J. Phys. Chem. 1987,91, 3195-3200
3195
The ring structure also leads to strain in the C-0 bonds in dioxirane, as seen from their bond deviation indices, 0.052. For the C - 0 bond in peroxytrifluoroacetic acid, on the other hand, X = 0.012. As expected, this bond is weaker in dioxirane, with a calculated bond order of 1.19 compared to 1.26 in the former. Finally, the strengths of the 0-H bonds in the peroxides show a striking consistency. The bond orders are all between 1.59 and 1.62, regardless of which conformer of H 2 0 2is involved and even when the CF,C(=O)- group is present. The effect of the latter is evidently not transmitted through the 0-0 bond, an observation that has been made earlier in a different context.3s
A
Figure 4. Calculated STO-6G bond paths and reference paths for dioxirane: (A) 0-0 bond path; (B) C-O bond path; (C) 0-0reference paths; (D) C-0 reference paths.
0-0 bond in dioxirane a significant degree of strain-and hence instability-that is not present in the corresponding bonds in the peroxides. Bond Orders. The 0-0bonds in the three hydrogen peroxide conformers and in peroxytrifluoroacetic acid have very similar bond orders [as calculated from eq 31, ranging from 1.19 to 1.21. The 0-0 bond order in dioxirane, however, is significantly less, 1.12. According to the bond strength-bond order correlation that was discussed earlier in this paper,** this bond should therefore be markedly weaker in dioxirane than in the peroxy systems. This conclusion is fully consistent with the relative bond lengths that are given in Table I, and with our finding that there is a considerable amount of strain associated with the 0-0 bond in dioxirane. It seems justifiable to view this bond weakness as a consequence of the ring structure rather than attributing it to the -0-0-group being forced into a cis-type geometry, because the relevant properties of the 0-0bond in the cis conformer of H202 are essentially the same as in the trans and the equilibrium str~ctures.~~
Summary An interesting point that is brought out by our analyses of hydrogen peroxide and peroxytrifluoroacetic acid is the rather limited sensitivity of the -0OH group to the remainder of the molecule. The structural parameters, the 0-0 bond deviation indices, and the bond orders of both the 0-0 and 0-H bonds are essentially unchanged by either rotation around the 0-0 bond in HzOzor the substitution of the electron-withdrawing CF3C(4)group. The latter factor does, however, significantly affect the electrostatic potential; the negative regions associated with the peroxide oxygens become weaker, especially the one nearer to the substituent. Thus a substantial degree of polarity is introduced into the 0-0 bond of peroxytrifluoroacetic acid. Our study has shown that the 0-0 bond in dioxirane is qualitatively different from those in hydrogen peroxide and peroxytrifluoroacetic acid. In dioxirane this bond is considerably strained, and consequently weaker than in these peroxides. The C - 0 bonds are also weakened by strain. The highly reactive nature of dioxirane, and its ability to act as an oxygen atom transfer agent, are thus readily understandable. Acknowledgment. We express our appreciation to Dr. Jane S. Murray for very helpful discussions and computational assistance. We also thank the Office of Naval Research for its support of this work, through Contract NOOO14-85-K-0217. Registry No. 02.7782-44-7;dioxirane, 157-26-6;hydrogen peroxide, 7722-84-1; peroxytrifluoroaceticacid, 359-48-8.
(39) Peters, D. Tetrahedron 1963, 19, 1539.
(40) We are indebted to Dr. Kenneth B. Wiberg for bringing up this p i n t .
Spectroscopic Properties and the Edge Inversion Process in Tetrahedral AF, Molecules David A. Dixon* and Anthony J. Arduengo, 111 E. I . du Pont de Nemours & Co.. Central Research and Development Department,t Experimental Station, Wilmington, Delaware 19898 (Received: October 7 , 1986: In Final Form: January 13, 1987)
Edge inversion in tetrahedral AF4 molecules, A = C, Si, Ge, Sn, has been investigated with ab initio molecular orbital theory. The rd and D4*structures have been optimized with at least a polarized double f basis set. The D4hstructures are all transition states characterized by one imaginary frequency. The D4hstructures are 128.9, 62.6, 47.6, and 37.0 kcal/mol above the ground-state Td structures at the MP-2 level for CF,, SiF,, GeF,, and SnF,, respectively. For CF,, the D4hstructure lies above the C-F bond dissociation energy. For the three remaining AF4 compounds, the D4* structure is bound with respect to dissociation of an A-F bond. The vibrational frequencies and infrared intensities for the Td and D,, structures have been calculated. The edge inversion process is shown to be the high-energy motion of the Td e bending mode. The potential energy curve connecting the Td and D4h structures has been calculated, and the two structures are shown to lie on the same surface.
Introduction We have recently shown that appropriately substituted tricoordinate pyramidal pnictogens (group VA) (group 15)35 8-Pn-3, (pn = p, A ~ Sb) , can invert by a new mechanism.1,2 This mechanism is described as the edge inversion of a tetrahedron whereby inversion occurs via a planar T-shaped transition state 'Contribution No. 4052.
with the lone pair in the molecular plane. This new process (Scheme I) was first predicted for fluorinated phosphines' and experimentally demonstrated for a saturated ADP0 (5-aza-2,8dioxa- l-phosphabicyclo[3.3.O]octa-2,4,6-triene)system.2 The edge (1) Dixon, D. A,; Arduengo, A. J., 111; Fukunaga, T. J . Am. Chem. SOC. 1986, 108, 2461. (2) Arduengo, A. J., 111; Roe, D. C.; Dixon, D. A. J . Am. Chem. SOC.1986, 108, 6821.
0022-3654/87/2091-3195$01.50/00 1987 American Chemical Society
Dixon and Arduengo
3196 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 SCHEME I
TABLE I: Calculated Geometries and Energies for Td and D,,, AF, Structures orooertv CF, SiF, .
L
2
R(Td)' R(D4h)LI
E(TAECFb
E~D'&F~ E( Td)MP-2' E(D4,,)MP-2'
1.301 (1.319)' 1.372 -435.766993 -435.516022 -436.551882 -436.346453
1.556 (1.552)d 1.587 -687.084957 -686.977030 -687.84061 2 -687.740776
GeF,
SnF,
1.672 (1 .67)e 1.693 -2473.359 127 -2473.270819 -2474.1 18304 -2474.042424
1.870 (1.88)' 1.884 -641 9.85301 0 -6419.793804 -6420.519085 -6420.460142
'Bond distances in A. Experimental values in parentheses. bTotal energies in au. 'Reference 17. dReference 18. eReference 19. /Reference 20. This distance is that for the axial Sn-F bond in polymeric SnF,.
inversion process has also been predicted to occur in perfluoroarsine and perflu~rostibine.~The edge inversion process should be contrasted with the inversion process associated with ammonia where inversion occurs through a planar trigonal structure with a lone pair perpendicular to the plane. This inversion process is appropriately described as vertex inversion of a tetrahedron. The edge inversion process plays an important role in providing a chemically accessible transition state for species with electronegative substituents, and with central atoms heavier than Ne. We now wish to generalize the edge inversion process to a four-coordinate tetrahedral ( Td)group IVA (group 14) compound, AX4, where a ligand replaces the lone pair found in the corresponding group VA (group 15) compounds. This suggests that edge inversion of an appropriately substituted Tdspecies can occur through a square planar (D4h)transition state. Such a process occurring at low energies becomes important to consider since it is well-known that optically active Td Ge and Sn compounds can readily racemize whereas the corresponding carbon analogues do not.4 To substantiate the proposal that the edge inversion process occurs at chemically accessible energies for group IVA (group 14) elements, we have examined the edge inversion process for CF4, SiF4, GeF4, and SnF, with large-scale ab initio calculations. In order to more fully characterize the process, we have determined the force fields for the optimum Td and D4h transition-state structures and examined the potential energy surface connecting the two ~ p e c i e s . ~
Calculations Geometry optimizations for the Tdand D4hstructures were done at the S C F level using gradient techniques6 with the program HONDO' on a IBM-3081 computer. Force fields and MP-2 cor(3) Dixon, D. A.; Arduengo, A. J., I11 J . Am. Chem. SOC.1987, 109, 339. (4) Gielen, M. In Inorganic and Organometallic Stereochemistry; Geoffrey, G. L., Ed.; Interscience: New York, 1981; p 217. (5) These data have been presented in preliminary form. See: Arduengo, A. J., 111; Dixon, D. A.; Stewart, C. A. Abstracts of the 10th International Conference on Phosphorus Chemistry, Bonn, FRG, Sept. 1986. (6) (a) Komornicki, A.; Ishida, K.; Morokuma, K.; Ditchfield, R.; Conrad, M. Chem. Phys. Lett. 1977.45, 595. McIver, J. A,; Komornicki, A,, Jr. Ibid. 1971, 10, 303. (b) Pulay, P. In Applications of Electronic Structure Theory; Schaefer, H. F., Ed.; Plenum: New York, 1977; p 153. (7) (a) Dupuis, M.; Rys, J.; King, H. F. J . Chem. Phys. 1976.65, 111. (b) King, H. F.; Dupuis, M.; Rys, J. National Resource for Computer Chemistry Software Catalog Vol. 1, University of California-Berkeley, Berkeley, CA. Program Q H 0 2 (HONDO), 1980.
rections8 were determined with the rapid analytical techniques9 on a CRAY-1A computer. incorporated in the program GRADSCFIO Only the valence electrons were included in the MP-2 calculations. For CF,, a polarized double { (DZ + P) basis set of the form (9s5pld)/[4s2pld] was used."J2 For SiF4, the geometry was optimized with a D Z + P basis set of the form ( l l s 7 p l d l 9 ~ 5 p l d ) / [ 6 ~ 4 p l d / 4 ~ 2 pin l dthe ] order Si, F.I2 The final energy and force field calculations were done with a DZ P basis set in the order Si,13 of the form (1 3s9pld/9~5pld)/[6~4pld/4s2pld] F." The fluorine basis set for GeF4 and SnF4is the [3s2pld] basis set given above. For Ge the basis set is of better than D Z P quality and has the form (14sl lp6d)/[lOs8p3d]. Following previous work,I4 the exponents and contraction coefficients are from Dunning's ~ompilation.'~ The first five s orbitals are contracted together, as are the first four p orbitals and the first four d orbitals. The remaining orbitals are left variationally free. The exponent of the final d function is 0.2699 obtained by a geometric progression based on the final two d exponents given by Dunning. For Sn, the basis set has the form (15sl lp8d)/ [ 10s7p5dI and was constructed in a similar fashion again from an atomic basis set of Dunning.16 Based on previous work on GeH4,I4we only contracted the first six s functions, the first five p orbitals, and the first four d orbitals. The final d orbital exponent was 0.2069 obtained as described above. The Sn basis set is given in Table VI. The geometries for the calculation of the potential energy surface connecting the Td and D4h structures were chosen as
+
+
(8) (a) Mdler, C.; Plesset, M. S. Phys. Reo. 1934, 46, 618. (b) Pople, J . A.; Binkley, J. S.; Seeger, R. Int. J . Quantum Chem. Symp. 1976, 10, 1. (9) King, H. F.; Komornicki, A. In Geometrical Derivatives of Energy Surfaces and Molecular Properties; Jorgenson, P., Simons, J., Eds.; Reidel: Dordrecht, 1986; NATO AS1 Series C, Vol. 166, p 207. King, H. F.; Komornicki, A. J . Chem. Phys. 1986, 84, 5645. (IO) GRADSCF is an ab initio gradient program system designed and written by A. Komornicki at Polyatomics Research and supported on grants through NASA-Ames Research Center. (1 1) Dunning, T. H., Jr. J . Chem. Phys. 1970, 53, 2823. (12) Dunning, T. H., Jr.; Hay, P. J. In Methods of Electrocic Structure Theory; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; Chapter 1. 3dr(Si) = 0.40. (13) McLean, A. D.; Chandler, G. S. J . Chem. Phys. 1980, 72, 5639. (14) Eades, R. A.; Dixon, D. A. J . Chem. Phys. 1980, 72, 3309. (15) Dunning, T. H., Jr. J. Chem. Phys. 1977, 66, 1382. (16). (a) Dunning, T. H., Jr., private communication. (b) Dixon, D. A,, unpublished results.
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3197
Tetrahedral AF4 Molecules
TABLE II: Vibrational Freauencies (cm-') and Infrared Intensities (km/mol) SiF4
A
1010 (909)b 477 (435)b 1462 (1283)* 691 (632)b
E T2 T2
835 (goo)*268 (268)* 1075 (1032)b 401 (389)b
1491 (970)c 29 (9.0)c
GeF4
849 20 1
78 1 216 842 292
SnF,
721 156 750 209
387 198
312 228
D4h
927 427 845 1005 4461 1101 812
*I,
BI, B2,
A, B2u
E" a Experimental
821 68 1 525 521 230i 1098 503
98 2134 0.6
values in parentheses.
792 112
703 629 293 209 1551 750 252
103 362 206
113 280 118
Reference 24. 'Reference 22.
A
7c
186
762 653 412 308 207i 848 360
TABLE 111: Energy Barriers to Edge Inversion AE, kcal/mol molecule SCF MP-2 MP-2/ZPEa
6C
CF4 SiF4 GeF4
sa
SnF4
40
157.5 67.6 55.4 37.2
128.9 62.6 47.6 37.0
126.9 62.5 47.5 36.9
SiFI
E (Ksal)
A
GeF4
Calculated AE including zero-point energy differences.
30
20
10
0
1
-.7s
-.so
-.IS
0.0
0.2s
E d g e I n v e r s i o n Cooidinst.
0.50
0.1s
1.0
(r)
Figure 1. Potential energy curve for the edge inversion process in SiF,, GeF4, and SnF, as a function of r , the normalized distance between the edges.
follows. The variation in bond length between the Td and D4h structures was assumed to be a linear function with respect to { where {is the out-of-plane angle defined as { = 0.5 (180 - e) with 0 the FAF bond angle. This is also a linear function in R'where R'is the distance between the two edges of the tetrahedron which are inverting. R'is defined as 2R/3 a t the Td structure with R the bond length and is 0 a t the planar D4h structure. The normalized values ( r ) for R' are plotted in Figure 1 where r( Td) is defined as 1.0 ({ = 32.25O) and r(D4J = 0.0 (( = O.Oo). The bond distances for the Td and D4hstructures are given in Table I together with the total energies. The bond distances for the Td structures agree well with the known experimental valu e ~ . ~ ' - *The ~ C-F bond length is shorter than the experimental value, a result typically found for fluorocarbons with good basis sets.21 The calculated Si-F and Ge-F bond distances are essentially identical with the experimental values. The molecule SnF, is not known but we can compare with calculated value to that for the axial Sn-F bond from the crystal structure for polymeric SnF4?0 again excellent agreement is found. (17) Smart, B. E. In Molecular Structure and Energetics, Liebman, J. F., Greenberg, A., Eds.; Verlag Chemie: Deerfield, FL, 1986; Vol. 3, Chapter 4. (18) Stull, D. R.; Prophet, H. JANAF Tables, Natl. Stand. ReJ Data Ser., (US.)Narl. Bur. Stand, 1971, No. 37 and Supplement. (19) Rochow, E. G. In Comprehensioe Inorganic Chemistry; TrotmanDickenson, A. F., Ed.; Pergamon: Oxford, England, 1973; Vol. 2, p 1. (20) Hoppe, R.; Dahne, W. Naturwissenschaften 1967, 49, 254. (21) Dixon, D. A.; Fukunaga, T.; Smart, B. E. J. Am. Chem. SOC.1986, 108, 1585, 4027.
The bond distances for the square planar D4hstructures are all longer than those for the Td structures. The difference R(D4h) - R(Td) decreases with increasing atomic size of the central atom. The Dlh structures are true transition states characterized by one imaginary frequency (see below). The vibrational frequencies and infrared intensities for the Td and D4hstructures are given in Table 11. For CF4, both the frequencies and infrared intensities are known e ~ p e r i m e n t a l l y . ~ ~ - ~ ~ The calculated frequencies for CF4 are too large due to our neglect of correlation corrections and anharmonic effects. An average scale factor of 0.90 is needed for CF,. Our calculated value for the intensity of the degenerate C-F stretch is too high by about 50% while for the degenerate F-C-F bends, the intensity is too high by about a factor of 3. Such differences are typically found for infrared intensities if appropriate basis sets are employed. For SiF,, only the experimental frequencies are known24 and our calculated values are in very good agreement with an average scale factor of 0.97 required for agreement with experiment. The intensity for the degenerate stretch in SiF4is about 60% of that in CF4 while the intensity for the degenerate bend is about 7 times larger than that in SiF,. The frequencies for GeF, and SnF, have not been reported and we suggest that the scale factor of 0.97 from SiF, is appropriate. The intensities show the interesting variation that the A-F triply degenerate stretch intensity decreases with increasing atomic number while the intensity for the triply degenerate bend is approximately constant for the fluorides of the three heavier elements. If the doubly degenerate bend is taken to a high enough vibrational level, the molecule can access the square planar D4h structure and invert its configuration. Thus extending this bend to a high vibrational level corresponds to the edge inversion process. The energy differences between the T ,and D4hstructures are given in Table I11 at both the S C F and MP-2 levels. The D4hstructure for CF,, as expected, is very high in energy and is above or comparable to the C-F bond dissociation energy.25 Thus bond ~
~~~~~~
(22) Golden, W. G.; Marcotte, C.; Overend, J. 0. J . Chem. Phys. 1978, 68, 208 1. (23) Smith, M. A. H.; Rinsland, C. P.; Fridovich, B.; Rao, K. N. In Molecular Spectroscopy: Modern Research; Rao, K. N., Ed.; Academic: New York, 1985; Vol. 111, p 111. (24) Shimanouchi, T. In Tables of Molecular Vibrational Frequencies, Consolidated; National Bureau of Standards: Washington, DC, 1972; Vol. I, NSRDS-NBS 39. (25) De (C-F) = 130.5 kcal/mol for CF4. See ref 16.
3198 The Journal of Physical Chemistry, Vol. 91,No. 12, 1987
TABLE V Orbital Energies (eV) for AF4 Molecules
TABLE IV: Electronic Properties of AF4 Molecules
property qA(
Td)
qF( Td) qAd( Td) qA(D4h) qF(D4h) qAd(D4h)
%(Td)b
Dixon and Arduengo
CF4
SiF,
GeF,
SnF4
0.84 -0.21 0.32 0.96 -0.24 0.32 12.76 14.96
1.91 -0.48 0.44 1.93 -0.48 0.62 14.97 15.51
2.08 -0.52 10.01 2.00 -0.50 10.22 17.75 18.21
2.66 -0.67 20.40 2.57 -0.64 20.51 20.21 20.54
Mulliken charge on central atom. q F = Mulliken charge on fluorine. qAd = Mullinen d orbital population on central atom. All populations in units of e, bPolarizabilityin au3. "qA =
dissociation is likely to occur before edge inversion will occur. This result is consistent with the high inversion barrier (77.9 kcal/mol) found at the SCF level for NF3 which proceeds by vertex inversion rather than by edge inversion (barrier = 142.9 kcal/mol).26 We also note that the correlation correction to AE is significant for CF4. In contrast to the results found for CF,, the Dlh structure for SiF4 is only 67.7 kcal/mol above the Tdstructure at the SCF level and only 62.6 kcal/mol at the MP-2 level. The MP-2 correlation correction to AE is much smaller for SiF4 as compared to CF4, consistent with the more energetically accessible structure found for SiF,. For CF,, the S C F value for AE is greater than the C-F bond dissociation energy. The C-F bond is significantly longer, 0.071 A, in the D4h structure as compared to the Td structure whereas the Si-F bond is only 0.031 8, longer in the D4hstructure when compared to the Tdstructure. Thus it is not surprising that there is a larger correlation correction to AE for CF,. The edge inversion process for SiF4 is much lower than the SiF bond dissociation energy of at least 140 k c a l / m 0 1 ~and ~ the inversion process can occur without breaking an Si-F bond. The edge inversion processes occur at even lower energies, 47.6 and 37.0 kcal/mol at the MP-2 level, for GeF, and SnF,, respectively. Extrapolating from known A-X (X = halide) bond dissociation energies,28the edge inversion process is still well below the Ge-F and Sn-F bond dissociation energies. The inversion barriers for GeF, and SnF, are accessible thermally and the edge inversion process should be observable with appropriately chosen substituents. The calculated edge inversion barriers are most likely upper limits as a better treatment of electron correlation, e.g., MCSCF CI, could lower the barriers. As mentioned previously, the Dlh structures are transition states characterized by one imaginary frequency. This frequency is of Bzusymmetry and corresponds to one of the E modes of the T d structure. The imaginary frequency for CF, is much higher than those for SiF,, GeF4, and SnF,, consistent with the lower edge inversion barriers found for the latter molecules and tighter curvature at the transition state for CF,. As expected the imaginary frequencies decrease with decreasing barrier heights and increasing group IVA (group 14) atomic number. In order to demonstrate that the D4i structures are on the appropriate potential energy surface for edge inversion, we calculated the S C F energy at a number of points on the inversion surface. The points were chosen as described earlier. The results for SiF,, GeF,, and SnF4 are shown in Figure 1. Clearly the D4h and Td points are on the same potential energy surface, that for edge inversion. It is interesting to note that the inflection points correspond to about a 50% change in the edge inversion coordinate. The frequencies for the D4,, structures are given in Table 11. The frequencies for CF,(D,,) behave quite differently from those found for the other fluorides consistent with the very high energy of the CF4 transition state. For example, the degenerate stretching
+
(26) Dixon, D. A.; Arduengo, A. J., 111, unpublished results. (27) (a) Farber, M.; Srivastava, R. D. J . Chem. Soc., Faraday Trans. I 1978, 74, 1089. (b) Walsh, R.Acc. Chem. Res. 1981, 14, 426. ( c ) Schlegel, H. B. J . Phys. Chem. 1984, 88, 6254. (28) (a) Cotton, F. A,; Wilkinson, G . Advanced Inorganic Chemistry; 2nd ed.; Wiley-Interscience: New York, 1966; p 457. (b) Dasent, W. E. Inorganic Energefics; Penguin: Harmondsworth, England, 1970; p 105.
orbital"
CF,
SiF4
GeF,
SnF4
Td
occ occ
HOMO LUMO unocc
20.95 (e) 19.48 (t2) 18.62 (tl) -9.34 (al) -9.35 (t2)
19.96 (e) 19.44 (t2)
18.51 (tl) -4.56 (al) -4.97 (t2)
19.28 18.64 18.46 -2.75 -5.44
(e)
19.74 19.50 18.31 17.81 17.78 17.37 17.12 -0.82 -1.02
(b2,) (a2J
(t2)
(tl) (a,) (t2)
18.32 17.98 17.81 -0.88 -4.39
(e) (tl) (t2)
(al) (t2)
D4h
occ
occ occ occ occ OCC
HOMO LUMO unocc
22.52 22.46 19.16 18.45 17.89 16.91 16.72 -1.12 -4.65
(a2,) (b2g)
20.67 20.02 18.71 (e,) 18.65 (e,) (bZu) 17.91 (big) 17.75 (a2,) 16.90 (a2") -1.60 (al,) -1.89
(b2J
(a2J (e,) (big) (e,) (b2J
(a2,) (al,) (a2,)
(e,) (e,) (b2J (b1J
(a2,) (a,,)
(a2")
18.41 18.36 17.59 17.38 17.35 16.89 16.46 0.15 -0.22
(b2&
(azu) (e,) (b2,)
(e,) (a2,) (bl,) (al,)
(a2")
"Orbitals given in order of increasing energy. occ = occupied. unocc = unoccupied. HOMO = highest occupied molecular orbital. LUMO = lowest unoccupied molecular orbital. Positive values are bound orbitals. Negative values are unbound orbitals. mode in CF4(D4&is 360 cm-' less than the degenerate stretch in the Tdstructure. This suggests a significant decrease in the C-F bond force constant and a weakening of the C-F bond. For the other fluorides, the degenerate stretches are of comparable size for the D4h and Tdstructures suggesting little variation in the A-F bond force. constants. The totally symmetric A,, stretch again shows the largest difference for the Td and D4h structures for CF4 but the difference is not as pronounced as it is for the degenerate modes. The other large difference is in the A, mode which is the out-of-plane umbrella mode corresponding to the fluorines moving in +z and the central atom moving in -z ( z is the 4-fold axis). For CF,, this is a very high energy mode, the second highest mode. For the other fluorides, this mode is much lower in frequency and is more like a normal bend. A variety of electronic properties are given in Table IV for the Tdand D4hspecies. The Mulliken populations show the qualitative trend that the molecules become more ionic as the size of the central atom increases consistent with trends in electronegativity. There is a dramatic increase in the ionic character between CF4 and SiF,. The difference in ionicity between Gel and SnF4 is substantial. By the time SnF4 is formed, the central atom has more than 2.5 units of positive charge. The amount of d orbital particpation varies in an interesting manner for the Tdstructures. There is a significant amount of d orbital population in CF4 and this increases in SiF4 as expected since the virtual 3d in the atom is more available for Si. For GeF,, there is only a O.0le valence d population above the 10 electrons required for filling the inner 3d shell. For SnF,, this has increased to 0.40e in the valence shell (20 electrons in the filled 3d and 4d inner shells). The variation of the d populations between SiF4and GeF, occurs because of the ionicity of the A-F bond and because of the presence of a filled 3d inner shell in Ge. Backbonding from the "F"to the virtual d orbitals on Ge will lead to repulsive interactions with the inner-shell d orbitals and decrease the amount of d character as compared to Si where backbonding does not lead to such repulsive interactions since no inner-shell d orbitals are present. There is a larger contribution of backbonding in SiF4 as compared to CF4 consistent with more available "d" orbitals on Si and a higher ionic character to the Si-F bond. For SnF,, the d orbitals again play a larger role because there is significantly more ionic character in the Sn-F bond (due to the very positive Sn) leading to a larger role for backbonding. In the D4,,structures, the negative charge flow in CF4 is from the carbon to the fluorines giving a more positive central atom in the D4hstructure. For SiF,, there is essentially no charge flow in the D4hstructure while for GeF, and SnF,, the negative charge flow is reversed and is from the fluorines to the central atom in the Dlh structure. Thus the D4h structures become slightly less ionic. The differences in d orbital populations in the Td and D4h
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3199
Tetrahedral AF, Molecules TABLE VI: Contracted Gaussian Basis Set for Sna
exponent
coefficient
orbital
633400.0 95370.0 21 770.0 6220.0 2072.0 763.8 296.2 92.73 43.27 18.42 7.747 2.63 1 1.176 0.2089 0.0862 4918.0 1135.0 357.70 132.38 53.34 20.39 8.654 3.08 1 1.250 0.3678 0.0958 351.6 97.53 34.27 13.24 5.265 1.941 0.6369 0.2069
0.000747 0.005742 0.029437 0.1 13226 0.325195 0.6 2 39 84 1.o
s
1 .o
1.o 1.o 1 .o 1.o 1 .o 1.o 1.o 0.004612 0.038729 0.1771 30 0.440938 0.48521 1 1.o 1.o 1 .o 1.o 1.o 1.o 0.016414 0.12841 1 0.419595 0.598178 1 .o 1.o 1.o 1 .o
s S S
s s s S S
s
P
Dunning, Jr., T. H., private communication. structures also show interesting trends. For CF,, there is no difference in the d populations. For SiF, there is an increase of 0.18e in the D4hstructure while for GeF,, the increase is 0.21e. For SnF,, the change in d populations is an increase of only 0.1 le. The molecular polarizabilities defined as a. = 1 / 3 ( a X XaYy azz)are also given in Table I v . The polarizability of the D4h structure is always more than that for the Td structure. However, the difference decreases with increasing group IVA (group 14) atomic size and is consistent with the changes in charge flow described above. The difference in a. is largest for CF:, where negative charge flows toward F in the D4,,structure and is smallest in SnF, which has the largest charge flow in the opposite direction. The various orbital energies are given in Table V. For CF,, SiF,, and GeF,, the H O M O is of type t , symmetry and the N H O M O has type t2 symmetry. This is reversed for SnF,. The H O M O S are all quite strongly bound and decrease with increasing central atom size. These H O M O values correspond to the molecular ionization potential. Since they are obtained from Koopmanns’ theorem, we are probably overestimating the experimental values. Most of the electron density in the top eight orbitals (t, + t2 e) is of lone pair character on the fluorines. The LUMO is predominantly localized on the group IVA (group 14) atom and has a large s character (al symmetry). The NLUMO is of type t2 symmetry. As the central atom becomes larger, the LUMO approaches zero so that the L U M O for SnF, is almost bound. For the D4h structures, the orbitals show a more extensive variation. The H O M O for D4h CF,, SiF4, and GeF, are of azg symmetry while the HOMO for D4hSnF, is of bl, symmetry. The a2, H O M O has no occupancy on the central atom whereas the b,, HOMO incorporates some d9-9 character on the central atom. The variation in the H O M O eigenvalues (ionization potential) of the Dah structures differs from the Tdbehavior. The ionization potentials actually increase from CF4 to GeF, and then decrease for SnF, when the orbital symmetry switches. The b,, orbital is worth examining in more detail as it suggests that inner-shell d orbitals can mix into the valence space. In SiF, with no occupied
+
+
+
d orbitals, the b,, orbital is four orbitals below the HOMO. The bl, becomes the NHOMO when there is a filled 3d shell as found in GeF,. Thus this orbital involving fluorine lone pairs is being somewhat destabilized by its interaction with the filled dX2-y~ pair. In SnF,, the b,, orbital is further destabilized by its interaction with two filled dX2-y2inner shells (the higher energy one is also more accessible) and is now the HOMO. The other occupied orbitals show some variations. Of interest is the location of the a2u occupied orbital which i s the first occupied orbital with character on the central atom. This orbital is quite removed from the HOMO, and we note that the coefficients on the central atom are not large (the largest is 0.31 found for CF,). Thus there is not a large amount of back donation from the fluorine out-of-plane lone pairs into this orbital. The LUMO for CF4 is of the type azu corresponding to an out-of-plane pz orbital on the central atom. The NLUMO (al,) is an s orbital on the central atom. For SiF,, GeF,, and SnF,, the opposite is true and the LUMO is of type a,, symmetry. The LUMO’s are all of low energy and for D4h SnF,, the LUMO is predicted to be bound. The a2uNLUMO is quite close in energy to the LUMO and is, thus, also accessible. Since the LUMO for D4hSnF4 is bound, it is not surprising that SnF, forms a polymer in the crystal with a pseudooctahedral environment with two bonded axial fluorines and four equatorial bridging fluorines.20 There are two other calculations that relate to this study. Schleyer and coworkers calculated a value for AI? of 114 kcal/mol between the Td and D4h structures of SiH4 with an STO-3G* basis set at the S C F leveLZ9 On the basis of the molecular orbitals from this calculation and in comparison with those for CH,, Schleyer and c o - w ~ r k e r ssuggest ~~ that a-donor, o-acceptor substituents should stabilize the D4h geometyy. More recently, the differences in energy between the Td and D4h structures for SiF,, GeF,, and SnF, were calculated30at the S C F level with the STO-3G basis set. The respective values are 70, 64, and 48 kcal/mol, all higher than our more extensive calculations. Furthermore, S C F calculations on SiF4 with the somewhat larger 3-21G(*) basis set give a AE of 75 kcal/mol which is in the opposite direction to our value determined with a much larger basis set. On the basis of the orbitals for SiH,, they30suggest that the LUMO is of azusymmetry and that a-donors can interact with the LUMO. We find very little evidence for back-donation to the pz orbital. Furthermore, it is not even the proper symmetry of the LUMO for SiF,, SnF,, and GeF,. These authors find that the LUMO for CH4(D4J is of b,, symmetry and that the HOMO is of aZusymmetry. They suggest this as the reason for the high energy of the D4h structure for a variety of a-donor structures. We note that this is not the case for CF, where the LUMO is of type a2,, symmetry and is energetically accessible. On the basis of our results we prefer a simple ligand field type model. As shown by the charge distributions, these structures are quite ionic. Thus an important factor is to minimize the F-F interactions. The Td structure minimizes these interactions for four ligands. For CF, to invert, the bond length increases to minimize the F-F interaction which is at a minimum for Td CF, (2.12 A). For CF,(D4,J R(F-F) is 1.94 8, and there is significant repulsion. For SiF,, GeF,, and SnF,, the values for R(F-F) are 2.24, 2.39, and 2.66 A, respectively. These values are all greater than the minimum value of 2.12 A seen in fluorocarbons for gem-difluoro interactions and for Sn are approaching the sum of the van der Waals radii for two fluorines. Thus as the size of the central atom increases, the F-F interactions in the D4h structure are decreased in energy leading to a lower energy transition state. Of course electronegativity and orbital effects can play a role in fine-tuning the energy of the D4h structure. Although a variety of optically active tetrahedral Sn and Ge compounds are known to racemize? the usual mechanism involves (29) (a) Wurthwein, E.-U.; Schleyer, P. v. R. Angew. Chem. Inr. Ed. Engl. 1979,18, 553. (b) Krogh-Jesperson, M.-B.; Chandrasekhar, J.; Wurthwein, .-U.; Collins, J. B.; Schleyer, P. v. R. J . Am. SOC.1980, 102, 2263. (30) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio
Molecular Orbital Theory; Wiley-Interscience: New York, 1986; p 432-6. This work appeared after the completion of our work.
J . Phys. Chem. 1987, 91, 3200-3203
3200
the coordination of one4 or two solvent molecules.30 Our results suggest that there is an energetically accessible transition state through which these compounds could pass without the need of solvent to form a penta- or hexacoordinate transition state. Thus it is quite possible that the loss of optical activity is due to an energetically accessible edge inversion pathway. This can also be extended to silicon systems. There is one reported3’ experimental example (1) of a lowenergy inversion process at Si with AE = -26 kcal/mol. The
i
0’
\o 3
to be planar32from experiment while the edge inversion process in PF, has AE = 68.4 kcal/mol at the SCF level (53.8 kcal/mol at the MP2 level)., It has also been ~ u g g e s t e dthat ~ ~ ,compounds ~~ with the central fragment of 3 may also have a low barrier or even be planar33 although the latter point is in dispute.34
Acknowledgment. The authors thank Dr. T. H. Dunning, Jr. for the Sn basis set. Registry No. CF,, 75-73-0; SiF,, 7783-61-1; GeF,, 7783-58-6; SnF,, 1783-62-2.
2 1 value of 26 kcal/mol for AE is not inconsistent with the value of AE found for SiF4 since the ligands bonded to silicon are so different. Indeed, the lower value of 1 is consistent with what is observed in ADPO (2) as compared to PF3. ADPO is known (31) Martin, J. C.; Stevenson, W. H., 111; Lee, D. Y. In Organosilicon and Bioorganosilicon Chemistry: Structure, Bonding, Reactivity and Synthetic Application; Sakurai, H., Ed.; Ellis Horwood: Chichester, U. K., 1985; Chapter 13, p 141.
(32) Culley, S. A,; Arduengo, A. J. 111J . Am. Chem. SOC.1984,106, 1164. (33) (a) Meyer, H.; Nagorsen, G. Angew. Chem., Int. Ed. Engl. 1979, 18, 5 5 1 . (b) Nagorsen, G.; Meyer, H. Zbid. 1980, 19, 1034. (34) (a) Dunitz, J. D. Angew Chem., Znt. Ed. Engl. 1980, 19, 1034. (b) Schomburg, D. Angew. Chem., Znr. Ed. Engl. 1983,22,65. (c) Bibber, J. W.; Barnes, C. L.; Helm, D. V. D.; Zuckerman, J. J. Angew. Chem. Suppl. 1983, 688. (35) In this paper the periodic group notation in parentheses is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is eliminated because of wide confusion. Groups IA and IIA become groups 1 and 2. The d-transition elements comprise groups 3 through 12, and the p-block elements comprise groups 13 through 18. (Note that the former Roman number designation is preserved in the last digit of the new numbering: e.g., I11 3 and 13.)
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Quantitative Infrared Spectroscopic Investigations of Hydrogen-Bond Cooperativity H. Kleeberg,* D. Klein, and W. A. P. Luck Fachbereich Physikalische Chemie, Philipps- Universitat, 0-3550Marburg, FRG (Received: October 31, 1986)
Infrared spectra of solutions of 1,4-butanedioland aprotic solvents B in CC14 and of methanol in aprotic solvents demonstrate the presence of cooperative effects. The OH frequencies of OH-OH-B complexes of 1,Cbutanediol in CCll and of methanol dimers in B are compared with those of 0H.s.B interactions. In comparison to complexes with only one H bond (Le., OH-OH or OH-B) the mutual cooperative influence of the formation of the second H bond amounts to about 20%. For short H-bonded chains like 1,4-butanediol dimers in CC14 the cooperative effect seems to increase to about 123%. The similarities of the frequencies in 1,4-butanediol dimers and crystalline alcohols may be interpreted in terms of cooperativity.
Introduction In 1957 Frank and Wen’ postulated qualitatively the presence of cooperative effects between H bonds. This means that, for example, an existing H bond between an alcoholic O H group and an aprotic H bond acceptor B (Le., OH-B) would be strengthened by the formation of a second H bond between another alcohol R O H and the OH group already involved in ROH-B (Le., OH-OH.-B). On the other hand the strength of the H bond between the two alcohol molecules in O-H...O-H...B
/ R
/
R
would also depend on the H-bond acceptor strength of B. The presence of cooperative H-bond effects has been supported by theoretical calculations.*” Some theoretical papers concluded “the nonadditive component of the interaction energy to be small”.7 Therefore, experimental tests seem to be necessary. Some experimental indications were found for HF* and for alcohol^.^ ‘Presented in part at the Tenth International Conference on Non Aqueous Solutions, Leuven, Aug 18-22, 1986, and the Gordon Conference, New Hampshire, Aug 4-8, 1986.
0022-3654/87/2091-3200$01 S O / O
Matrix alcohol and water spectra lead to the conclusion that cooperative effects exist.1° Recently we found” that the usual OH frequency shifts Au~H-.B (AuOH...B = ugas - uOH ...B) of DOH-B complexes (B = H-bond (1) Frank, H. S.; and Wen, W.-Y. Discuss. Faraday SOC.1957.24, 133. (2) Kollman, P. A.; Allen, L. C. J . Am. Chem. SOC.1970, 92, 753. (3) Del Bene, J.; Pople, J. A. Chem. Phys. Lett. 1969, 4, 426. (4) Hankins, D.; Moskowitz, J. W.; Stillinger, F. H. Chem. Phys. Lett. 1970, 4, 527. (5) Clementi, E. Lecture Notes in Chemistry; Springer Verlag: Berlin, 1976; Vol. 2. (6) Schuster, P. Angew. Chem., Znt. Ed. Engl. 1981, 20, 546. (7) Clementi, E.; Kolos W.; Lie, G. C.; Ranghino, G. Int. J. Quantum Chem. 1980, 17, 371. (8) Couzi, M.; Le Calv&,J.; van Huong, P.; Lascombe, J. J. Mol. Slruct. 1970, 5, 363. (9) Symons, M. C. R.; Thomas V. K.; Fletcher, N. J.; Pay, N. G. J. Chem. SOC.Faraday Trans. 1 1981, 77, 1899. Symons, M. C. R. Acc. Chem. Res. 1981,14, 179. Symons, M. C. R., Fletcher, N. J.; Thompson, V. Chem. Phys. Lett. 1979, 60,323. (10) Luck, W. A. P.; Schrems, 0. Horizons in H-bond Research, VIth European Workshop, University of Leuven, Leuven, Aug 22-27, 1982. (11) Kleeberg, H.; Heinje, G.; Luck, W. A. P. J . Phys. Chem. 1986, 90, 4427. Heinje, G. Thesis, University of Marburg, Marburg, FRG, 1986.
0 1987 American Chemical Society
