3712
J . Phys. Chem. 1993,97, 3712-3715
Ab Initio Vibrational Frequencies of the Triflate Ion, (CF3S03)Shridhar P. Cedi, Kersti Hermansson, and Jan Lindgren’ Institute of Chemistry, University of Uppsala, Box 531, S-75121 Uppsala, Sweden Received: November IO, 1992; In Final Form: January 7 , 1993
The optimized geometry, harmonic vibrational frequencies and infrared intensities of the trifluoromethanesulfonate (triflate) ion, CF3S03-, have been determined with a b initio self-consistent Hartree-Fock theory by using 3-2 1G* and 6-3 1G* Gaussian basis sets. Second-order Maller-Plesset perturbation calculations were also carried out with 6-31G* basis. A normal mode analysis shows that the vibrations assigned as symmetric and antisymmetric CF3 stretching involve other internal coordinates as well, viz., CF3 bending and CS stretching. The corresponding SO3stretching modes, on the other hand, are almost entirely described with SO stretching coordinates. The assignments of the symmetric and antisymmetric SO3 and CF3 stretching vibrations from Mdler-Plesset theory are seen to be different from those reported in the literature. Recent infrared spectroscopic experiments of the triflate ion coordinated to the zinc or lead ion in poly(ethy1ene oxide) complexes support the conclusions from second-order perturbation theory. The vibrational frequencies and infrared intensities show a strong dependence on basis set and electron correlation.
Introduction The trifluoromethanesulfonate (triflate) ion possesses several features that makes it interesting for a theoretical study. It is seen to be thermally and chemically stable.’ It shows a low tendency to form ion pairs and also a strong resistance to both reductive and oxidative cleavage. The triflate ion has been used in thermodynamic ion transfer measurements.2 The conjugate acid known as triflic acid, a very strong monoprotic organic acid, finds many useful applications in the synthesis of coordination compounds and in organometallic chemi~try.~The triflate ion has for these reasons become one of the most important anions in polymer electrolytes. The lithium complex of the triflate ion is used in polymer mixtures as a solid amorphous electrolyte in thin-film batteries. The lithium and triflate ions in polymer electrolytes are believed to be involved in complex formation of various types such as Li(CF3SO3) ion pairs and higher clusters, viz., Li(CF3S03)2-, Li(CF3S03)32-,which would influence the conducting properties greatly. The formation of these ion pairs or higher complexes can be detected by infrared and Raman spectroscopy when the characteristic internal vibrations of the triflate anion are known, which, however, is complicated since the internal vibrations of the CF3and SO3groups fall in the same regions of the spectrum. Miles et ale4have reported infrared and Raman spectra of the triflate ion in sodium and barium trifluoromethanesulfonates. The normal mode analysis given by these authors was based on a comparison with other molecules containing the CF3and SO3 groups. The vibrational frequencies for the SO3symmetric and antisymmetric stretching modes for the triflate anion in Na(CF3S03)were different from those reported earlier by Haszeldine and Kidd.5 Biirger et a1.6 have followed the work of Miles and co-workers and have also given the additional symmetry assignments for some of the infrared bands in the metal triflates in ref 4. Recently, polarized infrared and Raman spectra of the crystalline ammonium triflate have been analyzed by Varetti and co-~orkers,~ who report CF3 and SO3 symmetric and antisymmetricstretching frequenciesin accordancewith the work of Miles et ala4Manning and Frechs have measured infrared and Raman spectra of alkali-metaltriflates dissolved in poly(propy1ene oxide) and used the assignments of Miles et al. in their interpretation. Wendsjd et aL9-’ have reported the infrared spectra for nickel, zinc, and lead triflates complexed with PEO (poly(ethy1ene oxide)). The assignments of the CF3and SO3stretchingsreported 0022-3654/93/2097-3712SO4.00/0
by these authors were based on the band splitting behavior and on the expectation that it is the polar SO3end that interacts with the cations, whereas the less polar CF3 end does not participate in any strong bonding. The degenerate antisymmetric so3 stretchingfrequency for a noncoordinated triflate ion was reported as 1271 cm-I and the correspondingCF3 mode at 1157 cm-I. This is in contradiction to the results by Miles et al.4 On the other hand, the recent work of Bencivenni et al.I2 shows that the ab initio vibrational frequencies for the asymmetric CF, and SO3 stretchings in the triflate anion agree well with those reported by Miles et al.4 These authors have also predicted the CS stretching at a higher frequency than the experimental 321 cm-I. In order to resolve this discrepency of the stretchingvibrationalfrequencies of the triflate anion, the present work has been undertaken. The computational method is outlined in the following section. COmputatiOMl Method
Ab initio Hartree-Fock (HF) self-consistent field molecular orbital calculations have been performed by using the GAUSSIAN 90 suit of programsI3with the internally stored 3-21G* and 6-31G* basis sets. The equilibrium geometries in the H F calculations were obtained by the gradient relaxation method of Pulayl4 using Berny’s algorithm,l5which evaluates the gradients analytically. For evaluation of force constants and frequencies, analytical first-derivative techniques were used, and the second derivatives of the energies were computed numerically. The optimized geometries and vibrational frequencies have also been computed with correlated second-order Maller-Plesset (MP2) theory using the 6-31G* basis. For the H F and MP2 derived forceconstant matrices additional normal mode analyses were performed, where potential energy distributions (PEDS)expressed in internal vibrationalcoordinates were obtained. These calculations were made by using a local modification of a normal coordinate analysis program originally written by Gwinn.16
Results and Discussion The resulting optimized geometries, normal modes, force constants, vibrational frequencies and infrared intensities from the ab initio calculations are discussed in the following. Optimized Geometries. Optimized geometry parameters for bond lengths and bond angles of the triflate anion from the ab initio HF/3-21G*, HF/6-31G*, and MP2/6-31G* calculations Q 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3713
Vibrational Frequencies of the Triflate Ion TABLE I: Optimized Geometry of the Free and Cryscrlline Triflate Anion Bond Lengths (A)and Bond Angles (deg) HF/3-21G*
HF/6-31G*
MP2/6-31G*
R(s-0)
1.776 1.441
1.817 1.443
1.835 1.477
R(C-F)
1.354
1.323
1.353
LCSO
102.2
102.6
102.1
LFCS
112.1
1 1 1.8
1 12.0
R(C4)
experiment,I 85 K 1.829(2) 1.441(1) 1.456(1) 1.434(1) 1.327(2) 1.322(2) 1.3 18(2) 104.5(1) 104.0(1) 103.3(1) 1 13.2(1) 116.9(1) 1 1 3.1( 1)
TABLE II: PED Matrix (from MP2/631C**)of the Triflate Anion intcoordinate 67 204 204 313 345 345 509 509 571 53.7 C S stretch S - 0 1 stretch S-02 stretch S-03 stretch C-Fl stretch C-F2 stretch C-F3 stretch 14.3 74.8 38.7 01-S-C bend 99.8 46.7 10.0 02-S-C bend 31.2 57.7 18.9 24.0 5.4 0 3 4 4 bend 20.1 104.8 5.8 7.2 64.7 Fl-C-S bend 50.3 92.8 6.6 36.2 46.1 7.9 F2-C-S bend 122.6 5.8 68.5 11.2 F3-C-S bend 10.5 13.4 30.7 39.8 21.8 0243-01 bend 21.2 7.1 62.1 0 3 4 - 0 2 bend 7.5 26.6 53.1 34.4 F2-C-Fl bend 7.4 24.3 5.5 48.4 F3-C-F2 bend C-S torsion 100.3 normal mode frea. cm-1 intcoordinate
Figure 1. Geometry of the triflate anion.
are presented in Table I. The triflate anion in its staggered configuration is shown in Figure 1. Acomparisonofthe3-21G* and6-31G*geometriesattheHF level shows that the extension of the basis set leads to an increase in the C S bond length by 0.04 A and a decrease in the C-F bond length by 0.03 A. It should be noted here that the HF/6-3 1+G* theory leads to C-S, C-F, and S-0 bond lengths of 1.832,1.324, and 1.443 A, respectively.’2 The bond angles CSO and FCS are seen to be insensitive to the change of basis. The effect of electron correlation on the geometry of the triflate anion may be seen by a direct comparison of the H F and MP2 results for the 6-31G* basis set. The C-S, S-0,and C-F bond lengths from MP2 theory are seen to be 0.02,0.03, and 0.03 A longer than their HF counterparts. The effect of the MP2 correlation also leads to very small changes in the CSO and FCS bond angles. No experimental data are available for the geometry of the free triflate anion. However, the structures of the trifluoromethanesulfonic acid dihydrate at 85 and 225 K have been determined from X-ray crystallographic e~periments.’~The CF3S03-geometryat85 Kiscomparedwith theabinitiogeometry of the free triflate anion in Table I and the agreement is very good. As pointed out in ref 15, the experimental C-S, s-0,and C-F distances tend to be (erroneously) shorter at higher temperature sincethe ellipsoidalmodel usedin the crystal structure refinement does not describe the thermal motion of CF3 and SO3 groups adequately. It must be noted here that it is not known how the CF3SO3- geometry is affected by the intermolecular interactions in a crystal hydrate. We are currently performing geometry optimizations of cation-triflate complexes. The zero-point vibrational energies for the free triflate anion from HF/3-21G*, HF/6-31G*, and MP2/6-31G* theories are 8 1.80,8 1.44, and 74.26 kJ mol-’, respectively. The total electronic energy for the optimized geometry of the triflate anion is -953.403 369 au in the HF/3-21G* calculations. The 6-31G* optimized geometry lies 4.874 au lower in energy. The MP2 correlation energy contribution for the 6-3 lG* basis set results in an additional lowering of 1.354 au. The net atomic charges
C S stretch S - 0 1 stretch S-02 stretch S - 0 3 stretch C-Fl stretch C-F2 stretch C-F3 stretch 0144 bend 0 2 4 4 bend 03-S-C bend F l - C S bend F2-C-S bend F3-C-S bend 0 2 4 - 0 1 bend 0343-02 bend F2-C-Fl bend F3-C-F2 bend C S torsion
571 641 757 1046 15.9 30.1 30.1 30.1 12.6 12.6 12.6 9.3 16.2 18.4 16.2 11.9 6.3 5.6 6.4 7.2 6.5 6.3 5.6 17.7 9.7 37.1 9.5 8.2 7.3 35.7 8.0 7.2
1214 1214 1284 1310 1310 27.6 30.2 34.7 5.5 59.4 61.6 62.0 10.5 13.0 45.5 27.1 13.0 71.2 13.1 5.4 7.O 13.6 11.5
10.1 6.8 11.5 15.6 10.0 21.9
18.7
13.0, 12.8
from the Mulliken population analysis are 1.496,0.794,-0.730, and -0.367 for the S, C, 0, and F atoms at the HF/6-31G* geometry and 1.171, 0.607, -0.620, and -0.305 at the MP2 geometry. The Mulliken charges confirm the more polar character of the SO3 end of the ion. We have also performed optimization of all the geometry parameters,except theanglebetweenthe FlCSandOlCSplanes, for the eclipsed configuration of the triflate anion. The MP2/ 6-3 lG* calculationsshow that the staggered configuration of the triflate ion (CS bond length = 1.835 A, cf. Table I) is 17.56 kJ mol-’ more stable than the eclipsed one (CS bond length = 1.872 A). Bencivenni et a1.12 have found that the torsional barrier for CF3S03- is 17.5 kJ mol-’ with the 6-31+G* basis.12 Normal Mode Analysis. The triflate anion in its staggered configuration with C30point-group symmetry posseses 3N - 6 = 18 normal modes with the symmetry representations SA1 + A2 + 6E. The AI and E modes are both infrared and Raman active. The A2 mode is neither infrared nor Raman active and constitutes the internal torsion around the CS axis. In order to analyze the computed normal coordinates in terms of a moleculefixedcoordinate system, we defined a nonredundant set of the internal coordinates consisting of seven stretching coordinates (viz., CS, 3S0, and 3CF stretchings), 10 bending coordinates (30SC, 3FCS, 20S0, and 2FCF bendings), and the CS internal torsion. The CF3 and SO3 rocking coordinates are thus expressed as FCS and OSC bending coordinates. The PED matrix components greater than 5% from the MP2/6-31G* calculations are presented in Table I1 for all the normal modes. As may be readily noticed from Table 11, the symmetric and antisy”etricS03 stretchingsof the triflate ion involve practically
Gejji et al.
3714 The Journal of Physical Chemistry, Vol. 97, No. I S , 1993
TABLE III: Internal Force Constants, in mdyn A-l, of the Triflate Anion force constant
HF/3-21G*
ACF) ACF/CF) ASO) ASO/SO) AFCF)" AFCS)" AOSO). f(OSC)a ACS)
7.5 0.6 11.6 0.1 1.9 1.5 1.8 1.1 4.2
HF/6-31G* 7.6 0.9 10.9 0.2 2.1 I .6 I .7 1.1 4.1
MP2/6-31G* 6.2 0.8 9.5 0. I 1.7 1.4 1.3 0.8 3.2
a The bending constants were normalized with the factor ( r l d - I , rl and r2 being the lengths (in A) of the bonds forming the angle.
no other internal coordinates than the SO stretchings. On the other hand, the antisymmetric CF3 stretching involves the FCF and FCS bendings and the symmetric CF3 stretching involves CS stretching and FCFand FCS bendings. All bending normal modes are mixtures of virtually all internal bending coordinates. For several of the normal modes, the PED components do not sum up to loo%, indicating that the secondary (i.e., interaction) force constants are important and that a description restricted to the primary constants is actually too simplified. Force Constants. The primary internal force constants from the different levels of theory are presented in Table I11 for the stretching as well as the bending modes, along with some interaction constants for the CF and SO stretchings. The full force-constant matrix is available from the authors on request. Varetti et al.' have reported the primary internal force constants of the CF3SO3- anion in crystalline ammonium trifluoromethanesulfonate. The assignment of the CF3 and SO3 stretchings in their work was based on a comparison with the earlier reports in the literat~re.~" Moreover, their forceconstantsrefer to symmetry coordinates, which makes a direct comparison with the force constants in the present work rather difficult. It should be noted here that Varetti et al. have remarked that a proposed alternative assignment for the bands in the problematic 1350-1150 cm-I region results in "unacceptable negative values" for the SO/SO interaction constants and were for that reason discarded. The normal mode analysis from our ab initio calculations, where no a priori assignments were made, do not lead to any such negative interaction constants. Vibrational Frequencies. The vibrational frequencies of the triflate ion in the metal triflates as reported by Miles et al.4 and from our ab initio calculations are listed in Table IV. A comparison of the vibrational frequencies of the free triflate anion from HF and MP2 methods with the 6-31G* basis show that the CF3 and SO3stretching frequencies are lowered by 140 and 85 cm-I, respectively, by the MP2 correlation. Table IV also shows that the assignment of the ab initio frequencies differs from that presented in ref 4. The order of the SO3 and CF3 antisymmetric stretching modes is reversed. Our stretching N
frequencies from MP2 theory show the following order: v(S03) antisym > v(CF3) symm > v(CF3) antisym > v ( S 0 3 ) symm. If we use the present assignments for both the observed and calculated frequencies, it is seen that the ab initio MP2 antisymmetric and symmetric SO3stretching frequencies differ by 25 and 8 cm-I from the observed ones. The antisymmetric and symmetric CF3 stretching frequencies differ by 26 and 54 cm-I from the experiment. The fact that no splitting of the antisymmetric SO3stretching modes is observed in the sodium and barium triflates4 implies that the triflate ion is only weakly affected by the metal ions. A totally different situation was encountered for some divalent metal triflates dissolved in acetonitrile or poly(ethy1ene oxide),I0 where both noncoordinated and coordinated triflate ions were observed. In the case of zinc triflate dissolved in acetonitrile, the degenerate antisymmetric SO3 stretching of the noncoordinated triflate ion falls at 1271 cm-I. This band is split into two components at 1313 and 1241 cm-I on coordination of the triflate ion to zinc. The assignments of the antisymmetric SO3 stretching modes in ref 10 were in fact based on this splitting behavior. The bending and rocking vibrational frequencies of the free triflate ion from MP2 theory compare well with those observed for the triflate ion in sodium or barium triflates. The bending vibrational frequencies from MP2 theory deviate from the observed ones by a t most 10 cm-I. The assignments of the 637-, 580-, and 520-cm-' bands in the present work are in a good agreement with those for the triflate ion in crystalline ammonium triflate, as reported by Varetti et al.' The intense peak at 637 cm-' corresponds to a strong coupling of the bendings of the pyramidal CF3 and SO3 groups and the CS symmetric stretching as seen from Table 11. This band is also seen in the infrared spectra of the sodium and barium triflates presented in the work of Miles and co-~orkers,~ although these authors have not given any assignment for it. In contrast, using Raman spectroscopy, they have conjectured the presence of an accidental degeneracy of the symmetric and antisymmetric SO3 bendings at 580 cm-I. We have here assigned the 580-cm-I band to combined antisymmetric CF3 and SO3 bendings. A general observation concerning the experimental vibrational frequencies of the trifalte ion in different bonding situation^^*^.^-^^ is that, apart from the splittings of the antisymmetric SO3 stretching vibration, the other bands remain surprisingly constant, shifting by no more than 10cm-I. Yet the calculated frequencies differ by 26 and 54 cm-I from experiment for the antisymmetric and symmetric 'CF3 stretching" vibrations. It does not seem reasonable to explain this difference as a bonding effect. The inspection of Table IV shows that the MP2 correction has the largest effect on the CF3 stretching vibrations. It may be so that the CF3 stretching vibrations are particularly sensitive to the computational approximation level and that an MP4 calculation is needed here to bring the computed frequencies into closer agreement with experiment.
TABLE I V Vibrational Frequencies (cm-I) and Infrared Intensities (km mol-') (in Parentheses) of the Triflate Anion obs, ref 4 208 32 1 353 520 580 637 766 1038 1 I88 1230 1285
" ss
assignment" ref 4 CF3 r cs ss SO3 r CF3 ab so3 b
this work
cs t CF3 ab, SO3 ab cs ss
CF3 SS, CS ss
SO3 ab, CF3 ab SO3 ab, CF3 ab CF3 ab, SO3 ab so3 sb, CF3 sb, CS ss CF3 SS, CS ss
SO3 as CF3 SS, CS ss CF3 as
CF3 as CF3 SS, CS SS, CF3 sb SO3as
so3 SS
so3 SS
HF/3-21G* Y (int)
HF/6-21G* Y (int)
MP2/6-31G* Y (int)
82 (0.0) 226 (4.7) 352 (0.4) 381 (0.0) 554 (24) 625 (22) 702 (227) 805 (79) I 154 (22) 1349 (134) 1405 (61) 1452 (427)
73 (0.0) 224 (2.8) 348 (0.1) 383 (0.0) 565 (26) 631 (13) 717 (240) 840 (30) 1127 (13) 1343 (76) 1424 (88) 1398 (570)
67 (0.0) 204 (1.6) 3 13 (0.0) 345 (0.I ) 509 ( 1 7) 571 (9.7) 641 (172) 757 (14) 1046 (9.7) 1214 (140) 1284 (80) 1310 (368)
symmetric stretch; as = antisymmetric stretch, b = bend, sb = symmetric bend, ab = antisymmetric bend, t = torsion, r = rock.
Vibrational Frequencies of the Triflate Ion Infrared Intensities. As shown in Table IV the infrared inrensiries are sensitive to basis set quality and electron correlation effects. Extension of the basis set from 3-21G* to 6-3lG* is seen to lead to an enhancement of the infrared intensities of the CF3 and SO3 symmetric stretchings and the SO3 antisymmetric stretching mode. With the exception of the CF3 antisymmetric stretching mode, the normal mode intensities are lowered when electron correlation from second-order perturbation theory is included. Conclusions A new assignment for the stretching vibrational frequencies for the free triflate ion is proposed on the basis of the normal modeanalysisusing the forceconstants fromab initiocalculations including MP2 electron correlation. The antisymmetricS03 and CF3 stretching modes are seen to be reversed when compared with the assignments reported in the literature. The studies of the infrared spectra of the triflate ion coordinated to zinc or lead ions in PEO complexes support the conclusions from our MP2 calculations. The computed bending frequencies agree very well with those observed for the triflate ion in the crystalline salts. The stretching vibrational frequencies from the HF/6-3 1G* calculations are not only overestimated but even qualitatively incorrect. Acknowledgment. This work was supported by the Swedish Natural Science Research Council and the Swedish Natural Board
The Journal of Physical Chemisrry, Vol. 97, No. 15, 1993 3715 for Technical Development, which are gratefully acknowledged. We thank Dr. Anders Eriksson for useful discussions. References and Notes ( I ) Haszeldine, R. N.; Kidd, J. M. J . Chem. Soe. 1954, 4228. (2) Johansson, M.; Persson, 1. Inorg. Chim. Acra 1987, 127, 15. 0 ) Howells. R. D.: McCown. J. D. Chem. Reu. 1977, 77. 69. (4) Miles, M. G.; Doyle, G.; Corney, R. P.; Tobias, R. S.Specrrochim. Acra 1969, 25A, 1515. ( 5 ) Haszeldine, R. N.; Kidd, J. M . J . Chem.Soc. 1955,2901; 1957, 173. (6) Burger, H.; Burczyk, K.; Blaschette, A. Monarsh. Chem. 1970, 19. 607. ( 7 ) Varetti, E. L.; Fernhndez, E. L.; Ben Altabef, A. Spectrochim. Acta 1991, 47A, 1767. (81 . , Manning. J.: Frech. R. Polymer 1992. 33. 3487. (9) Wendsja, A.; Lindgren, J.; Thomas, J. 0.;Farrington, G. C. Solid Stale Ionics 1992, 53-56, 1077. ( I 0) Wendsjo, A.; Lindgren, J.; Paluszkiewicz, C. Electrochim. Acra 1992, 37. 1689. ( I I ) Wendsjo, A.; Lindgren, J.; Thomas, J. 0. Polymer, in press. ( I 2) Bencivenni, L.; Caminiti, R.; Feltrin, A.; Ramondo, F.; Sadun, C. J. Mol. Srruct. 1992, 257, 369. (13) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreman, 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 9 0 Gaussian Inc.: Pittsburgh, PA, 1990. (14) Pulay, P. Mol. Phys. 1969, 17, 197. (15) Schlegel, H. B . J . Comp. Chem. 1982, 3, 214. (16) Gwinn, W. D. J. Chem. Phys. 1971, 55,477. (17) Delaplane, R. G.; Lundgren, J. 0.;Olovsson, I. Acra Crysrallogr. 1975, 831, 2202. Lundgren, J. 0. Ibid. 1978, 834, 2428, 2432.
