Theoretical studies of the methyl rotational barrier in toluene

THEO CHEM Journal of Molecular Structure (Theochem) 362 (1996) 325-330

Theoretical studies of the methyl rotational barrier in toluene Hendrik F. Hamekaa3*, James 0. Jensenb aDepartment of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, USA bEdgewood Research, Development and Engineering Center, Aberdeen Proving Ground, MD 21010-5423,

USA

Received 27 April 1995; accepted 14 September 1995

Abstract We report computations of the rotational barrier of the methyl group in toluene. The computations are based on the use of the GAUSSIAN 92 Program Package with the 6-31 lG** basis set. The results are 2.69 wavenumbers at the HF level of approximation and 5.02 wavenumbers at the MP2 level. These results compare favorably with the experimental value of 4.9 wavenumbers. It is shown that inclusion of the vibrational zero-point energy in the calculations is necessary for obtaining satisfactory results. Keywords; Configuration; Rotational barrier; Toluene

1. Introduction

A toluene molecule consists of a methyl group attached to a planar benzene ring. The methyl group may be rotated around the C-C bond and the rotational motion has two stationary points, both corresponding to symmetric configurations. In the first, which is known as the eclipsed configuration, one of the methyl C-H bonds is in the plane of the benzene ring which forms a plane of symmetry. In the second, known as the staggered configuration, one of the C-H bonds is in a plane perpendicular to the benzene ring and this plane, perpendicular to the benzene ring, is a plane of symmetry. It was derived from the microwave spectrum [l] that the energy difference between the staggered and the eclipsed configurations is 14.0 cal mall’, * Corresponding author.

corresponding to 4.90 wavenumbers. A subsequent study [2] of toluene by means of supersonic molecular jet spectroscopy showed that the staggered configuration has the lower energy. Gordon and Hollas [3] presented a final analysis of the experimental data, confirming that the energy of the staggered configurations is lower by an amount of 4.9 wavenumbers than the energy of the eclipsed configuration. An ab initio theoretical study of the electronic structure of toluene was reported in 1980 by Pang et al. [4]. The calculation was based on a standard 4-2 1G Gaussian basis set and it predicted an energy difference of 3 cal mol-’ between the two configurations with the staggered being the lower of the two. Pang et al. [4] also found significant coupling between the ring C-C distances and the angle of methyl rotation. We recently reported computations on the ground and lowest excited singlet states of toluene

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and cresol [5] using a recent version of the GAUSSIAN 92 Program Package [6]. We intended to interpret the fluorescence of the two molecules from ab initio computations and we used therefore the 4 in 4 complete active space (CAS) multiconfigurational (MC) SCF method in order to calculate the energies, optimized geometries and vibrational frequencies of the two states. We also tried to determine the magnitude of the rotational barrier in toluene from these 4 in 4 CASSCF computations but we were unable to derive reliable frequency values for the eclipsed configuration by means of that approach. Since there seems to be some recent interest in ab initio computations of rotational barriers we decided to tackle the problem from a different perspective, still based on the GAUSSIAN 92 Program Package [6]. We calculated the rotational barrier in toluene by means of two alternative procedures, the first calculation being a straightforward HF/6-3 1lG** computation and the second an MP2/6-31 lG** computation. We found that the vibrational spectrum plays a significant role in determining the magnitude of the rotational barrier and we present an analysis of the vibrational spectra according to the two procedures. Finally we also address the coupling between the ring geometry and the methyl rotation.

2. General computations We used the GAUSSIAN 92Program Package [6] to derive the energy minima and the corresponding Table 1 Computed HF and MP2 energies of the staggered and eclipsed configurations of toluene; E(el) is expressed in hartrees, all other energies are in wavenumbers

ES, (cl) E,(el) A(el) & (ZP) E&P) A(zP) A(tot) st = staggered;

HF

MP2

-269.799 989 918 -269.799 980 796 2.0020 29718.3366 29719.0254 0.6888 2.6908

-270.771368 069 -270.777 285 594 18.1012 27862.2809 27849.1954 -13.0855 5.0157

ec = eclipsed.

Table 2 Computed Bond length

Cl-C3 Cl-C4 Cl-C8 C2-C5 C2-C6 C2-H7 c3-c5 C3-H9 C4-C6 C4-HlO C5-Hll C6-H12 C8-H13 C8-H14 C8-H15

362 (1996) 325-330

HF and MP2 bond lengths in Angstroms Staggered

Eclipsed

HF

MP2

HF

MP2

1.3894 1.3894 1.5109 1.3843 1.3843 1.0754 1.3847 1.0766 1.3847 1.0766 1.0758 1.0758 1.0872

1.4028 I .4028

1.3870 1.3919 1.5109 1.3820 1.3867 1.0754 1.3872 1.0763 1.3822 1.0770 1.0758 1.0758 1.0838 1.0862 1.0862

1.4016 1.4041 1.5096 1.3976 1.3997 1.0863 1.3994 1.0877 1.3972 1.0882 1.0866 1.0867 1.0932 1.0948 1.0948

1.5094 1.3986 1.3986 1.0863 1.3984 1.0879 1.3984 1.0879 1.0867 1.0867

1.0846

1.0955 1.0937

1.0846

1.0937

optimized geometries of both the staggered and the eclipsed configurations of toluene by means of HF/6-31 lG** computations. We imposed symmetry in both cases, for the staggered configuration we required a plane of symmetry perpendicular to the benzene ring containing the methyl carbon and for the eclipsed configuration we required that the benzene ring constituted a plane of symmetry. It should be noted that in the staggered configuration the benzene carbon and hydrogen atoms are slightly out of plane. We repeated the calculations at the MP2/6-3 1lG** level of approximation. The computed minimum energies, denoted by E(el), are listed in Table 1 and are expressed in terms of hartrees. We find that in both approaches the staggered configuration has a slightly lower energy than the eclipsed configuration, We denote the energy differences by A(e1) which are also listed in Table 1, and since the energy differences A are small we express them in terms of wavenumbers (cm-‘). It should be noted that the total energy difference between the staggered and the eclipsed configuration of toluene is the sum of the two contributions, the first being due to the electronic energies at the different optimized geometries and the second to the difference in vibrational zero-point energies between the staggered and the

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321

eclipsed configurations. It is to be expected that the vibrational frequency spectra of the two different configurations exhibit slight differences and they should be included in our theoretical predictions of their energies. In order to make a meaningful theoretical prediction of the rotational barrier in toluene we must therefore calculate the vibrational frequencies of toluene in both the staggered and the eclipsed configurations at both the HF/6-31 lG** and MP2/6-31 lG* level of approximation. Since we must calculate the vibrational spectra anyway we will analyze our data, compare them with the experimental spectra and assign the various vibrational modes. This will provide some useful insights in the changes in electronic structure due to the methyl rotation. We present this analysis in the following section.

3. Results Our computational results for the molecular energies of both the staggered and the eclipsed configuration are all listed in Table 1. We first report the total electronic energies corresponding to the optimized geometries E(e1) in terms of hartrees. The energy differences A( el) are converted to wavenumbers. In both the HF and the MP2 level of approximation we find that the staggered configuration has the lower energy but the computed energy differences A(e1) are very different for both calculations, about 2 wavenumbers in the HF case and as much as 18 wavenumbers in the MP2 case. The optimized geometries of the staggered and eclipsed configurations are presented in Table 2; the numbering of the atoms is shown in Fig. 1. Pang et al. [4] reported significant coupling between the ring C-C distances and the angle of methyl rotation. It is interesting to note that our HF computation exhibits about the same degree of coupling as Pang et al. but our MP2 computation shows an amount of coupling that is about half the size. We believe that HF computations have a tendency to overestimate ring assymmetries due to rotational motion in the substituents. We present all computed vibrational frequencies at both the HF and the MP2 level of

Fig.

1. Numbering

scheme for the atoms in toluene.

approximation for both configurations in Table 3. It may be seen that the predicted frequencies corresponding to the rotational motion of the methyl group are consistent with our finding that the staggered configuration has the lower energy since the frequencies are positive for the staggered configuration, indicating an energy minimum, and they are negative for the eclipsed configuration, indicating a saddle point. The frequencies are 23 and -24 wavenumbers in the HF calculation and 56 and -61 wavenumbers in the MP2 calculation. We have derived the zero-point vibrational energies E(zp) from the data in Table 3 by taking half the sum of all vibrational frequencies except the rotation of the methyl group. The differences of the vibrational zero-point energies for the staggered and eclipsed configurations are then reported as A(zp) in Table 1. In the case of the HF computation A(zp) is quite small and it increases A(e1) to a total value A(tot) of 2.69 wavenumbers. In the case of the MP2 computation the vibrational correction has the opposite sign

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Table 3 Computed

HF and MP2 vibrational

Assignment

Fxp.

181

frequencies

and their assignments

Staggered

C-H

bend

C-H3

bend

C-CH> stretch CC stretch

C-Hs

C-H

stretch

stretch

C-CH3 wag C-C bend

C-H

bend

C-CH3

rock

rot = rotation;

_ 348 522 622 788 1005 1005 1030 1084 1157 1182 1316 _ 1380 1450 1468 1211 1445 1497 1587 1606 2920 2963 2985 3032 3040 3065 3072 3079 220 407 467 698 132 841 898 _ 991 1041 a = antisymmetric;

23.08 366.57 561.51 679.67 846.43 1071.43 1082.61 1120.52 1167.49 1217.09 1288.05 1326.55 1463.84 1537.45 1608.52 1619.62 1313.17 1586.32 1653.11 1768.20 1795.17 3163.07 3217.80 3240.40 3308.30 3311.84a 3324.32 3333.82 3347.21 228.11 453.52 519.00 770.06 817.29 948.81 1010.09 1095.84 1112.80s 1161.05

first and out-of-plane

last)

Eclipsed

HF C-CH3 rot C-CH3 wag C-C bend

(in-plane

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MP2 a a s a s a s s a a s a a s s a s a s a s s s a s s a s s a s s s a s a s

s = symmetric;

56.21 337.59 521.35 626.27 799.27 1008.40 1010.24 1050.08 1112.10 1179.26 1201.91 1340.69 1474.15 1425.86 1503.90 1516.82 1246.04 1444.58 1527.16 1632.62 1654.07 3069.56 3148.86 3167.72 3192.45 3194.69 3208.12 3216.93 3229.32 202.11 388.76 403.80 442.71 713.96 829.00 860.68 889.90 895.07 1058.92

HF a a s a s a s s a a s a a s s a s a s a s s s a s a s a s s a s s s a s s a s

-24.26 365.70 560.92 679.62 845.68 1066.27 1086.42 1120.17i 1167.59 1217.45 1288.02 1329.38 1463.67 1537.89 1604.91 1621.67 1311.36 1587.29 1653.00 1768.44 1795.45 3164.93 3215.04 3241.66 3307.01 3312.57 3324.56 3334.06 3347.33 230.20 453.19 519.76 769.91 818.07 948.74 io10.10 1095.64 1112.74 1161.62

MP? o i i i i i i i i i i i i o i i i i i i i o i i i i i i o 0 o o o o 0 o o o

-60.59 o 337.87 i 521.21 i 626.31 i 798.92 i 1006.46 i 1013.24 i 1050.14 i 1112.0 i6 1179.14i 1202.09 i 1341.11 i 1474.30 i 1425.03 i 1500.19 0 1519.16 i 1245.77 i 1444.90 i 1527.22 i 1632.61 i 1654.32 i 3070.19 i 3148.93 o 3167.28 i 3191.04 i 3195.31 i 3208.26 i 3216.84 i 3229.61 i 204.22 o 384.54 o 392.19 o 438.84 o 713.59 0 828.58 o 859.52 o 889.21 o 893.48 o 1054.76 o

0 = out of pls me; i = in plane. See text for further

of the electronic energy difference and it lowers the rotational barrier A(tot) to a final value of 5.0157 wavenumbers. The agreement with the experimental value [ 1,2] is surprisingly good. Even the HF result A(tot) = 2.69 wavenumbers is not too bad. It should be noted though that it is essential to include the difference in zero-point

explanation.

vibrational energy in the computation in order to obtain an accurate theoretical prediction. We felt that it might be useful to also present the identification and assignment of all vibrational frequencies since we have the theoretical data available and since it might provide a better understanding of the coupling between the vibrational

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spectrum and the methyl rotation. The vibrational spectrum of toluene was first reported by Fuson et al. [7] but a more complete and precise analysis of the spectrum was presented by La Lau and Snyder [8] whose data we used for our analysis. It has been our experience that most of the spectral assignments are straightforward because the vibrational motion is localized and easily identifiable but there are always a few vibrational modes where the assignment is ambiguous. This may be due to delocalization of the vibrational motion, coupling between different modes or other reasons. In the last two cases the vibrational assignment becomes to some extent a matter of guesswork. It is not surprising that some of the assignments may be revised when additional information becomes available. We present all computed vibrational frequencies and the experimental results of La Lau and Snyder [g] in Table 3. The molecule has a plane of symmetry perpendicular to the benzene ring in the staggered configuration. In this configuration we differentiate between vibrations that are symmetric with respect to this plane (denoted by s) and vibrations that are antisymmetric relative to this plane (denoted by a). In the eclipsed configuration the plane of the benzene ring is a plane of symmetry and we again differentiate between symmetric vibrations (denoted by i) and antisymmetric vibrations (denoted by 0). It may be seen that the i-denoted vibrations are the out-of-plane vibrations except for a few motions involving the methyl group. Thanks to the additional symmetry information we are confident about the accuracy of our vibrational assignments. It may be seen from Table 3 that the differences between the staggered and the eclipsed frequencies are very small. Except for some of the vibrational modes involving the methyl group, the largest difference is 3.6 wavenumbers for one of the methyl C-H bending modes. It is also interesting to look at the differences between the HF and the MP2 frequencies; they are particularly large for the out-of-plane bending modes of the benzene ring. Finally we present the correction factors for the various vibrational modes derived from the

362 (1996) 325-330

Table 4 Correction (Corr.) factors for computed HF and MP2 tional frequencies (in-plane first and out-of-plane last) Assignment

C-C C-H C-C C-H C-C C-H

bend (i) bend (i) stretch (i) stretch (i) bend (0) bend (0)

329

vibra-

Corr. factor HF

MP2

0.9275 0.9254 0.9017 0.9203 0.9020 0.8901

0.9912 0.9739 0.9802 0.9500

1.0086 0.9932

i = in plane; 0 = out of plane.

HF and the MP2 calculations. These correction factors are obtained simply as the average of the ratio between the experimental and computed frequencies for a given vibrational mode. The rationale and an explanation of this particular approach were presented previously [9, lo]. The vibrational modes are chosen by their physical characteristics but the consistency of the ratios within a vibrational mode is a secondary consideration. We therefore differentiate between in-plane and out-of-plane vibrations because they tend to have different correction factors. It may also be seen from Table 4 that the MP2 correction factors are much closer to unity than the HF correction factors, which means that the MP2 frequencies are much closer to the experimental values than the HF frequencies. Nevertheless, the corrected HF frequencies and the corrected MP2 frequencies are not all that different, which supports the assumptions underlying our correction approach [lo].

4. Conclusions Our present calculations show that accurate predictions of the rotational barrier in toluene may be derived from ab initio quantum chemical computations as long as the effect of vibrational zero-point energy is included in the calculations. We believe that it is necessary to base the computations on the use of a sufficiently large basis set such as 6-3 1lG**. The MP2 level of approximation then gives a result of 5.0157 wavenumbers, which

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is in excellent agreement with the experimental value of 4.9 wavenumbers. The HF level of approximation gives a result of 2.6908 wavenumbers which has the correct order of magnitude even though its difference from the experimental result is significantly larger. Our intermediate results show that it is important to include the vibrational zero-point energies in the calculation in order to achieve satisfactory agreement with experiment.

Acknowledgment We express our appreciation to Edgewood Research, Development and Engineering Center (U.S. Army) for their support of the work as part of the Laser Standoff Detection Project, Project Number lC162622A553C Reconnaissance, Detection and Identification, and of the Basic Research Theoretical Chemistry Project, Project Number lL161102A71A. Both projects are under Contract No. DAAA 15-92-D-00 15.

(Theochem)

362 (1996) 325-330

References [II W.A. Kreiner, H.D. Rudolph and B.T. Tan, J. Mol. Spectrosc., 48 (1973) 86-99. 121P.J. Breen, J.A. Warren and E.R. Bernstein, J. Chem. Phys., 87 (1987) 1917-1926. 131R.D. Gordon and J.M. Hollas, Chem. Phys. Lett., 164 (1989) 2555259. [41 F. Pang, J.E. Boggs, P. Pulay and G. Fogarasi, J. Mol. Struct., 66 (1980) 281-287. 151H.F. Hameka and J.O. Jensen, J. Mol. Struct. (Theochem), 331 (1995) 203. 161M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. DeFrees, J. Baker, J.J.P. Stewart and J.A. Pople, GAUSSIAN 92, Revision B, Gaussian, Inc., Pittsburgh, PA, 1992. [71 N. Fuson, C. Garrigou-Lagrange and M.L. Josien, Spectrochim. Acta, 16 (1960) 106-127. [8] C. La Lau and R.G. Snyder, Spectrochim. Acta, Part A, 27 (1971) 2073-2088. [9] H.F. Hameka, A.H. Carrieri and J.O. Jensen, Phosphorus Sulfur Silicon Relat. Elem., 66 (1992) l-l 1. [lo] H.F. Hameka, J. Mol. Struct. (Theochem), 284 (1993) 189-195.