J. Phys. Chem. 1994,98, 8687-8692
8687
Structure and Vibrational Frequencies of the Molecular Trichloromethanesulfonic Acid and Its Anion from ab Initio Calculations Shridhar P. Gejji, Kersti Hermansson, and Jan Lindgren' Institute of Chemistry, University of Uppsala. Box 531, S-75121 Uppsala,Sweden Received: May 6, 1994; In Final Form: June 23, 1994"
The equilibrium structure, vibrational frequencies, and the infrared intensities of the trichloromethanesulfonic acid molecule and its anion have been investigated using the ab initio self-consistent Hartree-Fock method and second-order Mprller-Plesset perturbation theory with the 6-31G** and lower basis sets. A normal mode analysis shows that, unlike CCl3 stretchings, the SO3 stretching vibrations in the C C l 3 S O j anion are pure normal modes comprised of S-0 stretching coordinates only. The molecular point group for the trichloromethanesulfonic acid molecule is C1 and not C,. The vibrational frequencies and the infrared intensities are sensitive to the basis set choice as well as to the electron correlation effects.
Introduction The vibrational spectra of methanesulfonic acid'-3 and its methyl group substituted derivative@ and the related anions9J0 have been of considerable interest in the literature. The equilibrium structure and some of the vibrational frequencies for the methanesulfonic acid molecule and its anion have been calculated by Bencivenni et al.' using ab initio quantum chemical calculations. Thesecalculations have shown that the equilibrium structure for the free acid molecule has the staggered conformation, nearly 17 kJ/mol lower in energy than its eclipsed conformer, with the 0-H bond not in the plane of the SO2 group of the molecule. Miles et aL9 reported the first systematic studies on the normal vibrations for the CX3S03-anion and related systems. The assignment of the normal modes for the anions presented in this work was used by different authors until recently.1* Recently the present authors studied the infrared spectra of the free trifluoromethanesulfonic (triflic) acid, CF3SOsH, and its anion, CF3S03-with ab initio quantum chemical calculations including electron correlation from the second-order Mprller-Plesset perturbation (MP2) theory with the extended 6-31G** basis sets. These calculations suggested a new assignment for the SO3 and CF3 normal stretching vibrations in the free anion. Johnston and Shrive+ presented the same assignment for the normal modes of the free CF3SO3- anion. The assignment of symmetric CF3 and SO3 stretching vibrations for the free CF3S03H molecule presented by us was different from that given by Varetti.' As an extension of our work on the fluorine-substituted methanesulfonic acid, the chloro-analogues, viz. CCl3S03H and CC1$03-, have been studied in the present work. The infrared and Raman spectra of CCl3SO3H have been mea~ured.1~ The approximate descriptionsofthevibrational modes for the Raman wavenumbers have also been given by Edwards and Smith.14 The masses for C1 and S atoms are rather similar, and therefore the CC13 stretching and the CC13wagging and rocking modes are expected to be complex vibrations involving different CS and SO internal coordinates. The major difficulty in the assignment of normal vibrations of the CC13SO3- anion in ref 9 was a negative value for the primary force constant for the C-S stretching, which was considered a result of the constraints of the force field fitting and the setting of the values of the interaction constants. These problems might be overcome by a full ab initio force field calculation. The present work thus deals with the use of quantum chemical calculationsin determining the structure and vibrational frequencies of the free trichloromethanesulfonate anion CC13SO3and the acid molecule CC13S03H using the extended basis sets. Abstract published in Advance ACS Abstracts. August 1, 1994.
0022-365419412098-8687%04.50/0
TABLE 1: Optimized Geometry Parameters (Bond Lengths in A and Bond Andes in d e d for the CCIBOJ-Anion R(C-S) R(S-0) R(C-C1) LO-S-C LCI-c-s
HF 3-21G*
HF 6-31G'
MP2 6-31G*
1.869 1.439 1.790 101.9 110.5
1 A78 1.438 1.777 102.3 110.3
1.907 1.476 1.778 101.7 109.9
First the results of the anion are given, and then of the acid. Lastly we compare ab initio obtained geometries, force constants, and frequencies for different X3CSO3- ions and X~CSOIH(X = H and F) molecules.
Computational Method The structures of Cl3CS03H and its anion were optimized and the vibrational frequencies computed at the self-consistent field (SCF) and MP2 theory by an analytic gradient method with the Gaussian 90 suite of ~ r 0 g r a m s . l The ~ internally stored 3-21G* and 6-3 1G* basis sets with the addition of 2p polarization functions on H atoms were used. Additional normal-mode analyses for the HF- and MP2-derived force constants were performed, where the potential energy distributions (PED'S) expressed in internal vibrational coordinates are as described in ref 16.
Results and Discussion The optimized geometries, normal modes, force constants, vibrational frequencies, and infrared intensities obtained from the ab initio calculations are discussed in the following. Trichloromethanesulfonate Anion. Geometries. Optimized geometric parameters of the trichloromethanesulfonate anion obtained from theab initio HF/3-21G*, HF/6-3 1G*, and MP2/ 6-31G* calculations are presented in Table 1. The optimized structure for the anion as obtained from the MP2 calculations is depicted in Figure la. The C-Cl and C-S bond lengths are slightly affected by the extension of basis set. Both C-S and S - 0 bond lengths are more sensitive to the electron correlation effect, however. The 0-S-C and Cl-C-S bond angles are quite insensitive to both the basis set and the electron correlation. The geometry parameters for the free trichloromethanesulfonate anion are not available from experiments. The total electronic energy for the trichloromethanesulfonate anionasobtained from theHF/3-21G*, HF/6-31GS, and MP2/ 6-31G* calculations are -2028.856 77, -2038.370 98, and -2039.588 99 au, respectively. The net atomic charges derived from the Mulliken population analysiswere 1.632,-0.452,4).724, 0 1994 American Chemical Society
Gejji et al.
8688 The Journal of Physical Chemistry, Vol. 98, No. 35, 1994
TABLE 2
The PED Matrix (from MP2/6-31G*) for the CCl3SOp- Anion normal modes (freq in cm-I)
int.coordinate
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 (73) (166) (166) (229) (257) (257) (331) (331) (417) (529) (529) (606) (822) (825) (825) (1054) (1310) (1310)
37.7 C-S stretch S-01 stretch S-02 stretch S-03 stretch C-C11 stretch C-CI2 stretch C-C13 stretch 14.5 21.9 01-S-C bend 40.6 02-S-C bend 31.9 03-S-C bend 46.7 70.5 11.9 C11-C-S bend 17.2 118.0 13.7 C12-C-S bend 125.0 13.0 C13-C-S bend 02-S-01 bend 03-S-02 bend 13.3 13.4 Cl2-C-C11 bend 8.6 13.9 C13-C-C12 bend C-S torsion 100.0
9.9
54.6 31.2 31.2 31.2
8.8 12.7 22.0
25.4 49.5
45.3
11.4 8.5 37.4
10.2 26.0 34.2
15.0 15.0 15.0
9.8 9.8 9.8 19.5 22.3 19.6
8.5 10.8 16.6 38.1
71.8 43.9
7.9
11.9 19.8 17.9
73.6
40.5 58.0
70.6 25.5 11.2 13.5
13.2 8.9 12.8 14.8 14.1
14.2
46.1 60.3
26.3 65.2 8.7
19.2 23.9
25.5 10.7
109.9 11.2 41.6 11.6 14.5 15.1
25.1 30.6
TABLE 3 Internal Force Constants, in m d y d - 1 , of the CClfiOJ- Anion# f(CC1) f(CCl/CCl)
f(S0) f(SO/SO) f(ClCC1) f(C1CS)
f(OS0) f(CS)
HF/3-21G*
HF/6-31G*
MP2/6-31GS
3.2 0.4 11.6 0.1 0.9 0.3 1.7 0.8 2.8
3.6 0.4 11.1 0.2 1.o 1.o 1.7 1.o 3.0
3.2 0.4 9.5 0.1 0.9 0.8 1.3 0.9 2.3
The bending constants were normalized with the factor (rlr2)-', r l and r2 being the lengths of the bonds forming the angle.
Figure 1. (a, Top) Optimized geometry of the trichloromethanesulfonate anion as obtained from the MP2/6-31G* calculations. (b, Bottom) The
corresponding acid molecule.
and -0.003 for the S, C, 0, and C1 atoms, respectively, in the HF/6-3 lG* calculations. The zero-point energies for the CC13SOs- anion in the HF/3-21G*, HF/6-31G*, and MP2/631G* calculations were 64.57, 65.40, and 60.04 kJ-mol-l, respectively. Normal Mode Analysis, Force Constants, and Vibrational Frequencies. The free trichloromethanesulfonate anion in its staggered configuration with C3" point group symmetry has 3N - 6 = 18 normal modes with the symmetry representations SA1 + A2 + 6E. Except for the A2 mode, all other normal vibrations are both infrared and Raman active. The A2 mode, viz. the internal torsion around the C-S axis, is neither infrared nor Raman active. In order to obtain a more complete description of the atomic motion involved in the normal modes of the trichloromethanesulfonate anion and to aid in the vibrational assignment of the fundamentals, we have carried out the PED analysis of the normal vibrations. Here the force fields in Cartesian coordinates calculated by the Gaussian 90 program system were used. A nonredundant set of internal coordinates consisted of the following internal coordinates: (a) seven stretching coordinates, 3 S-0, C-S, and 3 C-Cl stretchings; (b) ten bending coordinates, 3 0-S-C, 3 Cl-C-S, 2 0-S-0, and 2 Cl-C-Cl bendings,
and (c) the C-S internal torsion. The CC13 and SO3 rocking coordinates are thus expressed as Cl-C-S and 0-S-C bending coordinates. The PED matrix components greater than 7% from the MP2/6-31G* calculations are presented in Table 2 for all the normal modes. As noted also in the case of the triflate anion,12 the symmetric and asymmetric SO3stretchings are comprised of S-0 stretching coordinates only. The asymmetric C-C1 stretchings, on the other hand, are more complex and also involve different C-Cl bending coordinates. The relatively pure symmetric CC13 stretching contains a small component of the C-S stretching coordinate. This may be attributed to the similarity of the S and C1 masses, which are nearly 3 times larger than that of the C atom. The bending normal modes are mixtures of virtually all internal bending coordinates. The PED components for several of the normal modes do not sum up to 10076, indicating that secondary force constants are important. The primary internal force constants from the HF/3-21G*, HF/6-31G*, and MP2/6-31G* calculations are presented in Table 3 for the stretching as well as the bending normal vibrations along with some interaction constants for the different C-C1 and S-0 stretchings. The full force constant matrices for all these calculations are available from the authors on request. It was pointed out by Edwards and Smith14 that a major inconsistency in the normal mode analysis for CCl3SO3- presented by Miles and co-workers9 was the negative value for the primary force constant for the symmetric C-S stretching. Our use of a full ab initio force constant matrix in the normal mode analysis does not show any such inconsistency for the primary force constants. The primary forceconstants reported herearein accord with the bond length parameters shown in Table 1. In Table 4 the vibrational frequencies of the trichloromethanesulfonate anion from the HF/3-21G*, HF/6-31G*, and MP2/ 6-3 lG* calculations are compared with those for the anion in the
Trichloromethanesulfonic Acid and Its Anion TABLE 4
544 544 616 812 1066 1260
TABLE 5 Optimized Geometry Parameters (Bond Lengths in A and Bond Angles in deg) for the CljCSOjH Molecule
Vibrational Frequencies
obs, assgnmt, ref9 ref9 177 247 261 333 410
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8689
assgnmt, present work
cs t
3-?%* int
Y
6-?%* int
Y
68 (0) 81 CC1, r CCI, ab + SO3ab 177 (1) 188 CCljsb CCI, sb + CS ss 244 (0) 250 CC13ab CCl, ab + SO,ab 272 (0) 279 CCl3 as + SO3ab 357 (0) 361 S03r C-CI~SS C - C I , 9s 419 (2) 442 SO3ab 605 (45) 593 SOjSb S03ab SO,sb 680 (317) 684 CSs CS ss + CC13sb 820 (119) 885 874 (58) 932 CC13as CCl, as 1151 (157) 1141 S03ss so, ss 1448 (265) 1405 SO,as SO,as
(0) (1) (0) (0) (0) (0) (39)
*!%6 Y
int
73 (0) 166 (1) 229 (0) 257 (0) 331 (0) 417 (0) 529 (26)
(296) 606 (206) (137) (23) (179) (307)
822 825 1054 1310
(122) (122) (123) (229)
a ss = symmetric stretch, as = asymmetric stretch, sb = symmetric bend, ab = asyFmetric bend, r = rock, and t = torsion.
sodium salt of trichloromethanesulfonate presented by Miles and co-workers.9 Except for the SO3 stretchings and the SO3 asymmetric bending, the frequencies increase when the larger basis set is used. A comparison of H F and MP2 calculations using the 6-3 lG* basis shows that the CC13and SO3asymmetric stretching frequencies are lowered by 107 and 95 cm-I, respectively, by the MP2 correlation. The symmetric and asymmetric SO3bendings in the anion, from the MP2/6-31G* calculations, occur at 529 and 606 cm-1. An accidental degeneracy for these vibrations was predicted by Miles et al.9 The bands at 177,247, and 261 cm-1 were observed in the Raman spectrum of a NaC13C S 0 3 aqueous solution. The experimental infrared spectrum shows bands at 758 (weak), 788 (strong), and 798 (strong) cm-I, which were considered as combination bands, and no vibrational assignment was presented for any of these bands. The 758 and 788 cm-1 bands could not be correlated with any of those in the present calculations. The 798 band, however, may be correlated with our relatively intense band at 822 cm-I (in the MP2/6-3 lG* calculations). We have assigned this band to a combined symmetric C-C stretching and CC13 bending. The nearly degenerate 822 and 825 cm-l infrared bands are comprised of several internal coordinates (cf. Table 2). As shown in Table 4, the MP2/6-31G* calculated infrared intensities below 417 cm-I are negligibly small. The intensities for the stretching bands are sensitive to the basis set as well as to the electron correlation. Except for the CC13 stretching, the infrared intensities for the stretching vibrations are lowered when the MP2 correlation is included. The strong dependence of the infrared intensitiesof theS03 stretchingvibrations on theelectron correlation may be readily noticed. Trichloromethanesulfonic Acid. Geometries. The different bond length and bond angle parameters for the free CC13S03H molecule from the different levels of the ab initio calculations are presented in Table 5. The MP2/6-31G**-optimized structure of the acid is shown in Figure lb. Some selected dihedral angles are also reported. As in the case of the anion, no experimental data on geometries were available for the acid molecule. Our comparison of different geometries is thus restricted to different levelsofcomputation. Theexpansionof thebasisset from 3-21G* to6-31G**resultsinachangeofthedifferentC-Clbondlengths between 0.012 and 0.016 A. The C-S bond length from the 6-31G** basis is 0.027 A longer than that in the smaller basis. The bond angles do not vary appreciably with the extension of the basis set. The H-01-S-02 dihedral angle varies by 10' with the change of a basis set. A comparison of the H F and MP2 calculations in the 6-3 1G** basis shows that the C-Cl bond lengths are very insensitive to the electron correlation. The variation in the bond angles or the dihedral angles is within 1-2O. It must be noted here that all
R(C-S)
R(S-0 1) R(S-02) R(S-03) R(C-C11) R(C-C12) R(C-(213) R(01-H) R(02-H) R(03-H) L OlSC L02sc L 03SC L CllCS L c12cs L c13cs L SOlH L H01S02 L 01sc02 L 02SC03 L CllCSCl2 L c12csc13
H F 3-21G*
HF6-31G**
MP2 6-31G**
1.817 1.559 1.419 1.412 1.776 1.779 1.770 0.972 2.500 3.221 99.0 107.9 107.6 107.6 109.3 110.1 117.1 5.2 112.8 133.9 119.1 120.9
1.845 1.566 1.417 1.409 1.760 1.766 1.758 0.951 2.417 3.187 100.6 107.4 107.3 107.1 108.9 109.6 111.1 15.3 113.2 133.9 119.3 120.7
1.874 1.622 1.454 1.446 1.760 1.766 1.756 0.973 2.444 3.247 99.6 107.3 107.3 106.3 108.3 109.1 107.6 16.6 113.1 135.4 119.1 120.8
these calculations show that the molecule belongs to the C l symmetry point group and not to C,, as suggestedin the literature.6 The total electronic energies for the free trichloromethanesulfonic acid molecule are -2029.350 38, -2038.866 97, and -2040.089 95 au in the HF/3-21G*, HF/6-31G**, and MP2/ 6-3 lG** calculations, respectively. The Mulliken charges on the atoms in the HF/6-31GS* calculations are 1.697, -0.489, -0.673,-0.644,-0.611,0.112,0.084,0.116,and0.409ontheS, C, 0 1 , 0 2 , 0 3 , C11, C12, C13, and H atoms, respectively. The zero-point energies for this molecule obtained from the HF/321G*, HF/6-31G**, and MP2/6-31G** computationsare 175.8, 176.0, and 166.8 kEmol-l, respectively. Normal Mode Analysis, Force Constants, and Vibrational Frequencies. A new set of nonredundant internal coordinates has been defined including the internal coordinates described above for CC13S03- and the addition of three new internal coordinates describing the degrees of freedom for the hydrogen atom in the acid, viz. (i) 01-H stretching, (ii) S-01-H bending, and (iii) the bending of H out of the SO2 plane of the molecule. The PED matrix components greater than 7% obtained from the MP2/6-31G* calculations are shown in Table 6. As may be readily noticed, the SO2 stretching and S-0-H bending at 1215, 1459, and 1161 cm-I are pure normal vibrations which do not have a significant contribution from additional internal coordinates. The S-0 stretching at 883 cm-1, however, has a relatively large contribution from the C-S stretching coordinate. The low-lying bending normal vibrations are rather complex with relatively large contributions from different bending coordinates. As shown in the table, the CC13stretching normal vibrations are comprised of bending internal coordinates in addition to the CCl stretchings. The different internal force constants in the trichloromethanesulfonic acid molecule obtained from the H F and MP2 methods are presented in Table 7. The force constant for the S-01 stretching is lowered by nearly 50% compared with that for the free anion. The S-02 and S-03 force constants increase by 1.2 and 1.7 m d y d - l . The CCl and C-S force constants increase by 0.4 and 0.5 m d y d - 1 , respectively, when the proton is added to the anion. The direction of the change in primary force constants is in accord with the change of the bond length parameters of the CC1;SOp- anion and its acid molecule. The different SO/SO interaction constants are rather small in the molecular CCl3S03H too. The vibrational frequencies for the CCl3SO3H molecule from the HF/3-21G*, HF/6-31G**, and MP2/6-31G** calculations
8690 The Journal of Physical Chemistry, Vol. 98, No. 35, 1994
TABLE 6
The PED Matrix (from MP2/6-31G1*) of CCl&O*
Gejji et al.
Molecule
normal modes (freq in cm-I) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 (74) (168) (175) (240) (249) (259) (296) (331) (356) (431) (454) (491) (586) (797) (860) (869) (883) (1161) (1215) (1459) (3804) CS stretch 26.7 9.5 22.2 38.0 56.9 34.5 01s stretch 48.0 41.4 0 2 s stretch 03s stretch 43.0 51.9 CllC stretch 9.8 12.7 63.3 18.5 C12C stretch 7.4 48.1 24.5 16.6 C13C stretch 14.0 60.1 20.5 100. 01H stretch 01SC bend 39.4 20.1 41.1 32.7 13.6 9.4 13.6 46.7 62.0 16.2 39.3 8.6 30.3 22.8 02SC bend 03SC bend 42.5 38.2 11.8 10.5 44.0 27.2 10.2 C11CS bend 12.6 13.7 101. 18.2 10.4 C12CS bend 19.5 89.9 8.2 7.9 8.0 20.9 12.8 C13CS bend 29.9 36.8 70.5 10.5 02S01 bend 21.2 23.2 12.4 67.5 27.2 03S02 bend 11.6 21.6 103. 51.4 Cl2CCll bend 19.8 37.6 33.2 10.0 31.9 C13CC12 bend 11.0 92.4 29.8 7.6 20.6 12.2 88.9 SOlH bend CS torsion 105. 02SO I H oplb 16.9 56.6 35.0
~~~
TABLE 7: Internal Force Constants, in mdyn.l(-l of the CIJCSO$ImoleculP force const HF/3-21G* HF/6-31GS* MP2/6-31G** f(CS) f(CC1l) f(CC12) f(CC13) f(S01) f(S02)
AS03
flow
f(CllCCl2) f(C12CC13) f(C1lCS) f(Cl2CS) f(Cl3CS) f(OlS02) f(02S03) f ( 01SC) f(O2SC) f(03SC) ASOlH) f(CCl1 /CC12) f(CC11 /cc13) f(S02/S03) f(SOl/SO2) f(SOl/SO3)
3.7 3.6 3.5 3.7 7.1 12.6 13.0 8.2 0.9 1.o 0.8 1.o 0.9 1.5 2.0 1.o 1.5 1.4 0.4 0.4 0.4
0.0 0.2 0.2
3.6 4.0 3.9 4.1 6.4 12.5 12.9 9.4 0.9 1.o 0.8 1.o 0.9 1.5 2.0 0.9 1.5 1.3 0.5 0.4 0.4 0.0 0.3 0.2
2.8 3.6 3.5 3.7 4.7 10.7 11.2 8.1 0.8 0.9 0.7
0.9 0.8 1.1 1.6 0.7 1.2 1.1 0.4 0.4 0.4 0.0 0.1 0.1
0 The bending constants were normalized with the factor (rlr2)-l, r l and r2 being the lengths of the bonds forming the angle.
are shown in Table 8. The OH and CC13 stretchings and the S-OH bending normal modes show an increase of -50 cm-1 with the expansion of the basis from 3-21G* to 6-31G**. The MP2/6-31G** vibrational frequencies for the SOz, SO, CCls, and OH stretchings are -90, 120,70, and 300 cm-l lower than the HF values, respectively. The remaining normal mode vibrational frequencies are relatively less sensitive to the extension of the basis set. Comparison with Experiments. A direct comparison of the present MP2/6-3 1G** vibrational frequencies and the infrared intensities with those from the infrared experiments is difficult. The calculated frequencies for the different SO2 stretchings are up to 200 cm-l too high, whereas the 0-H stretching is -580 cm-1 too high. The large deviation of the 0-H stretching frequencies is partly due to anharmonicity effects. Moreover, the experimental spectra refer to the acid in the solid state, where intermolecular interactions, e.g. hydrogen bonding, are present. The observed infrared bands at 621 and 893 cm-1 in the experiments were assigned as C-S and S - 0 stretchings,
respectively. Although no band at 621 cm-l was obtained in the present calculations, we have correlated this with our band at 797 cm-1. In the spectra of CF$03H,7 an out-of-plane S-0-H bending mode was observed a t -700 cm-1 for the liquid and at -660 cm-1 for the solid. If the band at 621 cm-l in CCl3S03H would correspond to such a mode, that should explain the difficulty in finding a good correlation with the calculations. It may be noted here that the C S and SO normal vibrations are alsocomprised of SOand CS internal coordinates, respectively. The rocking and deformation vibrational frequencies of the CC13 group in the Raman spectra show an excellent agreement with those obtained from the MP2 calculations. The largest calculated intensities are found for vibrations involving the SO2 and S-OH groups. Experimentally, the corresponding bands have been denotedasmediumstrong (ms) or medium (m). Theexperimental band at 828 cm-1 seems to be the strongest one observed and is denoted as strong (s). The intensity of the band probably correlates with the sum for the calculated values a t 860 and 869 cm-1. Comparison with Related Anions and Molecules. Some of the bond lengths and bond angles of the trichloromethanesulfonate anion are compared with those of the X3CSO3- anions (X = H and F) in Table 9. The geometry of the SO3 group of the free CC13S03- and CFsSOs- anions is strikingly similar, although some differences for H3CS03- may be noticed. The CS distance increases by more than 0.1 8,along the series X = H, F, C1. A comparison of the primary force constants in these systems is presented in Table 10. As may be expected on the basis of the similar geometry parameters, the SO force constants in the CC13S03- and CF3S03- anions are almost the same. The SO force constant in the H3CS03- is lower than that in the CC1$303anion. The CS force constant is almost the same for X = H and F whereas it is considerably smaller for X = C1. The increase in the C S distance between X = H and F is thus not reflected in any appreciable force constant change. A reversal of the order of the symmetric and asymmetric CX3 stretching vibrations is observed for X = F (Table 11). A comparison of the geometry parameters and the primary force constants in the X3CSO3H acid molecules in shown in Tables 12 and 13, respectively. As for the anions, the force constants for the SO stretchings of F3CSOsH and C13CS03H are nearly the same, which is in accordance with the geometry parameters. A lengthening of the C S distance for X = H, F, C1 analogous to that for the anions is found and in this case also reflected in changes for the corresponding stretching force constants. Some of the harmonic vibrational frequencies in the X3CSOsH molecules are reported
Trichloromethanesulfonic Acid and Its Anion
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8691
TABLE 8: Vibrational Frequencies (cm-l) and Infrared Intensities (km-mol-') (in parentheses) of Trichloromethanesulfonic Acid. obs, assgnmt assgnmt, HF/3-2 1G* HF/6-3 1G** MP2/6-3 1G** normal ref 14 ref 14 present work Y int Y int Y int mode CSt 109 120
S-OH t ccl3 t
178
CCl3 r
245 260
CCl3 sym def CCl3 asym def
315 418
SO2 r
455 518 62 1 764 828 893 1112 1158 1283 3225 0
SO2 wag SO2 def
cs s
CClj as CC13 as S-OH
so2 ss
+
+
+
CCl3 ss
so s
+ +
CC13 b SO2 b CCI3 b SO2 b CS s CC13 b SO1 b c c l 3 b CCl3 b S - O H oplb SO2 b + CCls b SO2 b + CC13 b CCl3 s CCl3 b O=S-O b SO2 b SO2 b
def
so s + cs s CCl3 s + CCll b CCl3 s + c c l 3 b cs s + so s S-OH b so2 s so2 s
SO2 as OH s
OH s
71
(3)
81
(3)
74
(2)
1
183 188 252 263 275 285 359 369 437 508 564 656 868 876 917 1003 1178 1320 1568 3833
(4) (9) (75)
182 189 26 1 273 280 33 1 358 391 457 507 560 659 918 932 940 1005 1252 1310 1552 4099
(3) (4)
168 175 240 249 259 296 33 1 356 431 454 49 1 586 797 860 869 883 1161 1215 1459 3804
(2) (4) (0) (14) (1) (42) (1) (36) (5) (34) (19) (159) (89) (105) (89) ( 146) (72) (156) (172) (145)
2 3 4
(0)
(1) (58) (2) (24) (3) (37) (49) (253) (70) (82) (13) (312) (71) (206) (233) (260)
(0.5)
(0) (1) (46) (2) (51) (5) (33) (40) (254) (54) (111) (89) (182) (87) (236) (266) (236)
5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
ss = symmetric stretch, as = asymmetric stretch, s = stretch, b = bend, sb = symmetric bend, ab = asymmetric bend, r = rock, def = deformation,
oplb = out of plane bend, and t = torsion.
TABLE 9 MP2/631G+ (or 6-316** for the CH 0 3 - ) Optimized Geometry Parameters (Bond Lengths in f a n d Bond Angles in deg) for the CXSO3- Anions (X = H, F, Cl) CH?SOr, ref 3 CF?SO?-. ref 12 cChS01~
R(CIS)
R(S-0) R(C-X) L L
0-s-c x-c-s
1.804 1.485 1.088 103.9 109.2
1.835 1.477 1.353 102.1 112.0
1.907 1.476 1.778 101.7 109.9
TABLE 1 0 Internal Force Constants in m d y d - l , of the CXJs03- Anions (X = H, F, Cl) from the MP2/6-31C* (MP2/6-31G** for X = H) Calculations force const CHoS03CF3SO3CC13SO3-
f(W f(XCX)
mcs)
f(OS0) f(0SC) flcs)
5.7 8.9 1.o 0.6 1.4 0.9 3.3
6.2 9.5 1.7 1.4 1.3 0.8 3.2
3.2 9.5 0.9 0.8 1.3 0.9 2.3
TABLE 1 2 MP2/6-31G** Optimized Geometry Parameters (Bond Lengths in A and Bond Angles in deg) for the CXSOSI (X = H, F. Cl) Molecules R(C-S) R(S-01) R(S-02) R(S-03) R(O1-H) R(02-H) R(03-H) L OlSC LSOlH L H01S02
CH3SO3H
CF3SOaH
CCI$3OiH
1.771 1.643 1.461 1.454 0.972 2.4 12 3.066 98.2 105.9 20.9
1.833 1.621 1.452 1.445 0.972 2.447 3.247 98.5 108.0 13.7
1.874 1.622 1.454 1.446 0.973 2.444 3.247 99.6 107.6 16.6
TABLE 1 3 Internal Force Constants, in mdyd-1, of the CXJs0J-JMolecules (X = H, F, Cl) from the MP2/631G** Calculations force const CHaSOnH CFnSOoH CC13SOaH 4.8 10.9 11.3 8.1 1.1 1.5 0.6 3.3
TABLE 11: MP2/631C* (or 631G** for H) Vibrational Frequencies (in cm-l) for the Stretching Vibrations in the CXSOj- Anions (X = H, F, Cl) SO3 sym
so3 asym
CX3 sym CX3 asym
1045 1268 3135 3250
1046 1310 1284 1214
1054 1310 417 825
in Table 14. A splitting of the degenerate SO3 stretching of the anion, as obtained from the MP2/6-3 1G** calculations, is found to be 244 cm-I for CCl$303H compared with 286 and 194 cm-I, respectively, for the CF3S03Hand CH3S03Hmolecules. Thus the SO3 splitting of the anions follows the order of their acid strengths.
Conclusions The structure and the vibrational frequencies of the trichloromethanesulfonic acid and its anion obtained from different ab initio calculations are reported here. The key conclusions of the present work are as follows. (i) The SO3 stretching vibrations
4.7 10.7 11.2 8.1 1.1 1.6 0.4 2.8
TABLE 1 4 MP2/6-31G** Vibrational Frequencies (in cm-I) for the Stretching Vibrations in the CXJS0J-I Molecules (X = H, F, C1) S-0 str SOH bend SO2 str SO2 str
CX3 str CX3 str OH str
CH3SOaH
CFjSOiH
CC13SO3H
835 1142 1224 1418 3283 3293 3818
845 1155 1184 1470 1293 1300 3808
797 1161 1215 1459 860 869 3804
in CCl3SO3- and its acid are pure SO stretchings. The CCl3 stretchings on the other hand are more complex and comprise both C-C13 bending and C-S stretching coordinates. A major inconsistency for the CC13SO3- normal mode assignment noted earlier in the literature is not present in our calculations; i.e. our calculations do not support the earlier prediction of an accidental
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The Journal of Physical Chemistry, Vol. 98, No. 35, 1994
degeneracy for the symmetric and asymmetric deformations in the anion. (ii) The trichloromethanesulfonic acid molecule possesses C 1point group symmetry and not C,. (iii) No single normal vibration could be uniquely assigned as the CS stretching in these molecular systems. (iv) The interaction of the proton with the free CCl3SO3- splits the degenerate SO3stretching of the anion by 244 cm-1, which is nearly twice as large as observed in the infrared spectra of solid CC13S03H. The splittings of the degenerate SO3 stretchings in the CF3S03H and CH3SO3H molecules obtained from the MP2 calculations are 286 and 194 cm-1. The qualitative trend for this splitting is thus in accordance with the acid strength.
Acknowledgment. This work was supported by the Swedish Natural Science Research Council. References and Notes ( I ) Mihalopoulous,N.; Barnes, I.; Becker, K. H. Afmos.Enuiron. 1992, 26A, 807. (2) Chackalackal, S.M.; Stafford, F. E. J . Am. Chem. SOC.1966, 88, 4815.
Gejji et al. (3) Bencivenni, L.; Caminiti, R.; Feltrin, A.; Ramondo, F.; Sadun, C. J . Mol. Sfrucf.1992, 257, 369. (4) Balicheva,T.G.; Ligus, V. I.; Fialkov, Yu. Ya. Russ. J. Inorg. Chem. 1973, 18, 12. (5) Katsuhara,T.G.;Hammaker,R.M.;Desmarteau,D.D.Inorg.Chem. 1980, 19, 607. (6) Edwards, H. G.M. Specfrochim. Acta 1989, 45A, 715. (7) Varetti, E. L. Spectrochim. Acfa 1988, 44A, 733. (8) Gejji, S. P.; Hermansson, K.; Lindgren, J. J . Phys. Chem. 1992, 97, 6986. (9) Miles, M. G.;Doyle, G.; Corney, R. P.; Tobias, R. S.Spectrochim. Acra 1969, 25A, 1515. (10) Btrger, H.; Burczyk, K.; Blaschette, A. Monafsh. Chem. 1970.19, 607. (11) Manning, J.; Frech, R. Polymer 1992, 33, 3487. (12) Gejji, S.P.; Hermansson, K.; Lindgren, J. J . Phys. Chem. 1993,97, 3712. (13) Johnston, D. H.; Shriver, D. F. Inorg. Chem. 1993, 32, 1045. (14) Edwards, H. G. M.; Smith, D. N. J . Mol. Sfrucz. 1991, 263, 11. (15) Gaussian 90. Frisch, M . J.; Head-Gordon, M.; Trucks, G.W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; 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. (16) Gwinn, W. D. J . Chem. Phys. 1971, 55,477.
