the microwave data to better than 1%. CHF2CH3. For 1,1-difluoroethane two experimental studies12,13 were found in the literature. The microwave study assumes all four C-H bond lengths to be equal and fixes the C-C bond distance at 1.540 Å, which is probably unrealistic. The value found by electron diffraction12 is 1.498 Å, which appears to be more representative of fluorinated compounds.14-16
10104 J. Phys. Chem., Vol. 100, No. 24, 1996 The experimental data obtained from electron diffraction were refined with a least-squares fit using vibrational amplitudes transferred from normal-coordinate calculations on related molecules. The electron diffraction study assigns a common radial distribution peak to identical C-H bond distances. This is not in agreement with the theoretical results, which estimate that the C-H bond length in the -CHF2 group is longer than all the others by 0.003 Å, a relatively small difference, but nevertheless outside the computed mean absolute error.7 The microwave study provides a value for the ∠FCF bond angle which is larger than tetrahedral, in contrast to both the electron diffraction study and our computed results. The electron diffraction study assumes that all ∠CCH bond angles in the -CH3 group are equal, owing to the 3-fold symmetry of the group, and provides a mean value for all ∠CCH angles. However, our computed values predict ∠C2C1H1 to be larger than ∠C1C2H2 by 5.5°. Both theory and experiment predict that the ∠C2C1F bond angles become larger when more F atoms are introduced. The computed rotational constants differ from the microwave values by 1-2%. CF3CH3. Experimental results for CF3CH3 from microwave17 and electron diffraction16 experiments are in good agreement with each other and verify the trends of our computed values. The computed rotational constants deviate from the experimental values by less than 2%. (ii) n ) 0, 1, and 2. For the remaining three clustered compounds, CF3CH2F, CF3CHF2, and CF3CF3, we find the following trends. When the fourth F atom replaces one of the three hydrogens on the second C atom, the C-C bond length increases. The C-C bond lengths continue to increase when the fifth and sixth F atoms are introduced. The effect of increasing the number of F atoms at the second C is to decrease the C2-F bond lengths. The computed value obtained for the C2-F bond length of CF3CH2F, 1.382 Å, is reduced to 1.358 Å when the fifth F atom is added; in CF3CF3, all C-F bond lengths are equal and have the smallest value found among all the molecules in the series, 1.339 Å. The C-H bond lengths of tetra- and pentafluoroethane are equal. The ∠CCF bond angles present the following trends: ∠C2C1F1 becomes larger by 2° in pentafluoroethane compared to 1,1,1,2-tetrafluoroethane, in which it is almost tetrahedral. This may be explained by the increase in the electrostatic repulsion between the F atoms. ∠C1C2F4 also increases by 1° in pentafluoroethane. However, the ∠C2C1F2 bond angle decreases by 3.3° in CF3CHF2 compared to that of CF3CH2F. The ∠HCH bond angle in 1,1,1,2-tetrafluoroethane follows the monotonically increasing trend observed in the earlier members of the entire series. The trends for the entire series, based on our computed results, are in agreement with those previously reported.5 The experimental study18 reports trends for the geometrical parameters in the series which are in agreement with our computed results. CF3CH2F. For CF3-CH2F a microwave19 and an electron diffraction study18 are available in the literature. The microwave study reports three sets of structural parameters, the best of which is considered to be that which optimally reproduces the observed moments of inertia. The structure based on this set carries with it the assumption that all C-F bond lengths of the -CF3 group are equal. A more extended discussion of the geometry of this molecule has been given in previous work.20 Electron diffraction obtains a C-C bond length shorter by 0.024 Å, but a C2F4 distance longer by 0.044 Å, than those found in the microwave study. Our computed results are in better agreement with those obtained from electron diffraction. The computed rotational constants, however, agree with the microwave values to within 1.5% or better.
Papasavva et al. CF3CHF2. Microwave21 and electron diffraction11 experiments have been performed for pentafluoroethane. The microwave structure assumes the -CF3 group to be symmetrical, with its axis collinear with the C-C bond, and the two fluorine atoms of the -CHF2 group to be equivalent. The ∠FCF values are consistent with the smaller than tetrahedral values in the ∠FCF bond angles found in all other compounds of the series, both experimentally and computationally. The experimental C-C bond length is in excellent agreement with the computed value. The computed ∠CCH value of CF3CHF2 is larger than the corresponding value in CF3CH2F, in agreement with the electron diffraction result, but in contrast to the microwave study. The computed rotational constants are within 2% of the experimental values. CF3CF3. The experimental electron diffraction22 results for CF3CF3 are in excellent agreement with our computed results and are consistent with the above-mentioned trends. Unclustered Fluoroethanes. Several ab initio calculations were found in the literature for the compounds in this series. Most of them use restricted Hartee-Fock (RHF) methods for the estimation of molecular parameters. The most recent study3 investigates the equilibrium geometries, barriers for internal rotation, harmonic vibrational frequencies, energies and thermodynamic properties for CHF2CH2F and CHF2CHF2 at the RHF/6-31G* level using the Gaussian-92 software. Martell and Boyd5 obtain results, in addition to those on the series of clustered ethanes, for the most energetically stable isomers of di-, tri-, and tetrafluoroethanes, which are the gauche conformation for the first molecule and the anti for the latter two. The geometry optimizations were performed at the MP2/6-31G* level, using the Gaussian-90 software. The two conformations, anti and gauche, of 1,2-difluoroethane have been investigated4 with RHF/6-311++G**. Two earlier studies24,25 using the HONDO and NDDO programs have examined a set of fluoroethanes. We carried out ab initio calculations at the MP2 level for the gauche and anti conformations of all three compounds in the series. Experimental results for the geometrical parameters are available only for stable conformers. The experimental and theoretical values are presented in Table 2. Both series qualitatively reproduce the pattern exhibited in the clustered case, with the single exception of the anti conformer of CH2FCH2F, whose C-C bond length is slightly larger than that of fluoroethane. CH2FCH2F. A 1960 study26 reports the vibrational spectrum of 1,2-difluoroethane. Subsequent work27-29 found that the gauche conformer is more stable than the anti conformer in the gas phase. Experimental results using infrared and Raman spectroscopy as well as NMR indicate that the gauche conformer is more favorable in the gas phase, with an energy difference4 in the range between 0.57 ( 0.09 and 1.98 ( 0.08 kcal/mol. Experimental structural parameters are reported only for the gauche conformer from electron diffraction29 and microwave experiments.30 Our calculations at the MP2 level also predict that the gauche structure is the more stable, by 0.15 kcal/mol. The results of our calculations at the MP2 level predict that for the gauche conformer the C-C and C-F bonds are shorter by 0.010 and 0.003 Å, respectively, whereas the C2H3 bond is longer by 0.003 Å, compared to those of the anti compound. In addition, the ∠F1C1C2 bond angle in the gauche structure is almost tetrahedral and is larger by 2° than in the anti. This corroborates the trends found in all previous ab initio studies.2,4,5,24 We predict an ∠FCCF dihedral angle for the gauche conformation of 68.7°. This value compares to the range of values, 70.4-69.3°, reported in previous theoretical work.2,4,5 The experimental values obtained from both electron diffraction
Ab Initio Calculations on Fluoroethanes and microwave techniques are in good agreement with each other, except for the C-C bond length and ∠C1C2H4 bond angle. The former is found to be shorter by 0.010 Å, and the latter smaller by 1.6° in the microwave study. The computed results from all ab initio studies are in better agreement with the electron diffraction experiment. Both experiments found a value of 71° for the dihedral angle. Our computed rotational constants obtained at the MP2 level agree with the experimental ones to within 2.5%. CHF2CH2F. A recent study28 is based on the examination of far- and mid-infrared spectra of the gas and solid states of CH2FCHF2, as well as Raman spectra from all of its phases. Prominent differences in the Raman spectra of gas, liquid, and solid states imply that the C1 structure is the more stable in the gas phase, in agreement with previous studies,31,32 whereas the Cs structure is more stable in the liquid phase, and only the Cs conformer exists in the crystalline form. Both experiment and theory, at the HF and MP2 levels, find that in the gas phase the conformer with C1 symmetry is the more stable. Our HF/6-31G** calculation predicts an energy difference, ∆E, between the anti (C1) and gauche (Cs) conformations, of 1.90 kcal/mol, identical with the value found3 with HF/6-31G*. At the MP2/6-31G** level we predict a ∆E equal to 1.60 kcal/mol, whereas ref 3 finds a value of 1.66 at the MP2/6-311G** level. An experimental study28 finds ∆E equal to 1.6 ( 0.4 kcal/mol. Electron diffraction15 of the gas at 265 K is consistent with the C1 structure. Our computed values at the MP2 level are in good agreement, to within 2%, with those of previous theoretical work2,3 with the HF method. The analysis of the experimental data assumes that all ∠CCF bond angles are equal, as well as all the ∠CCH angles. This is not borne out by any of the ab initio studies. The major discrepancy between the computed and measured geometrical parameters lies in the ∠H2C2H3 bond angle, which is found to be significantly larger, by 11°, in the electron diffraction experiment, than in all theoretical studies. The experimental value of the ∠HCCH dihedral angle is smaller by up to 15° than the calculated values. These discrepancies have been discussed previously.3 CHF2CHF2. Infrared and Raman spectra33 for CHF2CHF2 show that the anti conformation, which belongs to the C2h symmetry group, is energetically more stable in the gas phase than the gauche form, C2, in agreement with other work.28 Experimentally the energy difference between the anti and gauche conformations is determined to be between 1.2 and 2.4 kcal/mol, as summarized in ref 3. Our computations also found the C2h conformer to be more stable by 1.65 kcal/mol. This result agrees to within 5% with other computed values.3 The results of our calculations for both anti and gauche compounds are in good agreement with previous ab initio studies,3,5 to within 2%. The computed values of the C-C bond lengths of both molecules are almost equal and have approximately the same value found for the anti conformation of CH2FCH2F. The C-H bond lengths of both structures are equal; in fact, their values do not change substantially in the entire series of nonclustered fluoroethanes. The C-F bond lengths are slightly shorter, by 0.004 Å, in the gauche compound and follow the decreasing trend, similar to that found in the series of clustered ethanes as more F atoms are introduced into the molecule. The ∠C1C2F4 and the ∠FCF bond angles increase by 1 and 2°, respectively, in the gauche conformer, with respect to those found in the anti. The results of an electron diffraction study14 are in excellent agreement with the computed values with the only exception being the ∠CCH bond angle, which is found experimentally to be 2° smaller than the theoretical value.
J. Phys. Chem., Vol. 100, No. 24, 1996 10105 We were not able to find experimental rotational constants for either CHF2CH2F or CHF2CHF2. However, our HF/631G** results are within 1% agreement with those obtained by another study3 at the same level. II. Vibrational Frequencies. The harmonic-oscillator approximation is employed for the calculation of fundamental vibrational frequencies, generally resulting in values larger than those from experiment. A recent study,34 based on a comparison of a total of 1066 calculated frequencies for 122 molecules with corresponding experimental values, recommends that for frequencies computed at the HF/6-31G* level a scaling factor of 0.8929 should be applied, whereas at the MP2/6-31G* level the factor 0.9427 is suggested. Ab initio calculations at the MP2 level estimate frequencies below 800 cm-1, with better accuracy (3% on average) than higher frequencies (average error 10% or better). For this reason new scaling factors have been determined for obtaining corrections to the calculated fundamental frequencies in different regions of the spectrum.35 In an alternative approach,36 scaling factors were obtained for a series of chlorofluorocarbons calculated with HF/3-21G** using potential energy distribution weighted averages. On the basis of our calculations at the MP2/ 6-31G** level, we found for the series of fluorinated ethanes that the ratio of experimental to computed values is in the range 0.95-0.99 for frequencies
