J . Phys. Chem. 1986, 90, 2038-2043
2038
in a way similar to the present simple relations of ~ 1 and ~ nm* 3 quantum numbers, cf. eq 4.11 and 4.12. One may therefore consider the present application of the Hose-Taylor criteriaI5 as an extension from one model providing exclusively resonances (Hitnon-Heiles) to a more realistic one providing molecular bound states as well as resonances (Thiele-Wilson). Extrapolating the present results,16 one should be able to correlate the distinguished ABA hyperspherical modes with quantum numbers u1u3 = Ou, with the ground states of effective radial potentials U",(r),see Figure 1. This conclusion is closely related to Greene and Jungen's26 prediction of H 2 0 stretching states correlating with ground states of gD3(r)(neglecting the diagonal correction in eq 2.9). Further candidates of ~ 1 =~ Ou,3 hyperspherical modes have been reviewed in ref 16. The present analysis demonstrates, however, that the class of hyperspherical modes is by no means restricted to the case ~ 1 =~Ou,,3 cf. Table plotted I; an "extreme" counterexample is u1u3= 80, see in Figure 3. It is of course a challenge to detect highly excited hyperspherical modes experimentally. One possibility is based on the fact that the wave functions of, e.g., nmf = Omf local modes extend
(typically) into the potential valleys, whereas for u1u3 = Ou3 hyperspherical modes, they often extend across the potential ridge. As a consequence, dipole moment transition matrix elements will strongly depend on the type (1 or h) of initial and final states, implying perhaps the possibility of selective excitations of local or hyperspherical modes. This conclusion is supported by typical direct overtone excitations of CH, OH, etc. bonds which tend to populate local modes, see the analysis in ref 2-6. In contrast, a multiphoton study of the Htnon-Heiles system yields preferential excitation of Q' modes, corresponding to hyperspherical modes.27 At very high energies, one should observe mode-selective molecular dynamics, i.e. slow hyperspherical but fast local-mode decay of ABA r e s ~ n a n c e s . ' ~ ~ ' ~
(26) C. H. Greene and C. Jungen, Abstracts of Papers, Twelfth International Conference on the Physics of Electronic and Atomic Collisions, S. Datz, Ed., Gatlinburg, TN, 1981, p 1019.
(27) R. E. Wyatt, G. Hose, and H. S. Taylor, Phys. Reu. A , 28, 815 (1983). (28) J. Manz, Comments A t . Mol. Phys., 17, 91 (1985).
Acknowledgment. We thank Dr. K. C. Kulander for stimulating discussions and Prof. G. L. Hofacker for his kind hospitality and continuous support. Generous financial support by the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie and the CNPq (Brazil) are also gratefully acknowledged. The computations were carried out on the CYBER 175 of the Bayerische Akademie der Wissenschaften.
The Motecular and Electronic Structure of Perfluoro-1,&butadiene David A. Dixon Central Research and Development Department, Experimental Station, E . I . du Pont de Nemours & Company, Wilmington, Delaware 19898 (Received: October 15, 1985)
The electronic structure of perfluoro- 1,3-butadiene has been determined from ab initio molecular orbital calculations. A double {basis set augmented by a set of polarization functions on carbon (DZ + Dc) has been employed. A number of geometries on the torsional potential surface were gradient optimized. The minimum energy structure is a skew-cis structure with )I = 58.4O. The s-trans structure (optimized) is 1.8 kcal/mol and the s-cis structure (optimized) is 5.7 kcal/mol higher in energy than the optimum structure. The conformational potential was partially determined. The potential is quite harmonic near the minimum and very anharmonic for > 100'. The form of the potential has been used to explain the difference in the theoretical and experimental barrier heights. The vibrational frequencies and infrared intensities have been calculated analytically with a 6-31G*(C) basis set. These quantities are compared with experiment. The analysis of the molecular orbitals is consistent with the spectroscopic evidence.
+
Introduction The structure of 1,3-b~tadiene'-~ and perfluoro-1,3-butadiene1@I4have been the subject of a number of recent studies. The (1) (a) Almenningen, A.; Traeteberg, M. Acta Chem. Scand. 1958, 12, 221; (b) Kuchitsu, K.; Fukuyama, T.; Morino, Y .J. Mol. Struct. 1968,1, 463. (2) Lipnick, R. L.; Garbisch, E. W., Jr., J . Am. Chem. SOC.1973, 95,6370. (3) Carriera, L. A. J . Chem. Phys. 1975, 62, 3851. (4) Dung, J. R.; Bucy, W. E.; Cole, A. R. H., Can. J . Phys. 1976, 53, 1832. (5) Squillacote, M. E.; Sheridan, R. S.; Chapman, 0. L.; Anet, F. A. L. J . Am. Chem. SOC.1979, 101, 3651. (6) Furukawa, Y.; Takeuchi, H.; Harada, I.; Tasumi, M. Bull. Chem. SOC. Jon. 1983. - r ~- 56. 392. (7) Bock, C. W.; George, P.; Trachtman, M.; Zanger, M. J . Chem. S O ~ . Perkin Trans 2 1979, 26. (8) Bock, C. W.; George, P.; Trachtman, M. Theor. Chim.Acta 1984,64, 293. (9) Bruelet, J.; Lee, T. J.; Schaefer, H. F., 111 J . Am. Chem. SOC.1984, 106, 6250. (10) Albright, J. C.; Nielsen, J. R. J. Chem. Phys. 1957, 26, 370. (11) Brundle, C. R.; Robin, M. B. J . Am. Chem. SOC.1970, 92, 5550. (12) Chang, C. H.; Andreassen, A. L.; Bauer, S. H. J . Org. Chem. 1971, 36, 920. (13) Wurrey, C. J.; Bucy, W. E.; Durig, J. R. J. Chem. Phys. 1977, 67, 2765. ~~
1
~
~
1
~
1,3-butadiene moiety is the simplest conjugated system and as such is a model for other types of linear conjugated polyenes. The perfluoro derivative is the simplest fluorocarbon with a conjugated double bond and is thus a model for linear perfluoro conjugated polyenes, e.g., perfluoropolyacetylene. 1,3-Butadiene has two energy minima, a trans form and a twisted form which we define about the C-C bond of as skew-cis with a torsion angle, 30-40°,8!9 with s-cis defined as 0' and s-trans as 180'. The barrier between the two skew-cis structures is at the s-cis geometry and is very small, between 0.48 and 0.79 kcal/mol. This result comes from theoretical calculations since the experimental results are not precise enough to define the structure in this region. The cis-skew conformation is 3.15 kcal/mol above the most stable s-trans structure, again from theory.8 The experimental estimate of this difference is 873 cm-I (2.5 kcal/mol)., Perfluorobutadiene has also been investigated for a number of years. The initial vibrational studies'O showed that the molecule does not have the trans form, but could not distinguish between the s-cis and skew-cis forms. Brundle and Robin" interpreted
+,
(14) Choudhury, T.; Scheiner, S., J . Mol. Struct. (Theochem) 1984, 109, 313.
0022-3654/86/2090-2038$01.50/00 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 10, 1986 2039
Structure of Perfluoro- 1,3-butadiene TABLE I: Geometry Parameters for Perfluorobutadiene Conformers"
DZ + De
3-21G
parameter T(CIC2) r(c 2c 2')
r(C1F2)
r(C,F,) r(C2Fd W2CIC2) WIClF,) 0(F,ClC2) O(FlC2Ci) WIC,C,) ~(CIC2C20 !4C,C,C2G)
~
skew-cis
s-trans
s-cis
skew-cis
skew-cis opt
s-trans
6-31G*, skew-cis opt
1.302 1.445 1.325 1.327 1.356 124.5 112.0 123.5 119.1 115.7 125.2 46.0'
1.304 1.439 1.328 1.324 1.354 123.3 11 1.9 124.8 118.9 115.7 125.4 180.0
1.314 1.483 1.300 1.299 1.330 123.5 11 1.3 125.2 117.2 112.8 130.0 0.0
1.310 1.465 1.298 1.303 1.330 124.5 111.9 123.6 119.4 1 15.4 125.1 45.5
1.311 (1.327)b 1.462 ( 1.478)b 1.298 (1.309)b 1.303 (1.314)b 1.334 (1.345)b 124.6 11 1.9 123.6 119.3 115.5 125.2 65.5c (58.4)d3e
1.314 1.465 1.301 1.299 1.334 123.6 111.5 124.9 118.5 115.3 126.1 180.0
1.308 1.459 1.294 1.298 1.332 124.6 111.7 123.7 119.0 115.5 125.5 58.d
Bond distances in angstroms. Bond angles in degrees. Values in parentheses are scaled as described in the text. -748.112195 au. eThis is the lowest energy structure. f E = -747.910612 au.
their photoelectron and UV spectra in terms of a nonplanar structure and predicted a twist angle of 42' f 15'; they thus favor a skew-cis structure. An electron diffraction study12 was also consistent with a skew-cis structure and the dihedral angle was predicted to be 47.4 f 2.4O. More recently the vibrational spectrum of perfluorobutadiene was assigned and is consistent with a C, structure (skew).13 The torsional motion was assigned and the barrier to planarity via the s-trans structure was determined as 986 f 150 cm-' based on a model potential cal~u1ation.l~ Although there are many theoretical calculations on 1,3-butadiene, there is only one such study of perfl~orobutadiene.'~ Choudhury and Scheiner14 studied the structure of perfluorobutadiene using the MNDO, PRDDO, and a b initio (STO-3G basis) molecular orbital techniques. Geometries were optimized at the M N D O level for the full rotational potential. The M N D O potential has a skew-trans ($ > 90') minimum. Geometry optimization of the s-trans and skew-cis structures with PRDDO and ab initio (STO-3G) calculations gave values of $ = 27' and J, = 37' for the skew-cis structure. In both cases, the s-trans structure is more stable. At the PRDDO level the energy difference, AE, is 1.7 kcal/mol and at the STO-3G level, AE is 1.5 kcal/mol. Single p i n t calculations with 4-31G basis set at the STO-3G geometries lowered AE to 0.8 kcal/mol although the s-trans structure is still more stable. We have been carrying out a systematic study of the properties of fluorocarbons at the a b initio level.I5 As part of this study we have determined the structure of perfluorobutadiene and examined the rotational potential. We have also calculated the vibrational frequencies and infrared intensities at the minimum geometry. Computational Method All calculations were done with the computer program H O N D O ~ ~ on an IBM 3081 computer. Calculations were done at the S C F (restricted Hartree-Fock) level. Optimum geometries were determined by using gradient t e c h n i q ~ e s . Initial ~ ~ calculations were done with the 3-21G basis.ls The final calculations were done with a double {basis set of the form (9,5/4)/[3,2/2] augmented by a set of d polarization functions on the carbon atoms.I9 This (15) Dixon, D. A., unpublished results. (16) (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, Program QH02 (HONDO), 1980. (1 7) Pulay, P. In Applications of Electronic Structure Theory; Schaefer, H. F., IV, Ed., Plenum: New York, 1977; p 153. (18) Binkley, J. F.; Pople, J. A.; Hehre, W. J. J. A m . Chem. SOC.1980, 102, 939. (19) Dunning, T. H., Jr.; Hay, P. J. In Methods of Electronic Srructure Theory; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; p 1.
expt (ref 12) 1.336 1.488 1.323 1.323 1.323 124.5 111.0 124.5 121.0 113.2 125.8 47.4
E = -748.1 12105 au. E =
basis set is the minimum level required for a good description of fluorocarbon structures and energetics.20 This gives 114 basis functions for the 39 electron pairs in perfluoro-1,3-butadiene.The calculations were done in C2, symmetry for the s-trans structure ($ = 180°), C2, symmetry for the s-cis structure ($ = O'), and C2 symmetry for intervening structures. The force field and infrared intensities were determined analytically2' with the program GRADSCF'~ on a CRAY XMP-48 equipped with a solid-state disk (SSD). A 6-31G basis set23augmented by a set of d polarization functions on carbon (a = 0.80), 6-31G*(C), was employed for these calculations. The geometry was optimized with this basis set starting with the optimum D Z Dc geometry at $ = 65'. This geometry optimization was done in internal coordinates.
+
Results and Discussion Geometry and Conformational Analysis. The geometry of perfluorobutadiene was initially optimized with the 3-21G basis set at the s-trans and skew-cis geometries. The structures are given in Table I. The value determined for $ was 45". As shown below this may not be the minimum value for since the surface is very flat for the torsional motion in this region and the gradient in Cartesians is very small. At this level of calculation, the trans form is 3.9 kcal/mol more stable than the cis form. Geometries determined with the 3-21G basis set have C-F bonds that are too long in comparison with the experimental values and with those determined with larger basis set^.'^^^^ The geometric parameters for the C==C and C-F bond lengths at the 3-21G level were scaled /r3.2IG where the ratio was taken from calcuby the ratio rDZ+D lations on CzF3H.F5s20With the scaled geometries, the skew-cis form is more stable than the s-trans form by 1.5 kcal/mol when Dc basis set is used. It is clear that polarization the D Z functions on carbon are required to properly describe this torsional energy difference. Geometry optimization was done for the s-trans, skew-cis, and s-cis structures with the D Z + Dc basis set. These geometries are given in Table I. The torsional potential was then calculated every 20' by using the skew-cis geometric parameters. Rotation of 20' to $ = 65O lowered the energy by -0.5 kcal/mol relative to $ = 45'. This occurs because the gradient in Cartesian co-
+
+
(20) (a) Dixon, D. A.; Smart, B. E.; Fukunaga, T. J . Am. Chem. SOC.,in press. (b) Farnham, W. B.; Smart, B. E.; Middleton, W. J.; Calabrese, J.; Dixon, D. A . J. Am. Chem. SOC.1985, 107, 4565. (21) King, H. F.; Komornicki, A,, submitted for publication in J. Chem. Phys. (22) GRADSCF is an ab initio gradient program system designed and written by A. Komornicki at the Polyatomics Research Institute and supported on grants through NASA-AMES Research Center. (23) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acra 1973, 28, 213.
2040
The Journal of Physical Chemistry, Vol. 90, No. 10, 1986
ordinates is very small and is not efficient in optimizing the torsional mode which has a very low frequency. The structure for I) = 65' was reoptimized and this geometry is given in Table I. We now compare our calculated geometry with the experimental one. An incomplete set of geometric parameters was determined in the electron diffraction studylz since all the C-F bond lengths were presumed equal and the gem-difluoro groups were considered to be symmetric. As expected the calculated C=C and C-C bond lengths are shorter than the experimental values. The calculated C F bond lengths are above and below the values from experiment. This somewhat surprising resultZois due to the experimental averaging of r(C-F). The calculated angles show good agreement with the experimental values. Comparison of our calculated structure with the calculated structure for 1,3-butadiene shows that the C=C and C-C bonds are shorter in the perfluorinated compound. For the C=C bond, this follows from the trends observed in the fluoroethylenes where r(C=C) decreases as fluorine is substituted for hydrogen.20 The C-F and C=C bond lengths in perfluorobutadiene can be compared to those calculated for CzF3H.24 The C=C bond in C2F3His slightly shorter than that in perfluorobutadiene. The C-F bonds on the CF2 group are shorter in perfluorobutadiene while the Cz-F bond is only slightly longer than the C-F bond on the C H F carbon in C2F3H. We also note that the CF2=CF-C groups are twisted slightly about the double bond and that the atoms bonded to sp2 carbons are not all coplanar. We have previously suggested,20 based on CI calculations, that a correction factor of 0.016 A be added to the C = C bonds and 0.01 1 8, to the C F bonds. We have used the C=C bond correction factor of 0.016 A for the C-C bond. These "corrected" values are given in Table I and represent our best estimate of the actual bond lengths for perfluorobutadiene. The bond angles calculated at the S C F level are probably quite accurate. Averaging the scaled corrected C-F bond distances gives us the same average C-F value found in the electron diffraction study. Since we were employing the 6-31G*(C) basis set for the vibrational calculation, we reoptimized the geometry starting from the I) = 65' optimized geometry, this time taking advantage of the optimization in internal coordinate feature in GRADSCF. The calculated structural parameters are given in Table I. Excellent agreement with the DZ Dc parameters is found. The largest variation is found for the value of # which is 58.4' at the 631G*(C) level. A final calculation with the DZ + Dc basis set and the I) = 65' geometric parameters derived with this basis set at = 58.4' gave a lower energy by 0.06 kcal/mol. Thus the optimum value of I) is close to 60'; I)op,= 58.4'. The difference in the theoretical and experimental torsion values for the angle is not surprising as this value is very difficult to measure experimentally. This is especially true for a very asymmetric, weak potential. We also note that the torsion angle is larger in perfluorobutadiene as compared to the unsubstituted compound. The s-trans structure is essentially the same as that for the skew-cis structure except that it is rigorously planar. The s-cis structure is somewhat different from the skew-cis structure. The C-C bond significantly lengthens (-0.02 A) and the C=C bond slightly lengthens as compared to the skew-cis structure. The C=C-C angle increases by 4' for the s-cis structure. These geometric variations occur because of strong steric repulsion between the two inner fluorines in the s-cis form.
+
+
2 51
c-r
The F-F distance for fluorines bonded to C, and C18is 2.51 A. If the skew-cis structural parameters (planarized) are used for the s-cis structure the F-F distance (the distance between F, and F3,) is only 2.03 A and the energy is 13 kcal/mol higher than
-
(24) Bond lengths in C2F3H,F,F2C,=C2F3H. DZ + Dc: r(ClC2)= 1.307 A, r(F,C,) = 1.304 A, r(F2CI)= 1.310 A, and r(F3C2)= 1.331 A.
Dixon that found for the optimum structure. The fluorines on C2 and C , are also quite close in the optimum s-cis structure with an F-F nonbonded distance of 2.52 A. Both of these distances are probably significantly less than the closest contact point for van der Waals radii. There exists considerable ambiguity in the definition of the size of the van der Waals radius of fluorine bonded to carbon and whether it represents an L-J 6-12 u parameter, an L-J 6-12 r,, or some point higher on the repulsive There is also no good energetic criterion for describing this potential. Considering values of u as 1.45-1 SA,it is clear that the two short nonbonding F-F distances in the s-cis form are less than the van der Waals radii. The interaction between the fluorines on C, and C2! is less severe than that on C , and CIJsince C2 and Cz, are bonded. Consideration of the s-trans structure also shows steric interactions between nonbonded fluorines.26 The fluorines at C,(C,,) and C2(C2,)also interact at significantly less than the
van der Waals radius and again a steric destabilization is present. For the skew-cis structure, the nonbonded F-F interactions occur at larger distances and the steric interactions are minimized. The values are given for fi = 65' and for I) = 58.4' in parentheses. (3.041
'22.3'
F
F
F-2.89-F (2.84)
The energetics are consistent with this interpretation. The energy of the s-trans form is 1.8 kcal/mol higher than that of the skew-cis form. The energy of the s-cis form is 5.7 kcal/mol higher than that of the skew-cis form. The experimental estimate of the energy difference between the skew-cis and s-trans forms is 2.8 f 0.4 kcal/mol. Although we have calculated a somewhat lower value, the agreement is quite good considering that the experimental barrier height is estimated from low-lying torsional frequencies and this should lead to an overestimate of the actual barrier height. The size of the steric effects can be estimated from the energetics for 1,3-butadiene assuming that the energy differences are only due to steric effects. We assume that the skew-cis structure is constrained in both the unsubstituted and the perfluoro derivative. Since the s-trans form is more stable by 3.3 kcal/mol (6-31G*) in 1,3-butadiene, the s-trans form in the perfluoro derivative is destabilized by 5.1 kcal/mol. The s-cis structure for 1,3-butadiene is destablilized by 0.6 kcal/mol (6-31G*) relative to the skew-cis structure and thus the perfluoro derivative has an additional 5.1 kcal/mol of steric effects. From this simple analysis it seems that the steric effects in the s-cis and s-trans forms are of comparable size. We have studied the dependence of the energy on the torsion angle 4in order to examine whether the s-cis and s-trans structures are relative minima or are transition states on the energy surface. The angle $ was varied with geometric parameters taken from optimized structures, s-trans, s-cis, and skew-cis. The energies are plotted in Figure 1 and are given in Table 11. (The values are reported as $ at which the energy is calculated (geometric parameters taken from optimized geometry at this value for I)).) The energy for I) = 170' (I) = 180') is lower in energy than the (25) (a) Burkert, U.;Allinger, N. L. Molecular Mechanics; ACS Monograph 177; American Chemical Society: Washington, DC, 1982. (b) Allinger, N. L. J . A m . Chem. SOC.1977, 99, 8127. (26) We define the term steric effects generally as describing a repulsive interaction between two nonbonded atoms (or groups of atoms). This interaction is usually due to the size of the electron cloud about the interacting atoms and for fluorines will be predominantly composed of the three lone pairs.
The Journal of Physical Chemistry. Vol. 90, No. 10, 1986 2041
Structure of Perfluoro- 1,3-butadiene TABLE II: Total Energies (au) for 1,3-Perfluorobutadiene as a Function of the Torsion Angle
+
energy
0 10 20 45 58.4 65 85 105 120 125 140 145 160 165 170 180
+*corn
energy (+g"
0 0 0
-748.103 090 -748.103 927 -748.105 890 -748.111 177 -748.112 195 -748.112 105 -748.110 922 -748.109 680 -748.109620
45 65 65 65 65 180
-748.109 91 9
180
-748.109 666
180
-748.109381 -748.109252
180 180
= 45)
-748.082491
TABLE 111: Relative Energies for 1,3-Perfluorobutadiene for Different Torsion Angles from Various Calculations method +,ke,(min) energies ( J / ) O MNDOb 109 1.8 (180)
PRDDOb
180
STO-3Gb 3-2 1Ge
180 180 45 58.4
-748.1 11 177 -748.112058 -748.110845 -748.109 604
DZ + Dc (scaled' geom) DZ + Dc
exptd
-748.109267 -748.109 117 -748.108 269
47e
4 (0,' 1.7 (27) 12.5 (0) 1.5 (37) 3.9 (45) 1.5 (180) 1.8 (180) 5.7 (O)B 2.85 (180)
OEnergies in kcal/mol. Reference 14. 'This work. dReference 13. 'Reference 12. funrelaxed rotational barrier at J/ = 0 is 13 kcal/mol. tunrelaxed rotational barrier at $ = 0 is 18.6 kcal/mol. The shape of the potential curve provides insights into the discrepancy between the theoretical and experimental values for the barrier height to the s-trans conformation. The torsional curve rises sharply for J, < 65'. For the region between J, = 65' and J, loo', the curve shows a similar sharp rise (almost 1.4 kcal/mol) and then gradually increases to J, = 180' by only 0.4 kcal/mol. Thus the curve is quite harmonic near the minimum in J, and very anharmonic for J, > 100'. The experimental barrier is obtained by extrapolating from vibrational levels near the minimum. Since the curve changes so dramatically, extrapolation of these results will not include enough anharmonic character and will lead to too large a barrier height. The only prior theoretical study of perfluorobutadiene was done with a semiempirical technique or with small basis sets.14 The barriers and optimum values for J, are summarized in Table 111 together with the present results. Only the MNDO method gives a skew structure as a minimum. The minimum is predicted to be skew-trans rather than skew-cis and the curve is quite flat from J, = 60' to J, = 120'. The barriers of 1.8 kcal/mol for J, = 180' and 4 kcal/mol for J, = 0' at the MNDO level are in reasonable agreement with our large basis set values. Both the FRDDO method and ab initio STO-3G calculations give the s-trans more stable than the skew-cis. The values for J, at the secondary minimum are betwen 30 and 40". Thus the minimum basis set calculations do not agree with either our higher level of theory or with experiment. The 4-31G basis set also gives the trans more stable than the skew-cis form as found at the 3-21G level. Furthermore, our optimized results for the cis structure demonstrate that the surface calculated assuming rigid rotation gives major errors for the energy at the s-cis geometry. This explains why the s-cis energy is always too high in the previous theoretical study.14 Vibrational Spectrum. In order to better understand the vibrational spectrum and to demonstrate that the cis-skew structure is a minimum on the potential energy surface, the force field was calculated with the 6-31G*(C) basis set. The harmonic frequencies and infrared intensities are given in Table IV together with the experimental values. The calculated frequencies are scaled by 0.9 to approximately account for both deficiencies in the wave function for the harmonic values and anharmonic effects.*' In general, there is very good agreement betwen the scaled frequencies and the experimental values. The experimental values are those recommended by Wurrey et aI.l3 based on both Raman and infrared spectra. There is also quite good agreement between the approximate intensities of the bands which were characterized by Wurrey et al.I3 as strong, medium, or weak and the calculated absolute intensities. We note that our intensities could be in error by a factor of 2. Although the agreement is in general good, a number of differences are found. We predict three bands in the region 1330-1380 cm-', two intense bands at 1328 cm-I (A') and 1346
-
6
PERFLUORBUTADIENE TORSIONAL POTENTIAL
"z'
\
1 1
OO
60
120
180
JI Figure 1. Torsional potential for rotation about the C-C bond. Energies are in kcal/mol. Circled points correspond to optimized geometries at this value of J/.
structure at J, = 180' (I)= 180') even though the geometry is not optimum; the energy for J, = 160' ( J , = 180") is even lower. This demonstrates that the s-trans structure is a transition state. Similarly, the s-cis structure is a transition state and the fall-off curve is steeper near J, = 0'. This can be seen by comparing the energies for J, = 10' ( J , = 0') and J, = 20' (J, = 0') to that for the s-cis structure. The energy curve from J, = 65' to J, = 180' has some complicating features. Rotation of the J, = 65' structure to give J , = 85' ( J , = 65') and J, = 105' ( J , = 65') shows a significant rise in energy in this region. The energy increase in going from J, = 65' to J, = 85' ( J , = 65') is comparable to that found in going to J, = 45O. The remaining two points on the curve are determined by using the s-trans structure. The energy at J, = 140' ( J , = 180') is lower than that at J, = 160' (J, = 180') as expected. However, it is also lower than the energy at J, = 120' ( J , = 180') and J, = 105' ( J , = 65') by 0.18 and 0.15 kcal/mol, respectively. The energy at J, = 120' ( J , = 180') is slightly higher than the energy at J, = 105O ( J , = 65O). Whether this represents a secondary minimum on the curve near J, = 140' cannot be ascertained without full geometry optimization at a number of points on the curve. This can be seen by comparing the energies for various IJdetermined from different starting geometries. Energy variations of up to 0.2 kcal/mol are easily observed. This portion of the surface could be quite sensitive to geometric changes such as twisting about the C=C bond which was not allowed in these rigid rotation calculations. Even if a shallow minimum exists on the surface. it is unlikelv to have bound vibrational levels and would thus simply perturb high-lying torsional modes and would not be Observed This is consistent with the Of Durig and co-workers'3 who suggest that Only One conformer is present in the gas phase.
(27! (a) Eades, R. A.; Scanlon, K.; Ellenberger, M . R.; Dixon, D. A,; Maryn,ck, D, S , J , phys, Chem, 1980, 84, 2840, (b) Komornicki, A,; pauzat, F.; Ellinger, T. J . Phys. Chem. 1983,87, 3847. (c) DeFrees, D. J.; McLean, A. D.J . Chem. Phys. 1985.82, 333.
2042
The Journal of Physical Chemistry, Vol. 90, No. 10, 1986
TABLE IV: Vibrational Freauencies for Perfluoro-1.3-butadiene A’
2045 1533 1476 1254
1841 1380 I328 1129
98.3 0.5 219.9 352.6
78 1 750
703 675
0.2 2.1
595 520 409
535 468 368
1.2 2.0 1.7
280 204 105 42
252 184 95 38
0.1
2020 1496 1319 1070 710 682 616 464 320
1818 1346 1187 963 639 614 554 418 288
308.3 311.1 173.8 234.9 10.4 9.5
227 119
204 107
6.8 0.8
1796 m 1379 w 1379 (?) 1128 vs 933 sh 702 vw 660 vw 616 529 w 408 (?) m 375 w 329 vw
0.6 0.8 0.0
181 w 94 w
A” 1765 s 1329 s 1189 m 972 s 633 ms 547 (?) m 520 (?) w 422 m 292 m 259 204 m
7.7 9.8 7.9
“0.9 uCalcd = uscIIc. See text. bInfrared intensity. ‘Reference 13. The assignments of intensities are given in the reference. s = strong, m = medium, w = weak, v = very. (?) shows that the assignment between theory and experiment is tentative.
cm-I (A”), and one very weak band at 1380 cm-’ (A’). Only two bands are observed experimentally. It is possible that the higher band has not been observed or that there is a significant overlap of the two lower intense bands that has not been separated. There is no theoretical counterpart for the observed fundamental 933 cm-’ (A’) obtained from the Raman spectrum. There is also no theoretical peak that accounts for the 616 cm-I (A’) transition. The peak at 408 cm (422 infrared, gas) may correspond to our predicted transition of 468 cm-l; the theoretical frequency at 468 cm-’ (A’) could also be equivalent to an observed peak at 461 cm-l (A’). It is unlikely that the reported transition at 329 cm-I (A’) is equivalent to our predicted value of 252 cm-’ (A’). Rather this predicted transition may be accounted for by the weak peak observed at 262 cm-l (A’). The frequency for torsion about the C-C bond is predicted to be very small, -40 cm-’ (A’), and has essentially zero infrared intensity. The low value of this frequency is consistent with our lower barrier height and with our suggested reinterpretation of the experimental barrier to rotation. The agreement between theory and experiment for the A” transitions seems to be somewhat better. It is likely that the observed transitions a t 547 and 520 cm-’ are equivalent to our predicted transitions at 614 and 554 cm-I. The observed transition at 259 cm-l (A”) does not have an equivalent theoretical peak in the A” sequence. It could be the A’ transition we find at 252 cm-l
Dixon although we note that it does depolarize experimentally and is weak. There is a predicted transition at 119 cm-I which could be one of the three infrared transitions observed between 95 and 105 cm-I. We suggest that some of the assignments be changed and that some of the weak transitions be reinvestigated. Electronic Structure. The molecular orbital eigenvalues for the two highest occupied molecular orbitals (OMO) and for several unoccupied molecular orbitals (UMO) are given in Table V. The ionization potential (IP) is predicted to increase on rotation from the s-trans form to the skew-cis conformer by 0.87 eV. Similarly the ionization potential for the second r-orbital (NHOMO) is expected to decrease by 0.87 eV on this rotation. This is consistent with the results of Brundle and Robin’’ in comparing the IPSfor the a-orbitals for 1,1,4,4-tetrafluorobutadienewith those of perfluorobutadiene as determined by photoelectron spectroscopy. The tetrafluoro compound has an s-trans conformation. The IP of perfluorobutadiene is 1.0 eV higher than that of the tetrafluorobutadiene while the ionization energy of the second a-orbital decreases by 0.6 eV in the perfluoro compound as compared to the tetrafluoro compound. This is in good agreement with our predicted changes and is consistent with a loss of conjugation in the diene r bond system in the skew conformation. The ordering of the unoccupied molecular orbitals shows that there is at least one u* orbital between the a* orbitals. The ultraviolet spectrum of 1,3-butadiene is dominated by a symmetry-allowed HOMO LUMO transition (a a*). In buNLUMO transition is also a R a* tadiene the H O M O transition but is not symmetry-allowed. In the ultraviolet spectrum of perfluorobutadiene, there are two bands at 1620 and 1980 A.” This was interpreted as being evidence for a twisted structure since LUMO ( r a*) or NHOMO LUMO (a both HOMO a*) transitions are allowed in the lower symmetry. This interpretation may be somewhat more complicated in the skew-cis structure. The lower energy peak is clearly the HOMO LUMO (a a*) transition observed in other butadienes. The second LUMO ( R T * ) or peak could be either the N H O M O HOMO NLUMO (a a*). The observed energy difference between the two peaks, 11 000 cm-l, is consistent either with the energy difference between the HOMO and NHOMO or LUMO and NLUMO. (Both AE’s are 10000 cm-I.) All transitions are of course allowed. It is clear that the second peak is not due to the HOMO a*(2) transition since this would be expected at much higher energy. Examination of the U M O s for the s-trans LUMO ( R T * ) and structure shows that the H O M O H O M O NLUMO (a u * ) transitions are both symmetryallowed; the former is z polarized and the latter is x,y polarized. The presence of the allowed a D* transition demonstrates that although there are two peaks in the ultraviolet spectrum, the s-trans structure cannot be ruled out solely on the grounds of symmetry. The observed transitions are quite intense, = 5000-10000. It is unlikely that the x,y polarized band would be this intense in the planar trans form. The intensity of the bands LUMO (a a*) suggests that it is probably the N H O M O transition that makes up the dominant portion of the intensity of the higher energy transition although we cannot exclude a reasonable contribution from the HOMO NLUMO (a u * ) transition. The decrease in the “energy” of u* orbitals when a number of fluorines are present has been observed by us in other calculations on fluorocarbons and may be a general feature.28
-
- -
+
-
-
-
+
-
+
-
-
-
+
-
+
-
- -
-
-
-
-
-
TABLE V: Molecular Orbital Eieenvalues tau) for 1.3-Perfluorobutadieneas a Function of the Torsion Anele 450
00
sYm a2(1~)
b2(1~*) al(a*) b,(u*) a
~
(2) * orbital.
65’
eigenv
SYm
eigenv
-0.48 96 -0.3839 0.09 14 0.1736 0.235s 0.2519
a“(a)
-0.4752 -0.3994 0.1016 0.1688 0.2399 0.2466
a‘(r) a“(rr*) a‘(u*)
a”( u*)
a’(IT*)a
sYm a”( IT) a‘(*) a”(?r*)
a’(u*) a”(u*) a’(?r*)O
1800
eigenv -0.4 590 -0.4140 0.1082 0.1527 0.2405 0.2408
SY m a,(IT)
b&*) a,(**) b”(.*) bg(IT*)O
b,(U*)
eigenv -0.4910 -0.3820 0.0959 0.1739 0.2456 0.2480
2043
J . Phys. Chem. 1986, 90, 2043-2046 TABLE VI: Atomic Charges (e) in 1,3-Perfluorobutadiene as a Function of the Torsion Angle atom OD 45O 65' 180° 0.383 0.387 0.367 Cl 0.376
c2
F, F2
F3
0.121 -0.195 -0.153 -0.149
0.118 -0.197 -0.149 -0.154
0.113 -0.202 -0.147 -0.152
0.126 -0.197 -0.153 -0.142
The Mulliken charges are shown in Table VI. Before discussing the charges, we note that the skew-cis structure is predicted to have a dipole moment of 0.93 D (the s-cis structure has a dipole moment of 1.10 D). The charges show little dependence of the value of IC.. Carbon C, is not as positive as C1 since only one fluorine is bonded to it. The charges on the fluorines bonded to C1 are -0.15 e and are similar to the charges on fluorine in other (28) The positions of unoccupied molecular orbitals are, of course, strongly basis set dependent. The presence of low-lying u* orbitals is consistent with the observed structural effects in fluorine-substituted benzene radical anions. Yim, B. M.; Wood, D. E.J . Am. Chem. SOC.1976, 98, 2053.
perfluoro compounds, e.g., CF,. The charge on the fluorine bonded to C2 is somewhat more negative. Conclusions. We have demonstrated that the skew-cis structure is the minimum energy conformer for perfluoro- 1,3-butadiene at the level of a D Z Dc basis set. The energy difference between skew-cis and s-trans of 1.8 kcal/mol is probably a good estimate for this barrier height. The experimental estimate for this value is too high because the shape of the potential energy surface is more complicated than would initially have been expected. Analysis of the molecular orbitals is consistent with experimental spectroscopic results. The results suggest that even a substituent as small as fluorine could lead to nonplanarity in persubstituted polyacet ylenes.
+
Acknowledgment. We thank Dr. A. Komornicki of the Polyatomics Research Institute for allowing us to use GRADSCF. We thank CRAY Research for providing access to the CRAY XMP/48 and S. Graffunder of CRAY Research for assistance. B. E. Smart and T. Fukunaga are acknowledged for helpful discussions. Registry No. Perfluoro-1,3-butadiene,685-63-2.
A Theoretical Study of the Isovalent Diatomics Cp, Si,, and Sic Celeste McMichael Rohlfingt and Richard L. Martin* Theoretical Division, MS 5569, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (Received: October 17, 1985)
Ab initio calculationson the molecules C2,Si2,and S i c are performed to determine equilibrium geometries (R,) and spectroscopic constants (ue,u,x,, and De) for various electronic states. A large basis set including two d functions on each atom is used, and electron correlation is treated by two different methods. The first approach is that of M~ller-Plesset perturbation theory based on a UHF reference function. The second approach is that of externally contracted configuration interaction based on a multireference function of the complete-active-spacetype. Good agreement between theory and experiment is achieved for the homonuclear diatomics. The best theoretical value obtained for the ground-state harmonic frequency we of S i c is 940 cm-'. After consideration of the remaining basis set and correlation effects, an estimate of 975 & 10 cm-' is made for o,in the unobserved molecule Sic. Finally, a comparison is made between the two theoretical approaches used in this study.
Introduction The diatomic molecule S i c is believed to be an abundant component of carbon stars and also to be present in interstellar regions of space. Despite its apparent astrophysical importance, it has never been observed spectroscopically. Two recent expeximents1-2using laser vaporization of silicon carbide rods have attempted to synthesize Sic in the laboratory. Using slightly different techniques, Bondybey' produced Sic2, C,, Si,, and C3, while Smalley and co-workers, observed Sic2. The latter experiment suggested that detection of S i c would have been unsuccessful if its ionization potential were greater than 7.89 eV, the photon energy of the F, excimer laser used. The primary goal of this paper is to provide accurate ab initio calculations of the vibrational frequency of Sic to aid in its spectroscopic observation and identification. Both C2 and Si2 have been extensively studied experimentally and theoretically, so they provide a test for the completeness of the basis set and the methods of correlation employed here. In addition, two other published ab initio calculation^^*^ of S i c are available for comparison with the present work. The range for the harmonic frequency predicted by these earlier studies, 914-983 cm-', is too large to be useful by any astrophysical means of detection (such as infrared emission Present address: Theoretical Division, Sandia National Laboratories, Livermore, CA 94550.
0022-3654/86/2090-2043$01 .50/0
spectroscopy), and thus provides the motivation for this investigation. The series of diatomics C,, Si,, and S i c also offers an interesting theoretical study of bonding differences between first- and second-row atoms. These molecules contain eight valence electrons, but each has a different ground state. The low-lying states arising from the several possible electron configurations are ...7ru4
ago
---
...7ru3ag'
lxg+
'nu
3nu,
..n,,bg232;, 'Ag, 'Eg+ C2 and Si, have lZg+ and 32; ground state^,^ respectively, while S i c is believed to be a 311 specie^.^,^ Finally, two commonly used theoretical approaches to the electron correlation problem are employed in this study. This V. E. J . Phys. Chem. 1982, 86, 3396. (2) Michalopoulos, D. L.; Geusic, M. E.; Langridge-Smith, P. R. R.; Smalley, R. E., J . Chem. Phys. 1984, 80, 3556. (3) Lutz, B. L.; Ryan, J. A. Astrophys. J . 1974, 194, 153. (4) Bruna, P. J.; Peyerimhoff, S. D.; Buenker, R. J. J . Chem. Phys. 1980, 72, 5431. (5) Huber, K. P.; Herzberg, G. Constanrs ofDiatomic Molecules; Van Nostrand Reinhold: New York, 1979. (1) Bondybey,
0 1986 American Chemical Society
