The molecular structure of toluene

Journal of Molecular Structure, 66 (1980) 281-287 Elsevier Scientific Publishing Company, Amsterdam -

THE MOLECULAR,

FRANK

PANG

Department

STRUCTURE

and JAMES

of Chemistry,

PkTER PULAY

and G&A

Printed in The Netherlands

OF TOLUENE

E. BOGGS The University of Texas, Austin,

Texas 78712

(U.S.A.)

FOGARASI

Institute for General and Inorganic Chemistry, Budapest (Hungary)

EiituSs Lor&zd University,

H-1445

(Received 2 January 1980) ABSTRACT Discrepancies between two recently reported electron diffraction studies of toluene have provided the incentive for an ab initio structural determination at the 4-21 level. The methyl C-H bonds are on the average 0.011. A longer than the ring C-H bonds. While the average ring C-C and C-H distances are nearly identical with those of benzene, the ring exhibits marked asymmetry, including an unexpected coupling between the ring C-C distances and the angle of methyl rotation.

INTRODUCTION In a single recent journal issue, two simultaneous and independent electron diffraction investigations of the structure of toluene were reported [ 1, 2] . The results obtained by the two groups differed in quite significant ways, as shown in Fig. 1. Both investigations appear to have been done with care, but we would like to suggest that electron diffraction may not be the method of choice for obtaining answers to the two particular questions that are of importance in the structure of toluene. One question of interest is the relative length of the C-H bonds in the methyl group and on the benzene ring. This interest was emphasized in the introduction to one of the previous papers [ 11, which also contained a discussion of the relevance of the question to the use of toluene as a free radical scavenger in work on homogeneous gas kinetics. From chemical reactivity, it would be expected that the methyl C-H bend would be longer than the ring C-H bond, and intuition would suggest that the difference should be no larger than 0.01-0.02 A. Furthermore, one would expect the methyl C-H bond in toluene to be somewhat longer than that in CH, because of the greater ease of cleavage of the bond in toluene. This difference might be anticipated to be of the order of some thousandths of an A. The electron diffraction investigations attempted to test these intuitive expectations, but the low electron scattering power of hydrogen and the low molecular symmetry make such an experiment extremely delicate. One of the electron diffraction studies [l] found the methyl C-H band to be longer than the ring C-H by 0.047 _+0.032 A. Further refinement 0022-2860/80/0000-0000/$02.25

0 1980 Elsevier Scientific Publishing

Company

(A)

H4

,hr

=

(8)

H4

0.047(32)

Fig. 1. (A) Electron diffraction rastructure of ref. 1. Methyl C-H is longer than ring C-H by O-047(32) /I. (B) Electron diffraction data of ref. 1 reanalyzed in ref. 4. (C) Electron diffraction rg structure of ref. 2. Ring assumed to be hexagonal_ Methyl C-H is shorter than ring C-H by 0.01 A. (D) Computed r, structure of this work. See text and tables for geometry alteration on rotation of methyl group. Distance differences have much greater reliability than absolute values, as discussed in text.

indicated the difference to be larger than 0.025 A at the 99% confidence level and greater than 0.020 a at the 99.5% confidence level. The other paper [2] found a 0.009 a difference in the opposite direction. The other question of interest in the structure of toluene concerns the effect of the substituent in inducing asymmetric deformations in the benzene ring. We have recently demonstrated in a series of papers on cyclopropane derivatives that such induced deformations can provide useful probes of the nature of the electronic interactions [ 31. The first experimental study of toluene [l] yielded values for the ring asymmetry. A subsequent reanalysis of the same data [4] has provided an alternative set of data. Both of these are shown in Fig. 1, along with the results of the second experimental study [ 21 which assumed that the ring retained the symmetry of benzene. Our papers on cyclopropane derivatives [ 31, as well as others from this

283

Iaboratory and elsewhere, have shown that differences in geometrical parameters are very accurately reproduced by ab initio calculations within the Hartree-Fock approximation. Small differences in related parameters, as are of interest here, can be obtained with high reliability, and we believe that the quantities sought can be computed with greater accuracy than they can be obtained &om an electron diffraction experiment. Microwave spectroscopy might give comparable accuracy and, indeed, an extensive microwave investigation has been reported [ 53. In spite of the great effort expended, only partial structural information could be obtained. ~ET~OD

OF CALCULATION

We have used the program TEXAS [6] to optimize the geometry of toluene, using our standard Gaussian basis function set, denoted 4-21 [ ‘71. This basis is similar to the 4-31G basis of Pople’s group, with a slight mod~ication which saves considerable time in the integrdl and force calculation: the valence shell contains only three functions instead of four, split two-one. The program uses the ab initio SCF gradient method [S] for geometry optimization, providing a more rapid and more accurate approach to the calculation of equilibrium geometries. For reference, we have computed the equ~ibri~ geometry of CHq using the same basis set and optimization procedure. In a study to be reported separately, we have computed an ab initio vibrational force field for benzene, again using the same set. From this, we have abstracted the computed equilibrium geometry of benzene for comparison with the toluene result. In every case throughout this paper, geometries have been refined to +1 in the last digit shown or to at least -~3 in a digit shown as a subscript. RESULTS AND DISCUSSION

The geometry of toluene was optimized at two co~~formatiol~s. One, which we shall tail the planar form, is indicated in Fig. 1 and has one methyl C-H bond in the plane of the benzene ring. The other, called the orthogonal form, is obtained by a 30” rotation of the methyl group and has one methyl C-H bond perpendicular to the ring plane. These two conformations must represent extrema in the potential function for the methyl group rotation. The computation showed the orthogonal form to be more stable, but only by 3 cal mole- *. This value is completely unreliable quantitatively, but it confirms the expectation that the barrier, having a 6-fold leading term, must be very small. A microwave spectroscopic study has given a value of 14 cal mole- * [ 91. The geometries obtained in the calculation are shown in Table 1, The reZaatiue values will be discussed first, since these are expected to have high accuracy as directly computed. The ring C-H distances are seen to be nearly identical, as was assumed in both electron diffraction studies, with the greatest difference being only 0.0014 A. Any significance of this small

(1.089,,) (1.087,)

(1.508) (1.085) (1.084) (1.084)

1.518, 1.0730 1 a0724 1.0719

1.0850 1.0824

(1.400,) (1.396,) (1.395,)

‘1.388, 1.383, 1.383,

(1.403,) (1.508) (1.085) (1.084) (1.084) (1.084) (1.085) (1.086,) (1.088,)

(1.394,) (1.398,) (1.394,)

110.6” 111.0” 107.9”

120.7” 119.7” 120.0° 120.2”

118.6” 120.8” 120.2” 119.5”

1.3863 1.3856 1.3817 1.3855 1.3816 la3905 1.519, 1.0728 1.0723 1.0719 1.0724 1.0733 1.0818 1.0839 (1.398,) (1.398,)

Orthogonalb

PlanarC

(110.6”) (111.0”) (107.9”)

(120.7”) (119.7”) (120.0”) (120.2”)

(118.6”) (120.8”) (120.2”) (119.5”)

118.5,” 120.7,’ 120.1,” 119.5,” 120.1,” 120.7,” 121.1,o 119.6,” 120.0, 120.2,O 119.8,” 119.4, 111.1 3 110.7,” 108.1,’

PlanarC (118.5,“) (120.7,“) (120.1,“) (119.5,“) (120.7,“) (120.7,“) (121.1,“) (119.6,“) (120.0,“) (120.2,“) (119.8,“) (119.4,“) (111.1,“) (110.7,“) (108.1,“)

‘For numbering of atoms, see Fig. 1. Geometries have been refined to 1 unit in the last digit shown or at most 3 units in a digit shown as a subscript. Values in parentheses are the proposed true equilibrium parameters after correction as discussed in text. bConformer with one methyl C-H bond perpendicular to ring plane. ‘Conformer with one methyl C-H bond coplanar with ring. dHydrogen 7a is either in the ring plane or in the orthogonal C-H bond, eHydrogen 7b is either of the two equivalent methyl hydrogen atoms.

Cd-be

G-H,ad

Cd-4 Cd-L

c,-G c2-c, c,-cl cl-c, c5-G Q--c, c1-G C,-Hz c,---H, V-H,

Orthogonalb

Structure of tolueneR

TABLE 1

285

difference is questionable, but it is interesting to note that it varies in a uniform way from the ortho to meta to para positions. Within the methyl group, a variation of the C-H distances is seen as the methyl group is rotated, with a maximum change of 0.0032 a. In spite of the small m~itude of the variation, it is thought to be significantly determined in at least a semi-quantitative way. The C-H bond is shortest when the hydrogen atom lies in the ring plane and passes through a maximum at 909 Experimental verification of the asymmetry of the equilibrium methyl group C-H distances would be very difficult because of the extremely low barrier (-14 cal mole”’ [9]) restricting methyl group rotation in toluene. In this connection, it is interesting to note that infrared studies by Lascom be and co-workers [lo] of C6HSCDzH and C6DSCDZH in two crystalline solid phases have demonstrated modulation of the C-H stretching vibration as the methyl group rotates, following the method of McKean [ 111. Here, however, the methyl group is bound by crystal forces so that it does not have the quasi-free rotor character that it exhibits in the gaseous state. Nevertheless, the infrared spectrum of gaseous toluene [lo] showed a strong C-H band with a shoulder displaced by 14 cm-’ toward lower frequency. A similar pair of frequencies was observed in the Raman spectrum of the gas. The cubic force constant of the methyl C-H stretch in toluene is -31 aJ Aw3. Therefore, the calculated variation in the bond length of 0.0032 Ii should produce_ a force constant variation of ~0.05 aJ IIq2, and a frequency modulation of +15 cm- l. This estimate is in agreement with the empirical correlation given by McKean [ll].However, as pointed out by Lascombe and co-workers [lo], existent theory does not predict the splitting observed in the spectrum and a further analysis of the dynamics of the motion is required. In regard to the original question concerning the relative C-H bond distances, the calculation shows that the methyl C-H bonds are longer than the phenyl C-H bonds_ Because of the variation among the nonequivalent bonds, only an average difference of 0.011 a can be specified_ This result would appear to be of a reasonable magnitude and in the expected direction. Turning next to the interesting question of the effect of the substituent on the ring symmetry, one can see that the calculated ring angles are remarkably close to those derived in the one electron diffraction experiment where they were sllowed to vary [I]. The computed ring angles are shown in Fig. 1 for easy comparison with the experimental values. The largest angular distortion is a contraction at the point of substitution, and the effect is nearly independent of the orientation of the methyl group. The phenyl C-H groups come within, at most, 0.2” of bisecting the ring C-C-C angles, and even the ortho C-H angles are essentially unaffected by methyl group orientation.

286 TABLE

2

Variation in ring bond lengths for toluene r(planar) 1.3863 1.3856 1.3817 1.3855 1.3816 I .3905

C,-G c&--c, C,--c, C,-C, C,--C, C,-C, =Ar = r( planar) -

-0.001, + 0.001, -0.001, + 0.002, -0.002, + 0.002,

r(orthogonal).

The bond length asymmetries present a more complex and surprising picture. The orthogonal conformation has a symmetry plane perpendicular to the ring plane, and here the effect is simply a 0.004-0.005 A longer bond adjacent to the methyl group than further down in the ring. In the planar conformation, however, there is in addition a major “left-right” asymmetry which seems remarkably large for such a minor perturbation as is introduced by mere rotation of the methyl group. The effect can be most clearly understood as an alternating increase and decrease in the phenyl C-C bond lengths of the planar conformer from the corresponding bond lengths in the orthogonal form, as shown in Table 2. The entire carbon skeleton is constrained by symmetry to be coplanar in the planar conformation, and deviations from planarity in the orthogonal form are found to be vanishingly small. It has been shown [ 71 that calculation of similar bond lengths in related molecules with the 4-21 basis set gives values with a remarkably constant offset from the best experimental estimate of the true value. The calculated C-H bond length in methane, using the same procedure and basis set as for toluene, is 1.0815 II This may be compared with the average value of 1.0832 A found for the methyl C-H’s in toluene. This difference is in the direction that would be expected, and confirms the expectation of a weakening effect of the phenyl group on the methyl C-H bond. The average of the C-C bond lengths found for toluene is 1.384& identical with the value of 1.384& found for benzene using the same basis set. Similarly the calculated C-H distance in benzene, 1.072,A is essentially the same as the average for toluene. ACKNOWLEDGMENTS

This work has been supported in part by the U.S. National Science Foundation and the Hungarian Institute of Cultural Relations as part of the program of cooperative research of the University of Texas and the Hungarian

287

Academy of Sciences. It has also been supported in part by a grant from the Robert A. Welch Foundation. We would like to thank Dr. Istvti Hargittai for calling our attention to this problem. REFERENCES 1 R. Seip, Gy. Schultz, I. Hargittai and 2. G. Szabo, 2. Naturforsch., A, 32 (1977) 1178. 2 T. Iijima, Z. Naturforsch., A, 32 (1977) 1063. 3 A. Skancke, E. Flood and J. E. Boggs, J. Mol. Struct., 40 (1977) 263; A. Skancke, J. Mol. Struct., 42 (1977) 235; A. Skancke and J. E. Boggs, J. Mol. Struct., 50 (1978) 173; A. Skancke and J. E. Boggs, Acta Chem. Stand., A, 32 (1978) 893; A. Skancke and J. E. Boggs, J. Mol. Struct., 51 (1979) 267; A. Skancke and J. E. Boggs, J. Am. Chem. Sot., 101 (1979) 4063. 4 A. Domenicano, Gy. Schultz, M. Kolonits and I. Hargittai, J. Mol. Struct., 53 (1979) 197. 5 W. A. Kreiner, H. D. Rudolph and B. T. Tan, J. Mol. Spectrosc., 48 (1973) 86. 6 P. Pulay, Theor. Chim. Acta, 50 (1979) 299. 7 P. Pulay, G. Fogarasi, F. Pang and J. E. Boggs, J. Am. Chem. Sot., 101 (1979) 2550. 8 P. Pulay, Mol. Phys., 17 (1969) 197; P. Pulay, in H. F. Schaefer, HI (Ed.), Modern Theoretical Chemistry, vol. IV, Plenum Press, New York, 1977, p. 153. 9 H. D. Rudolph, H. Dreizler, A. Jaeschke and P. Wendling, 2. Naturforsch., A, 22 (1967) 940. 10 J. L. Breuil, D. Cavagnat, J. C. Cornut, M. T. Forel, M. Fouassier and J. Lascombe, J. Mol. Struct., 57 (1979) 35; D. Cavagnat, J. C. Cornut and J. Lascombe, Proceedings of the XIV European Congress on Molecular Spectroscopy, Frankfurt/Main, September, 1979. 11 D. C. McKean, Chem. Commun., (1971) 1373.