Molecular Structure and Conformation of tert-Butylbenzene - American

Mar 9, 1994 - Department of Chemistry, Chemical Engineering and Materials, University of L'Aquila, 1-67100 L'Aquila, Italy. Istvбn Hargittai*. Instit...
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J. Phys. Chem. 1994, 98, 11046- 11052

11046

Molecular Structure and Conformation of tert-Butylbenzene: A Concerted Study by Gas-Phase Electron Diffraction and Theoretical Calculations Anna Rita Campanelli and Fabio Ramondo Department of Chemistry, University of Rome "La Sapienza ", Cittb Universitaria, I-00185 Rome, Italy

Aldo Domenicano* Department of Chemistry, Chemical Engineering and Materials, University of L 'Aquila, I-67100 L 'Aquila, Italy

Istvhn Hargittai* Institute of General and Analytical Chemistry, Budapest Technical University, H-1521 Budapest, and Structural Chemistry Research Group of the Hungarian Academy of Sciences, H-I431 Budapest, Hungary Received: March 9, 1994; In Final Form: August 9, 1994@

The structure and conformation of tea-butylbenzene have been investigated by gas-phase electron diffraction, molecular mechanics (MM2 and MM3 force fields), and ab initio MO calculations at the HF/6-31G and 6-31G* levels. The theoretical calculations indicate that the coplanar conformation of the molecule, with a C-Me bond in the ring plane (0" twist), corresponds to a potential energy minimum. The perpendicular conformation, with a C-Me bond in a plane orthogonal to the ring, is 2-3 kJ mol-' higher in energy and corresponds to a rotational transition state. The experimental study supports these findings, since the coplanar model fits the electron diffraction data better than the perpendicular one. The effective twist angle of the substituent is 8.3 f 2.4", corresponding to a torsional barrier v 6 = 4.7 f 2.7 kJ mol-'. A model with a benzene ring of C2" symmetry and a tert-butyl group of C, symmetry was used in the analysis of the electron diffraction data. Differences between similar bond lengths were constrained from the MM2 calculations. = 1.398 f 0.003 A, r,(Cip,,-CMe3) The following C-C bond distances were determined: = 1.525 f 0.003 A, < r,(C-Me) > = 1S44 f 0.003 A. The deformation of the benzene ring consists primarily of a decrease of the ipso angle to 117.1 f 0.3" (from electron diffraction) and a lengthening of the Cipso-Cofio bonds with respect to Coho-Cmeta bonds (by 0.006-0.009 A, from calculations). With regard to the effect of the benzene ring on the tert-butyl group, the Cips0-C-Me angle lying in the ring plane is about 4" larger than the others, and the Cip,,-CMe3 bond is tilted from the ring axis by about 1.5".

Introduction The accurate measurement of structural substituent effects in benzene derivatives is an important tool for investigating the nature of the interaction between the benzene ring and the Substituent.' Of the C-C bond distances and C-C-C angles of the ring, the latter undergo more extensive variation, up to several degrees, and, being less affected by systematic errors, are more easily transferable from one technique of structure determination to another. These variations have received considerable attention during the last two decades. Gas-phase electron diffraction, microwave spectroscopy, liquid-crystal NMR spectroscopy, and X-ray and neutron crystallography have been used to obtain accurate geometries for a number of such molecules. More recently, a number of theoretical studies, especially ab initio molecular orbital calculations with geometry optimization, have also appeared.* Much effort has been devoted to determine and interpret even subtle variations in structural substituent effects, originating from conformational change^'^,^ and solid-state intermolecular interactions as well. Accurate structural information is, however, still missing for a number of reference molecules, including tert-butylbenzene, C6H5-CMe3. Here we report the structure and conformation of this molecule from a concerted study by gas-phase electron diffraction, molecular mechanics (MM), and ab initio molecular orbital (MO) calculations. This work is part of a systematic @

Abstract published in Advance ACS Abstracts, September 15, 1994.

0022-365419412098-11046$04.50/0

investigation of monosubstituted benzene derivatives in the gaseous phase; the molecules studied include toluene? fluorobenzene,6 trifluor~toluene,~ cyanobenzene,8 n i t r ~ b e n z e n e , ~ ~ phen01,~and ethynylbenzene.'O The analysis of the electron diffraction data for some of these molecules has been facilitated by the adoption of constraints from theoretical calculations.3c~gJ0 Such constraints were expected to be especially useful with tertbutylbenzene, in view of the relatively low symmetry of the molecule. Another interesting problem posed by tert-butylbenzene is the effect by the phenyl group on the geometry of the tertbutyl system. This effect is expected to depend critically on the conformation of the molecule. A preliminary account of some of the results from the present study has appeared.

Theoretical Calculations Ab initio molecular orbital calculations were carried out at the HF-SCFlevel, using the 6-31G and 6-31G* basis sets12 with gradient ~ptimization.'~The maximum forces on the distance and angle coordinates in the final optimizations were less than 0.0005 hartree bohr-' and hartree radian-', respectively. Two models were considered for tert-butylbenzene, one having a C-Me bond in the plane of the ring (la, coplanar conformation), and the other with a C-Me bond in a plane orthogonal to the ring (lb, perpendicular conformation). The 0 1994 American Chemical Society

Molecular Structure and Conformation of tert-Butylbenzene

Z ’ C E M e

/

Me

la

J. Phys. Chem., Vol. 98, No. 43, 1994 11047

T’

’

Me

M ‘e

.....E

19cm

lb

symmetry of the molecule was assumed to be C, in both models, the mirror plane coinciding with the ring plane in l a and being orthogonal to it in lb.14 The optimized geometries are reported in full in Tables S1 and S2 (see paragraph at the end of paper regarding supplementary material); selected parameters are shown in Table 3.15 Molecular mechanics calculations were run for various conformations of tert-butylbenzene, using Allinger’s MM216 and MM3” force fields. The geometries obtained for the coplanar and perpendicular conformations are reported in full in Tables S1 and S2, respectively; selected parameters are shown in Table 3.

Experimental Section A commercial sample of tert-butylbenzene (Aldrich, 99%) was used without further purification, following a check of the purity by gas chromatography. The electron diffraction photographs were taken with the Budapest EG-100A apparatus,18 using a so-called membrane nozzle1gat a temperature of about 337 K. The electron wavelength, 0.049 32 A, was calibrated with a TlCl powder pattern (a = 3.841 45 A).2o Nozzle-toplate distances of about 50 and 19 cm were used; seven and six plates, respectively, were selected for analysis. The tracing and data reduction were carried out as in refs 5b and 21. The ranges of the intensity data were 2.000 Is I 14.000 A-1 and 9.00 I sI 35.50 A-l, with data intervals of 0.125 and 0.25 A-1, respectively. The total experimental intensities are reported in Table S3. The molecular intensities and radial distributions are presented in Figures 1 and 2, respectively. The latter were calculated using an artificial damping factor exp(-0.002~~); theoretical values were used in the 0.00 I s < 2.00 A-1 region.

f(r)

1

CsH5CMe3

fi

k d D G -

I

-

2A

-

-

-

v

,,.,,,,,,,,,,,,,,,,

m T . l , , l l . , l . l . , l , , , , , , . , .

1

Analysis of the Experimental Data The least-squares method was applied to the molecular intensities as in refs 5b and 21, using a modified version of the program by Seip and co-workers.22 The inelastic and elastic scattering functions and phase shifts were taken from refs 23 and 24, respectively. The benzene ring was assumed to have CzVsymmetry. Small deviations from CzVsymmetry, amounting to a few thousandths of an angstrom in bond distances and a few tenths of a degree in bond angles, are suggested by the theoretical calculations (vide infra). However, they were ignored on the basis of our recent electron diffraction study of phe1-101,~ which indicated that inclusion of such deviations into the model has no significant effect on the other molecular parameters. At the beginning of the analysis we assumed C3” symmetry for the tert-butyl group. However, features of the radial distribution curve indicated that a model based on a tert-butyl group with C, symmetry, and having a C-Me bond in the plane of the ring, was superior to any C3,, model. Since the C, local symmetry is also supported by the theoretical calculations, it was adopted in all subsequent refinements. The angle of torsion C2-Cl-C7-C9 (see Figure 3 for the numbering of atoms) was, however, assumed to differ by 120” from C 2 - C l - C 7 - C 8 , again on the basis of the theoretical calculations (see Table Sl).

Figure 3. Numbering of atoms in tert-butylbenzene.

The three methyl groups were assumed to have C3vsymmetry and their C-H bonds to be of equal length. The minor deviations from C3” symmetry revealed by the theoretical calculations (see Table S1) were ignored. One of the C-H bonds of each methyl group was assumed to be anti to the Cl-C7 bond, in accordance with the MO and MM calculations. The five C-H bonds of the phenyl group were assumed to have equal length and to bisect the corresponding C-C-C angles, as in our previous studies of monosubstituted benzene derivative^.^'.^,^- lo

Under the above constraints, the molecular geometry of tertbutylbenzene was described by the following 15 independent parameters (see Figure 3 for the numbering of atoms and Figure 4 for the lettering of the bond distances and angles of a benzene ring of C2” symmetry25): (i) Two bond distances, r(Cl-C2) = a and r(C-H)ph.

11048 J. Phys. Chem., Vol. 98, No. 43, 1994

Campanelli et al.

TABLE 1: Selected Geometrical Parametere and R Factors of tert-Butylbenzene from Refinements A-E* refinements

parameter

r(c 1 -C2) LC2-Cl-C6 r(C 1-C7)' A4(C-C)d MC-CY r(C7-C8)' r(C7--C9)' A 1 (C-C-C)g LCl-C7-C8 Az(C-C--C)" LC 1-C7-C9' t'

RJ

A

B

C

D

E

1.4020(3) 117.2(3) 1.5360(5) -0.0024' -0,0048' 1.5336(5) 1.5384(5) 3.14' 11 1.7(2) 2.79' 108.9(2) 8.5(12) 0.0345

1.4008(2) 117.1(2) 1.5237(5) 0.0189' 0.0008' 1.5426(5) 1.5418(5) 2.82' 112.9(2) 4.47' 108.4(2) 8.1(11) 0.0317

1.4008(3) 117.1(2) 1.5237(5) 0.0189' 0.0008' 1.5426(5) 1.5418(5) 3.3(9) 112.8(3) 4.2(5) 108.6(4) 8.3(15) 0.0317

1.4008(3) 117.4(3) 1.5236(5) 0.0189' 0.0008' 1.5425(5) 1.5417(5) 2.82' 112.9(2) 4.47' 108.5(2) 0.0' 0.0330

1.4012(3) 116.7(2) 1.5244(5) 0.0145' -0.0045' 1.5389(5) 1.5434(5) 0.00' 106.6(3) -4.86' 111.5(3) 90.0' 0.0348

Bond distances (ra) are given in angstroms, angles in degrees. Least-squares standard deviations are given in parentheses as units in the last digit. * Refinements A-C differ in the assumptions on the geometry of the tert-butyl group: (A) assumptions from ab initio MO calculations, HF/6-31G* level; (B) assumptions from MM2 calculations; (C) as B, but refining Al(C-C--C) and Az(C-C-C). Refinements D and E refer to the coplanar and perpendicular conformation of the molecule, respectively. Dependent parameter. &(C-C) = r(C7-C8) - r(Cl-C7). e Assumed. fA5(C-C) = r(C7-CS) - r(C7-C9). 8 A,(C-C-C) = LC2-Cl-C7 - LC6-Cl-C7. * Az(C-C-C) = LCl-C7-C8 - LCl-C7-C9. Angle of torsion of the tert-butyl group, C2-Cl-C7-C8. j R = (&v[&,bs -~cd~]~~w~~b~)'". b

Figure 4. Lettering of bond distances and angles in a monosubstituted benzene ring of CzVsymmetry. (ii) Six differences between bond distances: Al(C-C) = r(Cl-C2) - r(C2-C3) = a - b, A2(C-C) = r(C2-C3) r(C3-C4) = b - c, A3(C-C) = r(Cl-C7) - r(Cl-C2), Q(C-C) = r(C7-C8) - r(Cl--C7), A5(C-C) = r(C7-C8) - r(C7-C9), and A(C-H) = ~(C-H)M~- T(C-H)ph. (iii) Four bond angles: LC2-Cl-C6 = a, LCl-C2-C3 = p, LCl-C7-C8, and LC-C-HM.,. (iv) Two differences between angles: Al(C-C-C) = LC2-Cl-C7 - LC6-Cl-C7 and A2(C-C-C) = LCl-C7-C8 - LCl-C7-C9. (v) The angle of torsion of the tert-butyl group, t = C2-Cl-C7-C8. The measurement of the small differences between the C-C distances of the benzene ring is especially difficult. Our MM and MO calculations have consistently indicated the differences a - b and b - c to be about 0.008 and 0.002 8, respectively. These (or similar) values were assumed in all refinements. The difference A(C-H) = r(c-H)~, - r(C-H)ph was also assumed from the theoretical calculations. As an additional constraint, the angle p was assumed to be linearly related to a, according to a previously established empirical relationship for monosubstituted benzene derivatives,lc AB = -0.591Aa - 0.301" (where A a and AB are deviations from 120'). Twelve mean amplitudes of vibration were also treated as independent variables. They were coupled in groups to other amplitudes with constrained differences. These differences and other assumed amplitudes were taken from spectroscopic calculations on toluenesa and ethylbenzene.26 The effect of altemative choices of the assumed differences on the other parameters was investigated, and the experience gained in these tests was utilized in the error estimation according to ref 27. Selected geometrical parameters from five refinements, A-E, are presented in Table 1. In refinement A the differences between bond distances and angles defining the deviation of the carbon skeleton of the tert-butyl group from C3" symmetry

[namely, &(C-C), A5(C-C), Al(C-C-C), and Az(C-C-C)] were taken from the MO calculations (6-31G* level). In refinement B they were taken from the MM2 calculations. In refinement C the bond distance differences, Ad(C-C) and A5(C-C), were the same as in B, while the angular differences, Al(C-C-C) and A2(C-C-C), were allowed to refine. Refinement D differs from B in that the angle of torsion of the tert-butyl group, t, was fixed at 0" (conformation la). The model used in refinement E has t = 90" (conformation lb).28 Our discussion is based on refinement C. Important molecular parameters from this refinement are presented in Table 2, showing also the coupling of the vibrational amplitudes; the complete list is given in Table S4. Correlation matrix elements having absolute values greater than 0.5 are shown in Table S5.

Results and Discussion Molecular Conformation. According to the MO and MM calculations the coplanar conformation of tert-butylbenzene, la, is more stable than the perpendicular one, lb, by 2-3 kT mol-'. MO (HF/6-31G level) and MM3 frequency calculations show that the coplanar conformation corresponds to a local minimum and the perpendicular conformation to a transition state. The latter is characterized as a frst-order saddle point by the presence of an imaginary frequency related to the torsion of the substituent about the Cl-C7 bond. MM2 and MM3 calculations carried out by varying stepwise the angle of torsion from 0" up to 30" show a monotonic increase of the potential energy.29 Thus, the energy difference between the perpendicular and coplanar conformations of the molecule equals the 6-fold potential barrier, v6, if higher terms are ignored. Additional evidence for the existence of only one potential energy minimum, corresponding to conformation la, comes from supersonic molecular jet laser s p e c t r o s ~ o p y . ~ ~ The electron diffraction results are consistent with the coplanar equilibrium conformation of tert-butylbenzene. Comparison of the results of refinements D and E (see Table 1) shows that the coplanar model fits the experimental data better than the perpendicular one, and this superiority has been observed under various refinement conditions. The angle of torsion determined by electron diffraction tums out to be different from 0' (Table l).31This is probably due to the large-amplitude torsional motion of the tert-butyl group, causing the efective molecular conformation obtained by

Molecular Structure and Conformation of tert-Butylbenzene

TABLE 2: Important Molecular Parameters of tertlutylbenzene from Electron Diffraction0 Distances and Mean Amplitudes of Vibration (A)b atom pair multiplicity r, 1 coupling scheme' 2 2 2 1 1 2 5 9 2 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1

1.4008(3) 1.3949(3)d 1.3927(3)d 1.5237(5)d 1.5426(5)d 1.5418(5)d 1.093(1) 1.105(1)d 2.438(2)d 2.842(4)d 2.426( l)d 2.767(2)d 2.391(3)d 2.389(2)d 2.572(6)d 3.853(4)d 4.365(4)d 3.825(4)d 2.530(6)d 2.554(5)d 2.904(14)d 4.295(13)d 5.186(9)d 4.987(4)d 3.855(5)d 2.490(6)d 3.538(12)d 4.699(10)d 5.064(6)d 4.383(9)d 3.107(1l)d 3.657(14)d 4.786(10)d 5.058(6)d 4.278(14)d 2.961(18)d 2.499(4)d 2.531(5)d

0.0469(4) 0.0469 0.0469 0.0523(6) 0.0533 0.0533 0.075(1) 0.077 0.056(1) 0.060(2) 0.056 0.060 0.056 0.056 0.066 0.068(2) 0.062(3) 0.068 0.066 0.073 0.102 0.097 0.104(6) 0.094 0.081 0.073 0.174(11) 0.174 0.144 0.107 0.1 12 0.174 0.174 0.144 0.107 0.112 0.073 0.073

i i

i 11 11

ii

... ...

111

ll1

iv V

iv V

iv iv

iv vi

vii vi iv iv V

vii

viii viii vi iv ix ix

viii vii V

ix ix viii vii V

iv

iv

Angles (deg) LC2-Cl-C6 LCl-C2-C3 LC2-C3-C4 LC3-C4-C5 LC2-c 1-c7 LCl-C7-C8

117.1(2) 121.4(1)d 121.O( l)d 1 18.1(2)d 123.1(5)d 112.8(3)

LCl-C7-C9 LC8-C7-C9 LC9-C7-C10 LC-C-HM,

te

108.6(4)d 108.2(2)d 110.3(4)d 109.5(2) 8.3(15)

Differences between Bond Distances (A) or Angles (deg) A I (C-CY Az(C-C)~ A3(C-C)' &(C-CY

0.00599 0.00229 0.1229(5) 0.01899

As(C-C)~ A(C-H)' Ai(C-C-C)" Az(C--C-C)"

O.Oo088

0.01 169 3.3(9) 4.2(5)

Refinement C. Least-squares standard deviations are given in parentheses as units in the last digit. To economize space, only C-C, C-H and C - C pairs are included in this table. The unabridged table, reporting all C-H pairs and important H-H pairs, is available as supplementary material (Table S4). The roman numerals indicate the groups within which the amplitudes were refined with constant differences between them. Dependent parameter. e Angle of torsion of the tert-butyl group, C2-Cl-C7-C8. fAl(C-C) = r(Cl-C2) r(C2-C3). 9 Assumed from the MM2 calculations. A*(C-C) = r(C2-C3) - r(C3-C4). A3(C-C) = r(Cl-C7) - r(Cl-C2). j A4(C-C) = r(C7-CS) - r(Cl-C7). A5(C-C) = r ( C 7 4 8 ) A,(C-C-C) = r(C7-C9). A(C-H) = T(C-H)M~- r(C-H)ph. LC2-Cl-C7 - LC6-Cl-C7. Az(C-C-C) = LCl-C7--C8 LCl-C7-C9.

electron diffraction to differ from the coplanar equilibrium conformation. Assuming a simple potential energy function, V(z) = (Vd2) (1 - cos 6r), the torsional barrier for the tert-butyl group, vf,,

J. Phys. Chem., Vol. 98, No. 43, 1994 11049 can be calculated from the average value of the angle of torsion, , by the approximate expression3* vf, = RT/(9n*). From the effective value of z obtained in the present electron diffraction study, 8.3 f 2.4", we obtain v6 = 4.7 f 2.7 kJ mol-'. This result is consistent with those from theoretical calculations (STO-3G, 3.0 kJ 6-31G, 2.8 kJ mol-'; 6-31G*, 2.9 kJ mol-'; MM2, 2.3 kJ mol-'; MM3, 1.9 kJ mol-'), if the rather large experimental uncertainty is taken into account. Furthermore, the barrier estimated from the electron diffraction effective torsional angle being larger than the theoretically predicted one makes it highly probable that this barrier originates from torsional motion, rather than from any deviation from coplanarity in the equilibrium structure. To our knowledge, no other experimental value of the torsional barrier is available for tertbutylbenzene. Benzene Ring Geometry. The geometry of the benzene ring obtained by electron diffraction using MM2 constraints on bond length differences (refinement C) is compared in Table 3 with the geometries obtained from theoretical calculations. To facilitate comparison, the calculated geometrical parameters are given with the same number of significant figures as the experimental ones. Whenever necessary, calculated bond distances and angles have been averaged to be consistent with the symmetry constraints adopted in the electron diffraction study. The most pronounced effect of the substituent on the ring geometry is in the ipso angle, a. The value of a from the present experimental study, 117.1 & 0.3", has shown little sensitivity to background modifications and refinement conditions and is thus well-determined. It agrees within experimental error with the values produced by MO and MM2 calculations, 117.2-117.3", and also with the average value, 117.4(1)", obtained from the data on several molecules containing the C6Hs-CC3 fragment which have been studied by X-ray crystallography.lb The deformation of the benzene ring in the present molecule is expected to be the same in the gaseous and solid states, due to the low polarity of the s ~ b s t i t u e n t . ' ~ ~ ~ The bond length changes in the benzene ring caused by the tert-butyl group are much less pronounced and could not be determined by electron diffraction. The theoretical calculations, however, indicate that a is 0.006-0.009 A longer than b, which, in tum, is about 0.002 A longer than c. MO and MM calculations for the perpendicular conformation of the molecule (see Table S2), as well as MM2 and MM3 calculations on intermediate conformations, show that the angle a and the differences a - b and b - c are virtually insensitive to conformational changes. Thus the component of the ring distortion conforming to C2" symmetry is due primarily to o electronic effects, rather than J-C effects or steric hindrance. The asymmetric attachment of the tert-butyl group in the coplanar conformation of the molecule is expected to cause small deviations from axial symmetry in the benzene ring.35 These are clearly seen in its angles (Table Sl). According to the MO and MM calculations the angles related by the 2-fold axis differ by about 0.2". The situation is less clear with bond distances, where the differences between symmetry-related values amount to 0.005-0.008 8,from the MO calculations but are less than 0.001 8, from the MM calculations. A different kind of distortion may occur in the perpendicular conformation of the molecule, where the benzene ring was not subjected to the planarity constraint. HF/6-31G and 6-31G* level MO calculations carried out on the perpendicular conformers of toluene, ethylbenzene, styrene, nitrosobenzene, benzaldehyde, and phenol, as well as on the pyramidal conformer of aniline, indicate that the ring adopts a very shallow boat-type

Campanelli et al.

11050 J. Phys. Chem., Vol. 98, No. 43, 1994

TABLE 3: Molecular Geometw of tert-Butylbenzene: Comparison of Experimental and Theoretical Results MO calculations MM calculations coplanar Perpendicular perpendicular electron diffraction' coplanar conformationd conformation conformation (with constraints from conformationd uarameteP MM2 calculations) 6-31G 6-31G* 6-31G 6-31G* MM2 MM3 MM2 MM3 1.399 1.398 f 0.003 1.390 1.390 1.388 1.398 1.399 1.398 1.388 (r(c-c)Ph) a

b C

a

B Y

6 (r(C-C)terJ r(Cl-C7) r(C7-CS) r(C7-C9) LC2-Cl-C7 L C 1-c7-c8 LCl-C7-C9 LC8-C7-C9 LC9-C7-C 10 (r(C-H)) r(C-H)ph r(C-H)Me LC-C-HM,

1.402' 1.396' 1.394' 117.1 f 0.3 121.4 f 0.2 121.0 f 0.2 118.1 f 0.3 1.539 f 0.003 1.525' 1.544' 1S44' 123.1 f 0.7 112.8 f 0.5 108.6 f 0.6 108.2 f 0.3 110.3 f 0.6 1.106 f 0.003 1.098' 1.110' 109.5 f 0.4

1.396 1.388 1.386 117.3 121.4 120.4 119.0 1.543 1.539 1.540 1.546 122.9 112.4 109.6 108.0 109.4 1.os0 1.073 1.084 110.9

1.394 1.386 1.384 117.2 121.5 120.4 119.0 1.539 1.539 1.536 1.541 123.0 112.4 109.6 107.9 109.4 1.082 1.075 1.085 111.1

1.396 1.388 1.386 117.2 121.5 120.4 119.0 1.543 1.541 1.546 1.544 121.4 108.6 111.5 108.9 107.4 1.os0 1.072 1.084 111.0

1.394 1.386 1.384 117.0 121.6 120.5 118.9 1.540 1.540 1.541 1.540 121.5 108.7 111.6 108.8 107.3 1.081 1.075 1.085 111.1

1.403 1.397 1.395 117.2 121.7 120.2 119.2 1.540 1.527 1.545 1.545 122.8 113.8 109.4 107.3 109.6 1.110 1.102 1.114 111.7

1.406 1.397 1.394 117.7 121.2 120.2 119.5 1.541 1.526 1.546 1.545 122.6 113.4 109.8 107.2 109.2 1.109 1.103 1.113 111.9

1.403 1.397 1.394 116.9 121.8 120.2 119.1 1.541 1.528 1.542 1.547 121.5 107.7 112.5 108.9 106.4 1.110 1.102 1.114 111.7

1.406 1.397 1.394 117.6 121.3 120.2 119.5 1.541 1.527 1.543 1.547 121.2 108.6 112.4 108.5 106.4 1.109 1.103 1.113 111.9

a Bond distances are given in angstroms, angles in degrees. Bond distances and angles of the benzene ring are lettered according to Figure 4. From refinement C; bond distances are rg values. Total errors are given as error limits; they have been calculated according to the expression^^^^^^ UT = [2u~s* (0.002r)2 (A/2)2]1/2(for bond distances) and UT = [2uu2 (N2)2]1/2(for bond angles), where ULS is the least-squares standard deviation, and N 2 is the effect of the constraints adopted in the refinement, estimated according to ref 27. Whenever necessary, bond distances and angles have been averaged to be consistent with the symmetry constraints adopted in the electron diffraction study. e The differences a - b, b - c, r(C7-C8) - r(Cl-C7), r(C7-CS) - r(C7-C9), and ~ ( C - H ) M~ r(C-H)ph have been constrained from the MM2 calculations for the coplanar conformation.

+

+

conformation, with deviations from planarity not exceeding a few thousandths of an angstrom.36 The substituent atom linked to the ring is, in general, more displaced than the ring carbons, up to about 0.05 A in some of these molecules. The decrease in total energy occumng upon relaxation of the planarity constraint is calculated to be 0.03-0.37 kJ mol-' for the molecules ~ o n s i d e r e d .Thus ~ ~ there is no strong driving force for departure from coplanarity. The MO calculations for the perpendicular conformer of tert-butylbenzene indicate a similar ring distortion, with C7 displaced by 0.05 8, on the same side as C8 (see Table S2). The MM2 and MM3 calculations, however, yield different distortions, with C7 displaced (by 0.01 and 0.04 A, respectively) on the side of the ring opposite to C8. The mean length of the ring C-C bonds from electron diffraction, = 1.398 f 0.003 A, is virtually the same as those of ethylbenzene,26 and benzene itself;37 all equal to 1.399 f 0.003 8,. It also agrees with the values from the MM calculations, 1.398 (MM2) and 1.399 8, (MM3), claimed17ato be also rg distances. The difference from the MO results, 1.390 8, (6-31G) and 1.388 8, (6-31G*), may originate from several sources, such as the inherent difference in physical meaning (rg versus re), basis set limitations, and neglect of electron correlation. With regard to the C-H bond distances and C-C-H angles of the phenyl group, the MO and MM calculations show that the two C-H bonds at the ortho positions, C2-H2 and C6-H6, are 0.001 -0.003 A shorter than the others. They are also bent away from the substituent by 2-4', see Tables SI and S2. This suggests that the effect may be due to steric hindrance; indeed, it depends on the conformation of the substituent. We see from Table S1 that the C2-H2 bond, syn to a C-Me bond in the coplanar conformation, is slightly shorter and bent more from the substituent than C6-H6, which is gauche to two C-Me bonds. Moreover, the MO and MM calculations for the

+

perpendicular conformation indicate that H2 and H6 are somewhat displaced from the ring plane on the same side as C8 (see Table S2). This would reduce the strain arising from the close proximity of H2 to H103 and H6 to H92.38 Geometry of the tert-Butyl Group. The MO and MM calculations yield contrasting results for the length of the C-C bonds in the tert-butyl system, see Table 3. According to the former the Cl-C7 bond is about as long as the C-Me bonds, while according to the latter it is ca. 0.020 A shorter, irrespective of the conformation of the substituent. Refinements A and B of the electron diffraction analysis (see Table 1) show that the use of MM2 constraints on bond length and angle differences gives better agreement with experimental data than the use of constraints from MO calculations. Since the MM2 and MO constraints differ primarily in the values of &(C-C) = r(C7-C8) - r(C1-7) and A5(C-C) = r(C7-8) - r(C7-C9), we conclude that the electron diffraction experiment favors the MM2 geometry for the tert-butyl system. The final experimental geometry (from refinement C, with MM2 constraints on bond length differences only) is compared in Table 3 with the geometries obtained from theoretical calculations. Electron diffraction r,(C-Me) values are compared for related molecules in Table 4. They appear to increase slightly with increasing molecular strain. Another possible indication of strain in the present molecule is the length of the Cl-C7 bond, rg = 1.525 f 0.003 A, which exceeds by about 0.015 8, the len th of the corresponding bond in toluene (rg = 1.511 f 0.008 and 1.507 f 0.004 A5b), 1,4-dimethylbenzene (rg = 1.512 f 0.003 and 1,3,5-trimethylbenzene (rg = 1.509 f 0.002 A).43 The effect of the phenyl group on the tert-butyl system is most pronounced in the C-C-C angles. This is indicated by the electron diffraction results as well as by the theoretical calculations. The Cl-C7 bond is tilted from the ring axis by

,f5a

Molecular Structure and Conformation of tert-Butylbenzene

J. Phys. Chem., Vol. 98, No. 43, 1994 11051

TABLE 4: Geometrical Parameters of the tertlutyl System from Electron Diffraction Studiee molecule H-CMe3 Me-CMe3 MeX-CMe3 Ph-CMe3

rg(C-Me) 1.535(1) 1.537 f 0.003 1.542(2) 1.544 f 0.003

rg(C-H)Me 1.113(2) 1.1 13(4) 1.110 f 0.003

LC-C-Me 109.5b 111.0(3) 112.8 f 0.5

H-C(CMe&

1.548(2)

1.11l(3)

113.0(2)

1.114 f 0.008

LC-C-Hw,

type of error

source

111.4(4)

3ULS

112.2 & 2.8 111.5(14) 109.5 f 0.4

total 2ULS total

ref 39 ref 40 ref 41 this work

114.2(10)

ULS

ref 42

108.6 f 0.6 Bond distances are given in angstroms, angles in degrees. Least-squares standard deviations as units in the last digit; total errors are given as error limits. Assumed.

LCl-C7-Me (")

112

110

4 f--+

i

108

4 1

I

I

0

I

30

1

1

I

60

I

I

7

(")

t 90

Figure 5. Variation of the Cl-C7-Me

angles of the tert-butyl group upon rotation about the Cl-C7 bond from theoretical calculations.

angle is enlarged by ca. 4", as compared with the other Cl-C7-Me angles. Both changes decrease the strain caused by the close proximity of the ring hydrogen H2 to the methyl hydrogens H82 and H83. Notwithstanding the deformation of the substituent, the H2-H82 and H2-H83 distances, 2.28-2.30 A,44are still slightly smaller than the distances H6-H93 and H6-Hl02 (2.32 A).& These values should be com ared with twice the van der Waals radius of hydrogen, 2.4 .45 The molecule is obviously more strained in the perpendicular conformation. Although one of the methyl groups of the substituent is well apart from the phenyl hydrogens, the other two have short contacts with H2 and H6.38 The theoretical calculations indicate a slight increase of r(Cl-C7), 0.001 10.0015 A, in going from the coplanar to the perpendicular conformation. The three Cl-C7-Me angles of the tert-butyl group change upon rotation about the Cl-C7 bond. This is shown in the curves of Figure 5 , obtained from MM2 and MM3 calculations at t = 0, 10, 20, 30°, as well as from MO, HF/6-31G* level calculations for the coplanar and perpendicular conformation^.^^ The same general shape characterizes all three curves. According to the calculations, some of the C-H bonds of the tert-butyl group appear to be 0.001-0.002 A shorter than the others, and the corresponding C-C-H angles are slightly enlarged (Tables S1 and S2). These C-H bonds lead to hydrogens which are at a short distance from the phenyl hydrogens; thus these variations may mean some decrease in the strain, similarly to the variation of the C-Hofio bonds and C-C-&,,h, angles of the phenyl group. ca. 1.5", while the Cl-C7-C8

w

Acknowledgment. We thank Mrs. Miria Kolonits (Budapest) for experimental work and Prof. Antonio Arcadi (L'Aquila) for checking the purity of the sample. This research has been carried out in the framework of the Scientific Cooperation Agreement between the National Research Council of Italy and the Hungarian Academy of Sciences; it has also been supported by the Hungarian National Scientific Research Foundation (OTKA, grant No. 2103).

(ULS)

and their multiples are given in parentheses

Supplementary Material Available: Tables S1 and S2 reporting the molecular geometry of tert-butylbenzene in the coplanar and perpendicular conformations, respectively, from ab initio molecular orbital and molecular mechanics calculations, Table S3 giving the total experimental electron diffraction intensities of tert-butylbenzene, Table S4 reporting the molecular parameters of tert-butylbenzene from electron diffraction (this is an unabridged version of Table 2 of the text), and Table S5 showing the correlation matrix elements with absolute values greater than 0.5 (22 pages). Ordering information is given on any current masthead page. References and Notes (1) (a) Domenicano, A.; Vaciago, A.; Coulson, C. A. Acta Crystallogr., Sect. B 1975, 31, 221 and 1630. (b) Domenicano, A.; Vaciago, A. Acta Crystallogr., Sect. B 1979, 35, 1382. (c) Domenicano, A,; Murray-Rust, P.; Vaciago, A. Acta Crystallogr., Sect. B . 1983, 39,457. (d) Domenicano, A. In Stereochemical Applications of Gas-Phase Electron Diffraction; Hargittai, I., Hargittai, M., Eds.; VCH: New York, 1988; Part B, Chapter 7. (e) Domenicano, A. In Accurate Molecular Structures: Their Determination and Importance; Domenicano, A., Hargittai, I.. Eds.; Oxford University Press: Oxford, 1992; Chapter 18. (2) See, e. g., Pang, F.; Boggs, J. E.; Pulay, P.; Fogarasi, G. J . Mol. Struct. 1980, 66, 281. Boggs, J. E.; Pang, F.; Pulay, P. J . Comput. Chem. 1982, 3, 344. Bock, C. W.; Trachtman, M.; George, P. J . Mol. Struct. (THEOCHEM) 1985, 122, 155. George, P.; Bock, C. W.; Trachtman, M. J . Mol. Struct. (THEOCHEM) 1986, 137, 387 and 1987, 153, 363. Bock, C. W.; George, P.; Trachtman, M. Theor. Chim. Acta 1986,69,235. Wang, Y.;Saeb0, S.; Pittman, C. U., Jr. J. Mol. Struct. (THEOCHEM) 1993,281, 91. (3) (a) Bock, C. W.; Trachtman, M.; George, P. J. Mol. Struct. (THEOCHEM) 1986,139,63. (b) Penner, G. H.; George, P.; Bock, C. W. J. Mol. Struct. (THEOCHEM)1987,152, 201. (c) Domenicano, A,; Schultz, G.; Hargittai, I.; Colapietro, M.; Portalone, G.; George, P.; Bock, C. W. Struct. Chem. 1990, I , 107. (4) Domenicano, A.; Hargittai, I. Acta Chim. Hung.-Models Chem. 1993, 130, 347. ( 5 ) (a) Seip, R.; Schultz, G.; Hargittai, I.; Szab6, Z. G. Z . Naturforsch., Teil A 1977, 32, 1178. (b) Domenicano, A.; Schultz, G.; Kolonits, M.; Hargittai, I. J . Mol. Struct. 1979, 53, 197. (6) Portalone, G.; Schultz, G.; Domenicano, A,; Hargittai, I. J . Mol. Struct. 1984, 118, 53. (7) Schultz, G.; Hargittai, I.; Seip, R. Z . Naturforsch., Teil A 1981, 36, 669. (8) Portalone, G.; Domenicano, A,; Schultz, G.; Hargittai, I. J . Mol. Struct. 1987, 160, 97. (9) Portalone, G.; Schultz, G.; Domenicano, A,; Hargittai, I. Chem. Phys. Lett. 1992, 197, 482. (10) Schultz, G.; Nagy, T.; Portalone, G.; Ramondo, F.; Hargittai, I.; Domenicano, A. Struct. Chem. 1993, 4, 183. (11) Campanelli, A. R.; Domenicano, A.; Hargittai, I.; Ramondo, F. Presentation at the 23rd Congress of the Italian Crystallographic Association, Venice, 19-22 October 1993; Abstracts, p 242. (12) Pokier, R.; Kari, R.; Csizmadia, I. G. Handbook of Gaussian Basis Sets: A Compendium for a b Initio Molecular Orbital Calculations; Elsevier: Amsterdam, 1985. (13) Pulay, P. Mol. Phys. 1969, 17, 197. (14) Note that in the perpendicular conformation of the molecule the benzene ring was not subjected to the planarity constraint. (15) All MO calculations were carried out on the IBM 3090/600J computer of Progetto NIC-Italia, using the Gaussian 90 system of programs (Frisch, M. J.; Head-Gordon, M.; Txucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn,L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. Gaussian 90; Gaussian Inc.: Pittsburgh, PA, 1990). (16) Allinger, N. L. J . Am. Chem. SOC.1977, 99, 8127.

11052 J. Phys. Chem., Vol. 98, No. 43, 1994 (17) (a) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J . Am. Chem. SOC.1989, 1 1 1 , 8551. (b) Lii, J.-H.; Allinger, N. L. J . Am. Chem. SOC. 1989, 111, 8566 and 8576. (18) Hargittai, I.; Hemidi, J.; Kolonits, M. Prib. Tekh. Ekrp. 1972,239. Tremmel, J.; Kolonits, M.; Hargittai, I. J . Phys. E 1977, I O , 664. Hargittai, I.; Tremmel, J.; Kolonits, M. Hung. Sci. Instrum. 1980, 50, 31. (19) Hargittai, I.; Hemkii, J.; Kolonits, M.; Schultz, G. Rev. Sci. Instrum. 1971, 42, 546. (20) Witt, W. Z . Naturforsch., Teil A 1964, 19, 1363. (21) Colapietro, M.; Domenicano, A.; Portalone, G.; Schultz, G.; Hargittai, I. J . Phys. Chem. 1987, 91, 1728. (22) Andersen, B.; Seip, H. M.; Strand, T. G.; Stglevik, R. Acta Chem. Scand. 1969, 23, 3224. (23) Tavard, C.; Nicolas, D.; Rouault, M. J . Chim. Phys. Phys. Chim. Biol. 1967, 64, 540. (24) Bonham, R. A,; S c h ~ e r L. , In International Tables for X-ray Crystallography; Kynoch: Birmingham, 1974; Vol. IV,Chapter 2.5. (25) The three different bond distances and four different angles of a benzene ring of Cz, symmetry (Figure 4) are linked by two equations of geometrical constraint, expressing the conditions of planarity and ring closure.1c Thus only five independent parameters are required to define the ring geometry. (26) Scharfenberg, P.; Rozsondai, B.; Hargittai, I. Z . Naturforsch., Teil A 1980, 35, 431. (27) Portalone, G.; Domenicano, A,; Schultz, G.; Hargittai, I. J . Mol. Struct. (THEOCHEM) 1989, 186, 185. (28) In this refinement the difference Al(C-C-C) was set equal to zero, while Al(C-C), Az(C-C), A4(C-C), As(C-C) and A2(C-C-C) were assumed from the MM2 calculations for conformation lb. The grouping of the vibrational amplitudes was, of course, appropriate to the model. (29) A 30" twist about the Cl-C7 bond converts l a into l b and vice versa. (30) Seeman, J. I.; Secor, H. V.; Breen, P. J.; Grassian, V. H.; Bemstein, E. R. J . Am. Chem. SOC. 1989, 111, 3140. The expansion process in the

Campanelli et al. molecular jet results in gas-phase molecules at nearly 0 K. Thus the groundstate energy minima can be isolated and studied, even when the interconversion barriers are very low. (31) The effective angle of torsion has been found to be rather sensitive to refinement conditions. Values ranging from 6.8" to 9.1" have been obtained in the course of the analysis. (32) Vilkov, L. V.; Penionzhkevich, N. P.; Brunvoll, J.; Hargittai, I. J . Mol. Struct. 1978, 43, 109. (33) Schaefer, T.; Penner, G. H. J . Mol. Struct. (THEOCHEM) 1986, 138, 305. (34) Hargittai, M.; Hargittai, I. J . Chem. Phys. 1973, 59, 2513. (35) See, e.g., Bock, C. W.; Trachtman, M.; George, P. Chem. Phys. 1985, 93, 431. Bock, C. W.; Domenicano, A,; George, P.; Hargittai, I.; Portalone, G.; Schultz, G. J . Phys. Chem. 1987, 91, 6120. (36) George, P.; Bock, C. W.; Trachtman, M.; Penner, G. H. J . Mol. Struct. (THEOCHEM) 1988, 180, 37. (37) Schultz, G.; Kolonits, M.; Hargittai, I. Unpublished results. (38) The distances H2-Hl03 and HbH92, which are symmetry-related in the perpendicular conformation of the molecule, are 2.11 A from the MO (HF/6-31G* level) and MM3 calculations. (39) Hilderbrandt, R. L.; Wieser, J. D. J . Mol. Struct. 1973, IS, 27. (40) Bartell, L. S . ; Bradford, W. F. J . Mol. Struct. 1977, 37, 113. (41) Bartell, L. S . ; Boates, T. L. J . Mol. Struct. 1976, 32, 379. (42) Burgi, H. B.; Bartell, L. S . J . Am. Chem. Soc. 1972, 94, 5236. (43) Almenningen, A.; Hargittai, I.; Samdal, S.; Brunvoll, J.; Domenicano, A.; Lowrey, A. J . Mol. Struct. 1983, 96, 373. (44) From the MO (HF/6-31G* level) and MM3 calculations. (45) Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Come11 University Press: Ithaca, NY,1960; p 260. (46) The MO calculations at the HF/6-31G and 6-31G* levels give indistinguishable curves.