J . Phys. Chem. 1992,96, 1702-1705
1702
lations presented here give no information. We should point out that in the comparable system H2CO-OH-differential solvation of OH- and HO-CH20- creates a situation in waterz3 which is inverted with respect to the gas phase and the reaction becomes endoenergetic. We suspect that the H3PO-OH- system also closely mimics the HzCO-OH- in water and that the generation of this condensed-phase anionic pentacoordinated system is an
endoenergetic process. Based on experimental data, formation of anionic pentacoordinated intermediates are proposed to have endothermic free energies (e.g. see refs 2 and 10).
Acknowledgment. The authors thank both the Algerian and French Governments for funding the collaborative effort reported here.
Ab Initio Study of Conformational Energies and Rotational Barriers in a Chiorofiuoroethane
H.L. Paige Materials Directorate, Wright Laboratory, Wright-Patterson Air Force Base, Ohio 45433-6533
and M. Schwartz* Department of Chemistry, University of North Texas, Denton, Texas 76203 (Received: September 23, 1991)
The geometries and relative energies of the equilibrium- and transition-state conformations of 1,1,2-trichloro-1,2,2-trifluoroethane were studied by ab initio calculations using basis sets ranging from 3-21G through 6-31lG(2df). Bond lengths and angles calculated with the 6-31G(d) and 6-31 1G(d) bases were in close agreement with each other and with experimental results. Comparable energies of the equilibrium conformers and torsional barriers were obtained by MP2 calculations using the 6-31G(d), 6-311G(d), and 6-31lG(2df) bases. The calculated equilibrium energy difference is in qualitative agreement with experimental results. Scaled vibrational frequencies calculated with the 6-31G(d) basis set are also in substantial agreement with experimental data for the equilibrium conformers. It was concluded that results using the 6-31G(d) basis set provide satisfactory structural parameters and conformational energies, comparable to those obtained using larger polarized bases.
Introduction An understanding of the properties and reactions of various halocarbon molecules is essential for the development of stable, high-temperature fluids and lubricants. Of primary importance are modes of decomposition and interactions with metal surfaces and an understanding of the effect of molecular structure on viscosity-temperature characteristics. Experimental investigations of systems of interest are in progress. Concurrent with these studies, we have undertaken a theoretical study designed to help interpret experimental results. The present paper describes a computational study of a chlorofluorocarbon, 1,l,Ztrichloro- 1,2,2-trifluoroethane (TCTFE). This molecule was selected because its structural, energetic, and vibrational properties have been well characterized experimentally and because the molecule is small enough to permit high-level ab initio calculations. While there have been several theoretical studies of dichloro- and difl~oroethane,'-~to the authors' knowledge, this represents the first quantum mechanical investigation of a chlorofluoroethane. Presented are comparisons of properties calculated with vairiousbasis sets and comparisons of calculated and experimental values.
convenience, the two equilibrium geometries, C,and C,,are termed gauche (G) and trans (T), respectively, to denote the relative positions of the lone fluorine (F,) on the first carbon atom and the single chlorine (Cl,) on the second carbon; the transition-state structures are called G T and GG'. Projections for the four conformations are given as follows.
G
Calculations Ab initio molecular orbital calculations were performed using the GAUSSIAN 905 program on a Cray X-MP/216 computer. For (1) Radom, L.; Baker, J.; Gill, P. M. W.; Nobes, R. H.; Riggs, N. V . J . Mol. Srrucr. 1985, 126, 271. (2) Wiberg, K. B.; Murcko, M. A. J . Phys. Chem. 1987, 91, 3616. (3) Miyajima, T.; Kurita, Y.; Hirano, T. J . Phys. Chem. 1987, 91, 3954. (4) Dixon, D. A.; Smart, B. E. J . Phys. Chem. 1988, 92, 2729. (5) Gaussian 90, Revision F; Frisch, M. J., Head-Gordon, M., Trucks, G . W., Foresman, J. B., Schlegel, H. B., Raghavachari, K., Robb, M., Binkley, J . S:,Gonzalez, C., Defrees, D. J., Fox, D. J., Whiteside, R. A,, Seeger, R., Melius, C. F., Baker, J., Martin, R. L., Kahn, L. R., Stewart, J . J. P., Topiol, S., Pople, J . A.; Gaussian, Inc.: Pittsburgh, PA, 1990.
0022-3654/92/2096- 1702$03.00/0
The equilibrium and saddle point geometries were gradient optimized6 with the following basis sets: 3-21G,' 6-31G,8 D95,9 (6) Pulay, P. In Applicarions of Elecrronic Structure Theory; Schaefer, H. F., 111, Ed.; Plenum Press: New York, 1977; p 153. (7) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; Defrees, D. J.; Pople, J . A.; Binkley, J. S. J . Am. Chem. Soc. 1982,104, 5039, and references contained therein.
0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1703
Energies and Conformations of a Chlorofluoroethane TABLE I: Calculated Structural Parameters"
T 1.38 (0.02,j 1.33 (0.014) 1.33 (0.014) 1.75 (0.027) 1.76 (0.02) 1.76 (0.02) 1O7.lc 108c (1.5) 108c (1.5) 112c (1.5) 112c (2.0) 112c (2.0) 108.7c 1 10.5c (1) 5 9 s (1.5)
1.363 1.345 1.345 1.829 1.821 1.821 106.1 108.7 108.7 112.6 111.3 1 1 1.3 109.2 1 1 1.6 180.0
1.529 1.373 1.360 1.360 1.801 1.808 1.808 105.5 108.3 108.3 114.6 112.0 111.9 107.7 111.6 180.0
1.552 1.324 1.313 1.313 1.751 1.756 1.756 105.6 108.0 108.0 114.0 111.3 111.3 107.8 111.4 180.0
1.549 1.330 1.318 1.318 1.749 1.754 1.754 104.9 107.6 107.6 114.5 111.6 111.6 107.9 111.6 180.06
G
GT
GG'
1.550 1.320 1.311 1.313 1.756 1.761 1.756 107.6 109.7 108.3 112.1 109.5 111.4 108.4 110.5 58.0
1.599 1.321 1.311 1.311 1.756 1.759 1.762 106.6 107.2 110.0 115.9 114.6 111.0 107.5 109.4 120.4
1.595 1.319 1.31 1 1.311 1.756 1.761 1.761 109.4 110.3 110.3 112.1 111.2 111.2 107.0 110.0 0.0
Bond lengths in angstroms and angles in degrees. bReference 18. cAssumed values from structures of CF2CICF2C1and CFCl2CFCI2.l9dQuoted experimental uncertainties in parentheses. 'Dihedral angle of the gauche conformer. @ = 180° was assumed for the trans conformation.
6-31G(d),8*10and 6-31 1G(d).IoJ1 Calculations on the four conformers were also performed with the 6-31 1G(2df)10J1basis set using the 6-3 11G(d) geometries. Single point second order Maller-Plesset12 (MP) correlation energy calculations, with the frozen core approximation, were performed with the 6-3 lG(d), 6-31 lG(d), and 6-31 lG(2df) basis sets. In addition, vibrational force fields and frequencies were obtained for all conformers using the 6-31G(d) basis set. For comparison, MND0,13 AMl,14 and PM315semiempirical energy calculations were performed with the program M O P A C . ~ ~ As above, all structural parameters were optimized for both equilibrium- and transition-state conformations.
Results and Discussion Geometries. Tabulated in columns 3-7 of Table I are the structural parameters for the trans conformer calculated with the various basis sets used in this study. The results from the D95 (double-f) basis set are not included since, not surprisingly, they are quite similar to those obtained with the 6-31G (doubly-split valence) basis. One observes that structural parameters determined with the two polarized basis sets, 6-31G(d) and 6-3 1lG(d), are generally quite close; calculated bond lengths are the same to within 0.002-0.006 A and bond angles differ by an average of LCCF, in the G rotamer is due to the fact that fluorine F2 has two gauche interactions with chlorine atoms compared to only one for F, (see diagram above). Simarly, LCCF, and LCCF, are greatest in the GG' transition state, which is the only conformation in which they eclipse chlorine atoms. Energies. Displayed in Table I1 are the energies and energy differences (relative to the T conformer) calculated at the SCF and MP2 levels using the various basis sets. One finds that all ab initio calculations yield negative values for the energy difference, M(G-T), which, at the SCF level, ranges from -0.7 to -0.8 kcal/mol for the two largest basis sets. The correlation energy correction is small, lowering AE by 0.0-0.2 kcal/mol. As seen in Table 111, there is no further correction to the equilibrium energy difference arising from zero point vibrational energy (ZPVE) and thermal contributions to the enthalpy (vide infra). Thus the final calculated range is M(G-T) = -0.6 to -0.7 kcal/mol, which is in qualitative agreement with experimental estimates; AH(exp) = AE(exp) = -0.25 to -0.35 22 kcal/mol. One sees also from the table that both transition-state energies, M(GT-T) and M(GG'-T), generally increase with the size of the basis set. The correlation energy correction to M(GT-T) is -0.0to -0.3 kcal/mol. Together with a -0.4 kcal/mol correction from A[ZPVE] and A[H(T) - H ( 0 ) ] (Table 111), one obtains a net energy barrier, AE(GT-T) = 8.7-9.1 kcal/mol (with the three largest basis sets). This value lies within the range determined (20) (a) Dixon, D. A.; Fukunaga, T.; Smart, B. E. J . Am. Chem. Sot. 1986,108, 1585,4027. (b) Dixon, D. A. J . Phys. Chem. 1986.90.2038. (c) Dixon, D. A.; Arduengo, A. J., 111. Ibid. 1987, 91, 3195. (d) Dixon, D. A. Ibid. 1988, 92, 86. (21) Braathen, G. 0.;Gatial, A.; Klaeboe, P. J . Mol. Struct. 1987, 157, 13.
(22) Klaeboe, P.; Nielsen, J. R. J . Mol. Spectrosc. 1961, 6, 379.
Paige and Schwartz
1704 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 TABLE II: Calculated Conformational Energies basis set HF/3-21G HF/6-31G HF/D95 HF/6-3 1G(d) HF/6-31 lG(d)
HF/6-311G(2df)//6-311G(d) MP2/6-31G(d) MP2/6-311G(d) MP2/6-31 lG(2df)//6-31 lG(d) HF/3-21G HF/6-3 1G HF/D95 HF/6-3 1G(d) HF/6-311G(d)
HF/6-311G(2df)//6-311G(d) MP2/6-3 1G(d) MP2/6-311G(d) MP2/6-311G(2df)//6-3 1 lG(d) MNDO AM 1 PM3 experiment
’Reference 21.
T G A. Total Energies (hartrees) -1743.84244 -1743.848 03 -1752.247 87 -1752.25068 -1752.31081 -1752.3 12 21 -1752.458 57 -1752.460 12 -1 752.630 64 -1752.631 75 -1752.673 92 -1752.675 17 -1753.624 56 -1753.62606 -1753.933 15 -1753.93424 -1754.27779 -1754.278 75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
B. Relative Energies (kcal/mol) -3.50 -1.76 -0.88 -0.97 -0.69 -0.79 -0.94 -0.68 -0.61 +0.82 +1.13 +0.81 -0.25’ -0.35‘
GT
GG’
-1743.831 07 -1752.234 13 -1752.296 76 -1752.443 56 -1752.615 42 -1752.658 76 -1753.61005 -1753.91797 -1754.263 01
-1743.83902 -1752.238 64 -1752.30086 -1752.447 07 -1752.618 83 -1752.661 81 -1753.613 10 -1753.921 11 -1754.265 66
+7.14 +8.62 +8.82 +9.42 +9.55 +9.51 +9.11 +9.52 +9.27 +5.17 +5.15 +2.86 +5.9b +5.10d
+2.15 +5.79 +6.25 +7.22 +7.41 +7.60 +7.19 +7.55 +7.61 +7.23 +9.21 +3.44
Reference 23. From torsional frequency (IR). ‘Reference 22. dReference 23. From ultrasonic relaxation.
TABLE 111: Thermodynamic Factors’ auantitv
ZPVE H(T) - H(O) A [ZPVE] A[H(T)- H(0)] net correction
G 15.07 5.56 0.00 0.00 0.00
T 15.07 5.56 0.00 0.00 0.00
GT 14.97 5.26b -0.10 -0.30 -0.40
GG’ 14.98 5.27b -0.09 -0.29 -0.38
‘Quantities have been calculated using frequencies scaled by 0.90. They are given at 298.15 K in units of kilocalories per mole. bThe torsional motion at the barriers was treated as free rotation. from ultrasonic relaxation mea~urements,2~ PE(GT-T) = 5.0-1 0.0 kcal/mol. It is somewhat higher than the estimate from the infrared torsional frequency;23however, this latter measurement was subject to potentially large errors.24 It is found that the second transition state, GG’, has a significantly lower energy than GT. With the correlation energy, A[ZPVE], and [H(T) - H(O)]corrections, AE(GG’-T) = 6.8-7.2 kcal/mol. The higher energy of the G T saddle point seems quite reasonable since there is a repulsive interaction between two eclipsed chlorine atoms which is not present in the GG’ conformation. Finally, we note that all three semiempirical method~’~-I~ predict that P E ( G T ) > 0, which disagrees with both experimental and ab initio results. Too, they predict that A(GT-T) < A(GG’-T), in contrast to the ab initio calculations and to chemical intuition. Vibrations. Vibrational frequencies, obtained with the 6-31G(d) basis set, are given in Table IV, together with experimental data for the G and T equilibrium conformers.2’ Calculated frequencies have been multiplied by the scale factor 0.90 to account for corrections due to anharmonicity and electron correlation. Scaled frequencies for the four vibrations above 1000 cm-l remain higher than the observed data, with average errors of 4.2 and 3.5% for the G and T rotamers, respectively. The agreement with experiment is markedly improved for the fourteen vibrational (23) Pethrick, R. A.; Wyn-Jones, E. J . Chem. SOC.A 1971, 54. (24) In addition to making the required, although not necessarily valid, assumptions that the torsional vibrations are simple harmonic and of low amplitude, the authors in ref 23 were able to observe only one of the two expected torsional vibrations in CC12F-CCIF2 and, hence, were required to assume that they were coincident. Since they observed as much as a 20-30cm-’ difference in other, similar molecules, the latter assumption can produce a large error in the barrier calculated from the torsional vibration.
TABLE IV: Calculated and Experimental Vibrational Frequencies“ib G T GT GG‘ v(ca1) u(exp)‘ u(cal) v(exp)C v(ca1) u(ca1) 1237 (a’) 1214 (a’) 1238 1254 1255 1210 1207 1212 (a”) 1232 1170 (a”) 1244 1178 1118 (a’) 1152 1154(a’) 1118 1144 1163 1039 1069 (a’) 1075 1041 (a’) 1085 1047 905 (a”) 907 (a’) 912 922 903 925 804 (a’) 873 (a”) 835 880 813 813 633 (a’) 624 653 (a’) 654 619 643 507 (a’) 514 505 (a’) 531 497 523 448 443 (a”) 452 449 (a’’) 452 460 436 436 (a’) 433 436 (a’) 435 443 383 (a”) 387 379 (a’) 392 375 388 371 372 (a’) 356 378 (a”) 348 350 316 (a”) 304 (a’) 343 304 310 315 298 315 (a’) 310 293 (a”) 286 288 248 (a’) 250 242 (a’) 240 251 240 215 (a’) 175 (a”) 229 201 178 197 214 (a”) 164 (a’) 203 164 163 168 72 62 76 72 (a”)
’Frequencies in units of cm-I. bCalculated frequencies have been scaled by the factor 0.90. Reference 21. modes below 1000 cm-I, with mean deviations of 1.2 and 1.8% from the observed frequencies. Fox and SchlegelZ5recently reported the results of a comprehensive investigation of the effects of the basis set on the calculated vibrational spectrum of difluoromethane. Of relevance to this study, they observed that increasing the basis set size and adding additional polarization and diffuse functions lowered the frequency of the CF2 stretching vibrations by 35-65 cm-I relative to values calculated with 6-31G(d). In contrast, there was little effect (
