Ab initio studies of methylated 1,3-butadienes

Journal of Molecular Structure (Theochem), 260 (1992) 347-393 Elsevier Science Publishers B.V., Amsterdam

347

Ab initio studies of methylated 1,3-butadienes”

Hong Guo and Martin Karplus

Department of Chemistry, Harvard University, Cambridge, MA 02138 (USA)

(Received 25 November 1991)

Abstract

To understand the effect of methyl substitution on substituted butadiene potential surfaces, the structures for the stable conformations and the potential energy functions about the central C-C single bond are determined for 18 different methylated 1,8butadienes from the 631G Hartree-Fock (HF) calculations with geometry optimization at each of the torsional angles. They are (E)-penta-1,3-diene ((E)-PD), (2)penta-1,3diene ((2)PD), 2- methylbuta-1,3-diene (MB), (E, E)-hexa-2,4-diene ((E, E)-HD), (E, Z)-hexa-2,Cdiene ((E, Z)- HD), (2, Z)-hexa-2,Cdiene ((2, Z)-HD), Cmethylpenta-1,3-diene (I-MPD), (E)-2-methylpenta- 1,3-diene ((E)-2-MPD), (E)-3-methylpenta-1,3-diene ((E)-3-MPD), (2)2-methylpenta-1,3-diene ((2)2-MPD), (2)3-methylpenta-1,3_diene ((2)3-MPD), 2,3-dimethylbuta-1,3-diene (DMB), 2,4- dimethylpenta-1,3-diene (2,4-DMPD), (2, Z)-3-methylhexa-2,4&ene ((2, Z)-8MHD), (2)-2,3- dimethylpenta-1,3-diene ((2)2,3-DMPD), (E, E)-3,4-dimethylhexa-2,4-diene ((E,E)-3,4- DMHD), (E, Z)-3,4-dimethylhexa-2,4diene ((E, Z)-3,4-DMHD) and (2, Z)-3,Cdimethylhexa- 2,4-diene ((Z, Z)-3,4-DMHD). The methyl substitutions at the 2(3) and terminal 2 positions of butadiene are found to have significant effects on the shape of the potential function due to the introduction of strong steric repulsions between the two ethylenic (or methylated ethylenic) units. Although the terminal E methyl group in the monomethyl- and dimethylbutadienes has little effect on the shape of the potential function, sizable effects of the (E)-methyl group were observed in the trimethyl- and tetramethylbutadienes. While the most stable conformation is s-trans for most (11) of the dienes, the major form for all the dienes (6) with both Z-4- and 2-positioned (or (2)-l- and Bpositioned) methyl groups is predicted to have a gauche or “orthogonal” structure with a C = C-C = C torsional angle (T) between 50’ and 90’. The present study confirms the earlier suggestion that the most stable conformer of (2)2-MPD has a gauche structure. For 2,4-DMPD the ab initio results agree with a nuclear magnetic resonance (NMR) analysis in that only one conformer should be populated; the calculated structure is also very close to that from NMR experiments. This is in contrast with the results of previous molecular mechanics calculations which suggested that non-planar s-cis and s-trans forms of 2,4-DMPD were both present with an energy difference of only about 0.3 kcal mol-‘. For (E, E)-DMHD the two stable conformations (s-trans and gauche) were calculated to have similar energies, but only one of them (s-trans) has been suggested

Correspondence to: M. Karplus, Department of Chemistry, Harvard University, Cambridge, MA 02138, USA. *Dedicated to the memory of Professor Charles A. Coulson.

348

experimentally. The ab initio conformations for (E, Z)-DMHD and (2, Z)-DMHD are similar to those from experiment. The calculations also give results that are of help in interpreting certain reactions. An energy function is proposed for analyzing the ab initio potential energy, and it is suggested that such an energy function is useful for estimating the increase of the torsional angle dependent steric interactions induced by methyl substitutions. The length of the central C-C single bond as a function of the torsional angle is examined for each of the methylated butadienes.

INTRODUCTION

The effects of alkyl substitution on the ultraviolet (UV) spectra of acyclic conjugated dienes are of considerable interest [l-6]. Most attention has been given to the strongly allowed transition that corresponds to the 1 ‘B: c 1 ‘A; excitation in unsubstituted 1,8butadiene. There is a regular variation (about 5nm red shift per alkyl group) of A,,, with alkyl substitutions which led Woodward [l] to develop a set of empirical rules in 1941; Woodward’s rules have been of value in the elucidation of organic structures. The observed spectral shifts are thought to be directly related to perturbations of the electronic structure and have been the subject of many theoretical investigations [7-111. In addition, alkyl substitutions may lead to spectral shifts that show less regularity and are believed to arise from conformational changes [2,4,6]. For instance, Forbes et al. [2] have observed that the introduction of a methyl substituent in the 2-position of 4-methylpenta-1,3-diene (4-MPD) (see Fig. 1 for definitions) gives rise to a significant reduction in intensity and to a hypsochromic wavelength dis- placement of 3.5nm, rather than a bathochromic shift as predicted by Woodward’s rules. They suggested that such deviations from Woodward’s rules are due to steric interactions which lead to non-planar conformations for compounds like 2,4-dimethylpenta-1,3-diene(2,4-DMPD). Vaida and co-workers [5,6] have studied the 1 ‘B,+ c 1 ‘A; transitions for a number of methylated butadienes. They found that 2-methylbuta-1,3-diene (MB), (E)-penta-l,&diene ((E)-PD), 2,3-dimethylbuta-1,3-diene (DMB), (E, E)- hexa-2,4-diene ((E, E)-HD) and (E, E)-3,4-dimethylhexa-2,4-diene ((E, E)- 3,4-DMHD) have absorptions similar to that of 1,8butadiene with intense transitions at A,,, = 214 to 230nm (n,,, x 210nm for 1,3-butadiene) both (E, 2)-3,4-dimethylhexa_2,4diene ((E, Z)-3,4DMHD) and (Z, Z)-3,4-dimethylhexa-2,4-diene ((2, 2 )-3,4-DMHD) have ethylene like spectra with the first I,,, at 171 and 168nm, respectively. It has been suggested [4] that these ethylene like spectra arise from transitions from non-planar ground states to highly twisted excited states. Significant effects of alkyl substitutions have been observed also in the photoelectron (PE) [12-151 and ion (He+ and H2+) impact spectra [16] of dienes and attributed to the conformational changes induced by steric repulsion.

349

(E)-PD

H’, or C’,H’, H’, or CleH13

/I\==\ (E,Z)-HD

A (Z)-3-MPD

-

+

2,4-DMPD

- 4-i - -

+

-

(E,Z)3,4-DMHD (Z,Z)-3,4-DMHD

(Z)-PD

/=--\I/

(Z,ZbHD

(El-2.MPD

(Z,Z)-&MHD

=F- )Ly_ -

I-MPD

T==

(Z)-2-MPD

r/ -

?

(Zb2,3-DMPD

(E,EbHD

(E)3-MPD

DMB

- Y-i - (B,Bb3,4-DMHD

Fig. 1. The atom labels of the dienes studied in this work.

The interactions which cause the conformational and spectral changes for the methylated butadienes are thought to arise from the steric repulsion between (Q-4- and 2-positioned (or (2)-l- and 3-positioned) methyl groups which leads to a non-planar lowest energy conformation [2,17]. Although this suggestion is in accord with the experimental observations discussed above, previous studies are not unequivocal. Masclet et al. [13] have

350

measured three alence ionization energies of (Z)- and (E)-2-methylpenta- l,&diene ((2) and (E)-2-MPD) by PE spectroscopy. The first two PE bands (denoted as x_ and R, ) are believed to correspond, within Koopmans’ approximation, to the ejection of an electron from one of the two highest occupied x orbitals (b, and a,, in planar butadiene symmetry notation). They found that the spectra for both isomers were almost identical with a x_ , n, ionization energy difference of about 2.05 eV (2.43 eV for butadiene). This suggests that the C=C-C=C torsional angle for both the isomers is the same and probably about 180”. Werstiuk and Timmins [14], however, argued that the 2 isomer should exist in a twisted conformation as found from molecular mechanics and semi-empirical calculations [14] and that the a _ , n+ splitting of the 2 isomer should be less than that of the E isomer. They suggested that the major component of the commercial sample of (2)2- MPD used previously was in fact the E isomer, and a redetermination of the ionization energies for (2)2-MPD resulted in a it_ , TC, splitting equal to 1.55 eV. Cunliffe and Harris [18] have examined the proton-proton coupling constants in the ‘H nuclear magnetic resonance (NMR) spectra of 2,4- DMPD under different conditions and concluded that it exists in a single non-planar conformation with an average z(C=C-C=C) dihedral angle of about 50’. This seems to be inconsistent with the results of molecular mechanics calculations [19] which predicted that non-planar s-cis and s-trans forms are both present with an energy difference of only about 0.3 kcal mol-‘. (E,Z)-3,CDMHD and (Z, Z)-3,4-DMHD were found to have essentially the same “orthogonal” conformation from gas-phase electron diffraction [20] with a C=C-C=C dihedral angle of about 66-67’. Schmid- hauser [17], however, has argued that (E,Z)-3,4-DMHD and (Z,Z)-3,4- DMHD should have different conformations about the central C-C single bond, because they behave differently in certain chemical reactions [4,17] in which the dienes are required to reach the s-cis conformation. For instance, while (E, Z)-3,4-DMHD participates in a Diels-Alder reaction with maleic anhydride [21] or sulfur dioxide [22], (Z, Z)-3,4-DMHD does not. He suggested that the different reactivities imply different conformations for (E, Z)-3,4-DMHD and (Z, Z)-3,4-DMHD. However, since whether a diene is capable of reaching the s-cis conformation for a reaction depends on the rotational barrier to the s-cis conformation rather than on the location of the stable conformation, a knowledge of the potential function about the central C-C single bond is necessary for an interpretation of these reactions.

For many methylated butadienes, a second stable conformer resulting from rotation about the central C-C single bond exists, as is the case for l,&butadiene. However, unlike butadiene for which considerable experimental and theoretical investigations are available concerning the torsional potential and the structure of the second stable conformer [23], methylated butadienes have attracted little attention in this respect except

351

for MB and DMB [3,24-271. Even for MB and DMB, the two relatively well studied substituted dienes, there is still controversy concerning the second stable conformer. Squillacote et al. [3] studied the UV spectra of the MB and DMB minor forms and observed that the UV maximum of the second stable conformer of MB is red-shifted from the s-trans rotamer as expected for cyclic cisoid dienes, and that there is 5 nm progression of A,_ in going from butadiene to isoprene as predicted by the Woodword rules [l]. In contrast, the higher energy form of DMB shows a blue-shift from s-trarzs- DMB and from the second stable conformer of MB. This has been con- sidered evidence that the torsional angle in the second stable conformer of DMB is substantially (about 30-50’) larger than that of MB [3]. Such a conclusion is inconsistent with recent ab initio calculations [25-271 which give a difference of less than 10’ in the torsional angles of the MB and DMB second stable isomers. Furthermore, DMB was found to have an activation barrier of 3.4 kcal mol-’ for the gauche to s-trans conversion from a kinetic study [3] which is much larger than the barrier (1.7-1.8kcalmoll’) from ab initio calculations [25,27]. The torsional angle of the minor form of MB has been estimated to be about 70’ from an electron diffraction investi- gation of a gaseous sample and an analysis of vibrational spectra [28], which is also significantly different from the ab initio results (about 40-45’) [25,27].

It is clear from the summary given above that a full understanding of even the ground state conformations is still lacking. In the present study we used ab initio methods to investigate the ground state conformational surfaces. We focus on two basic interactions, conjugation and steric repulsion, by examining the effects of methyl substitutions on the structure and the torsional potential of the ground state of butadiene. We briefly outline the calculational method and report the results obtained. The results obtained are discussed and conclusions are presented in the final section. A subsequent paper will be concerned with the results obtained for methylated cis- and trans-1,3,5-hexatriene.

METHOD

Ab initio calculations were performed at the Hartree-Fock (HF) level using the GAUSSIAN 82 program [29] with internally stored 4-21G, 6-31G and 6-31G* basis sets. The total energies and the torsional potentials about the central C-C single bond were determined for 18 different methylated butadienes: (E)-PD, (Z)-penta-1,3-diene ((.Z)-PD), MB, (E, E)-HD, (E, Z)- hexa-2,4-diene ((E, Z)-HD), (2, Z)-hexa-2,4-diene ((Z, Z)-HD), 4-MPD, (E)-2- MPD, (E)-&methylpenta-1,8diene ((E)-3-MPD), (Z)-2-MPD, (Z)-&methylpenta-1,3-diene ((Z)-&MPD), DMB, 2,4-DMPD, (Z, Z)-3-methylhexa-2,4-diene ((Z, Z)-8MHD), (Z)-2,3-dimethylpenta-1,3-diene ((Z)-2,3-DMPD), (E, E)-3,4-

352

DMHD, (E, Z)-3,4-DMHD and (Z,Z)-3,4-DMHD. Figure 1 shows the atom labels and the notation used; here primed and unpruned groups correspond to the two ethylenic units. HF/6-31G calculations were performed with geometry optimization at each of the C=C-C=C torsional angles to obtain an “adiabatic” map [30] (20’ intervals were used in most of the cases). The structures and energies for the stable conformations were also determined in each case (see Appendix). For the monomethyl- and dimethyl-butadienes as well as (E, E)-3,4-DMHD and (Z,Z)-3,4-DMHD, complete geometry optimization was performed. For the trimethylbutadienes and (E, 2)-3,4- DMHD for which the total number of geometrical parameters for optimization exceeds 50 (the limit of the GAUSSIAN az program), the following approximations were used. For 2,4-DMPD the C;H: and C;H: bond lengths (see Fig. 1) were fixed at 1.0730 and 1.0738 A, respectively, during geometry optimization which are the bond lengths found in the s-trans conformation of (Z)-2-MPD (see Appendix). For (Z, Z)-8MHD the C;HL and the C,H, bond lengths were fixed at 1.077 A as found in the stable conformations of (Z,Z)- HD (see Appendix); the C;H: in (Z)-2,3-DMPD was also fixed at 1.077 A. For (E, Z)-3,4-DMHD, the geometrical parameters in the (C!;)C:Hj group were fixed at the values (F) (C$;) = 1.503 A, r(CLH’1) = 1.080 A, r(CLH’2) = 1.087 A, r(CiH’3) = l.O87A, L(C;C;C;) = 128.7’, ,!_(C;C;H’l) = 114.0°, L(C;C:H’B) = 110E1~, L(CiCLH’3) = 110.5’, z(C$;C:H’l) = O.O”, z(C$;C:H’2) = 121.0’ and z(C9Z;C:H’3) = - 121.0°) close to those found in (E, E)-3,4-DMHD (see Appendix). These fixed geometrical parameters should not be sensitive to the rotation about the central C-C single bond, and the approximations are expected to have little effect on the shape of the potential functions and on the values of other geometrical parameters. To examine the effects of basis set and geometry optimization on the calculated torsional potentials, HF/4- 21G and HF/6-31G* calculations with geometry optimization were made for MB and DMB, and HF/6-31G single point calculations with the geometry optimized at the s-trans conformation (a “rigid rotation” map for the C=C-C=C torsional angle) were performed for DMB.

RESULTSANDDISCUSSION

We first describe the torsion potentials of the methylated butadienes and then introduce a new energy function for studying the steric interactions in the systems. Finally, we examine the effect of methyl substitutions on the central C-C bond length.

Torsional potentials

The total and relative energies for (E)-PD, (Z)-PD and MB at various Cp angles (4 = 180’ - z(C=C-C=C)) from the HF/6-31G calculations are listed

353

in Table 1 along with the results for butadiene [23] and the torsional potentials (AE) are plotted in Fig. 2; q5 instead of T is used here for con- sistency with previous publications [23-271. As is evident from Table 1 and Fig. 2, the methyl substitution at the (E&4-position has little effect on the potential function; i.e. the torsional potentials of butadiene and (E)-PD are almost identical. The methyl substitution at the (Z)-4-position has a larger effect on the shape of the potential function. For instance, the barrier for the rotation from the s-trans (4 = 0’) to the gauche (4 = 136.5’) conformation and from the gauche to the s-trans conformation decreases by about 1.5 kcal mol-’ in going from butadiene to (2)PD. The change in the potential function is due to the introduction of stronger 4 dependent steric repulsions (see below). There are also differences in the shapes of the butadiene and MB potential functions. For instance, the barrier in going from the s-trans to the gauche conformation is decreased by about 0.9 kcalmolC’ by the methyl substitution at the 2-position. To a first approximation the s-trans and s-cis energies are raised relative to the remainder of the curve, which has a similar shape to that of butadiene in the region between 80’ and 140°. The results for MB obtained by us are in agreement with those from previous ab initio calculations [24,25,27]; i.e. the minor form is calculated to have a gauche conformation with a q5 angle of

TABLE 1

Energetics of rotation about the central C-C bond for monomethylbutadiene”*b

4 (deg.) Butadiene (E)-PD (2)PD MB

E AE E AE E AE E AE

0.0 (trans) 20.0 40.0 60.0 80.0

100.0 120.0

gauche” 140.0 160.0 180.0 (cis)

- 154.86458 0.00 - 193.88815 0.00 - 193.88550 0.00 - 193.88617 - 154.86334 0.78 - 193.88689 0.79 - 193.88447 0.61 - 193.88489 - 154.86003 2.85 - 193.88352 2.90 - 193.88180 2.32 - 193.88166 - 154.85625 5.22 - 193.87970 5.30 - 193.87889 4.14 - 193.87854 - 154.85474 6.17 - 193.87820 6.24 - 193.87765 4.92 - 193.87765 - 154.85614 5.30 - 193.87962 5.35 - 193.87853 4.37 - 193.87926 - 154.85852 3.80 - 193.88204 3.83 - 193.88006 3.41 - 193.88148

- 154.85993 2.91 - 193.88346 2.94 - 193.88058 3.08 - 193.88251 - 154.85988 2.94 - 193.88342 2.97 - 193.88055 3.10 - 193.88251 - 154.85953 3.17 - 193.88303 3.21 - 193.87945 3.79 - 193.88175 - 154.85895 3.53 - 193.88241 3.60 - 193.87840 4.45 - 193.88096

0.00 0.80

2.83 4.78 5.34 4.34 2.94

2.29 2.29 2.77 3.26

“Except where otherwise noted, the results are from HF/6-31G calculations with complete geometry optimization. bTotal energy (E) in atomic units and the relative energy (AE) in kilocalories per mole. “The 4 values are 144.8O, 144.3O, 136.5’ and 140.3’ for butadiene, (E)-PD, (2)PD and MB, respectively.

354

0 30 60 90 120 LSO 180

&an4 4 (cis)

Fig. 2. The HF/6-31G AE curves for monomethylbutadienes and butadiene. (--- -) Butadiene; (-) (E)-PD; (. . . .) (Z)-PD; (-. - .) MB.

about 140’. This is inconsistent with the conclusion from UV spectroscopic studies of butadiene, MB and DMB [3] which suggested that the MB second stable conformer has a s-cis structure.

The HF/4-21G and HF/6-31G* energies for MB are listed in Table 2, and the potential functions from different calculations are compared in Fig. 3. The experimentally refined potential function (ERP) [24] derived by using ab initio results and experimental data on torsional frequencies is also plotted. As is evident from Fig. 3, while the HF/4-21G calculations give a barrier which is about 0.5 kcal mol-’ smaller, the HF/6-31G and HF/6-31G* potentials are rather similar except in the region between the s-cis and gauche conformations where larger deviations (about 0.3 kcal mol-‘) were found. The s-trans-gauche barrier from ERP is about 0.5 kcal mol-’ larger than those from the HF/6-31G* and HF/6-31G calculations. This is probably due to the fact that the low quality ab initio data were used in the refine- ment; i.e. the calculations were performed at only four different torsional angles in the determination of potential function with the use of a small basis set [(7s3p/4s2p)].

The HF/6-31G total and relative energies for nine different dimethylbutadienes ((E, E)-HD, (E, Z)-HD, (2, Z)-HD, 4-MPD, (IQ-SMPD, (2)-3- MPD, (E)-2-MPD, (Z)-2-MPD and DMB) at various 4 angles are given in Table 3; the results for DMB from single point calculations with use of the geometry optimized at the s-trans conformation are also compared. The

355

6-

T s-

‘ij a 2 4-

A 3-

4 2-

l-

01’ ’ I I I I I 0 30 60 90 120 150 180

(t=s) # (cis)

Fig. 3. Comparison of the AE curves for MB. (----) 4-21G; (p) 6-31G; (* . .) ERP; (-.-.) 6-31G*.

TABLE 2

HF/4-21G and HF/6-31G* energies for MB”

4 (deg.) HF/4-21G HF/6-31G*

E AE E AE

0.0 (trans) - 193.55347 0.00

20.0 - 193.55227 0.75 30.0 - 193.55088 1.63 60.0 - 193.54654 4.35 75.0 - 193.54587 4.77 80.0 - 193.54595 4.72 90.0 - 193.54658 4.32

100.0 - 193.54755 3.71 120.0 - 193.54957 2.45

- 193.95723 0.00 - 193.95598 0.78 - 193.95453 1.69 - 193.94971 4.72 - 193.94888 5.29

- 193.94963 4.77 - 193.95066 4.12 - 193.95273 2.82

gaucheb - 193.55032 1.98 - 193.95345 2.37 150.0 - 193.54997 2.20 - 193.95305 2.62 180.0 (cis) - 193.54848 3.13 - 193.95149 3.60

“See Table 1, footnote b. Complete geometry optimization. bThe 4 values are 138.20 and 137.0“ from HF/4-21G and HF/631G* calculations, respectively.

356

TABLE 3

Energetics of rotation about the central C-C bond for dimethylbutadiene”

4 (deg.) (E,E)-HD (E, Z)-HD (2, Z)-HD 4-MPD

E AE E AE E AE E AE

0.0 (trans) 20.0 30.0 40.0 60.0 80.0

100.0 120.0 gaucheb 140.0 160.0 180.0

- 232.91137 0.00 - 232.90887 0.00 - 232.90604

- 232.90862 1.72 - 232.90662 1.41 - 232.90454

- 232.90301 5.25 - 232.90223 4.17 - 232.90153 - 232.90159 6.14 - 232.90102 4.93 - 232.90052 - 232.90302 5.24 - 232.90190 4.37 - 232.90113 - 232.90540 3.74 - 232.90343 3.42 - 232.90204 - 232.90672 2.92 - 232.90391 3.12 - 232.90204 - 232.90670 2.93 - 232.90384 3.15 - 232.90022 - 232.90618 3.26 - 232.90260 3.93 - 232.89465 - 232.90549 3.69 - 232.90145 4.66 - 232.88841

0.00 - 232.90817 - 232.90717

0.94

0.00 0.63

- 232.90459 2.25 2.83 - 232.90176 4.02 3.46 - 232.90047 4.83 3.08 - 232.90124 4.35 2.51 - 232.90267 3.45 2.51 - 232.90310 3.18 3.65 - 232.90302 3.23 7.14 - 232.90170 4.06

11.06 - 232.90040 4.87

4~ (deg.) (E)-&MPD (Z)-3-MPD (E)d-MPD (2)2-MPD

E AE E AE E AE E AE

0.0 (tra ms) - 232.90594 0.00 - 232.90515 20.0 - 232.90469 0.78 - 232.90417 40.0 - 232.90128 2.93 - 232.90190 60.0 - 232.89802 4.97 - 232.89994 80.0 - 232.89722 5.47 - 232.89937

100.0 - 232.89899 4.36 - 232.90042 120.0 - 232.90130 2.91 - 232.90164 gauche’ - 232.90218 2.36 - 232.90185 140.0 - 232.90152 160.0 - 232.90104 3.08 - 232.89970 180.0 - 232.89999 3.74 - 232.89826

0.00 - 232.90936 0.00 - 232.96068 1.53 0.61 - 232.90808 0.80 - 232.90017 1.84 2.04 - 232.90492 2.79 - 232.89918 2.47 3.27 - 232.90190 4.68 - 232.89958 2.21 3.63 - 232.90105 5.21 - 232.90029 1.77 2.97 - 232.90267 4.20 - 232.90154 0.99 2.21 - 23290496 2.76 - 232.90288 0.15 2.07 - 232.90601 2.10 - 232.90311 0.00 2.28 - 232.90601 2.10 - 232.90287 0.15 3.42 - 232.90522 2.60 - 232.90109 1.27 4.33 - 232.90440 3.11 - 232.89960 2.21

potential functions (AE) for (E, E)-HD, (E, Z)-HD, (2, Z)-HD and 4-MPD are plotted in Fig. 4 and those for (E)-8MPD, (2)8MPD, (E)-2-MPD and (Z)-2-MPD are plotted in Fig. 5. As is evident from Fig. 4, the potential function for (E, E)-HD is almost identical to those of butadiene and (E)-PD (see Fig. 2) and the potential functions for (E, Z)-HD and 4-MPD are very close to each other and to the (Z)-PD potential (see Fig. 2). This is in agreement with the previous observation that methyl substitution at the (E)-4- or (E)-l’-position has little effect on the potential function. However, as we will see later, methyl substitution at the (E)-4[(E)-l’]-position has sizable effects on the potential function when molecules become more

357

TABLE 3 (continued)

4 (deg.) DMB DMB”

E AE E AE

0.0 (trans) - 232.90547 0.60 - 232.90547 20.0 - 232.90447 0.62 50.0 - 232.90126 2.64 - 232.96081 70.0 - 232.90033 3.20 - 232.89945 80.0 - 232.90042 3.17 - 232.89934 90.0 - 232.90084 2.90 - 232.89969

110.0 - 232.96209 2.12 - 232.90125 gauched - 232.90311 1.48 130.0 - 232.90237 150.0 - 232.90198 2.19 - 232.90134 180.0 - 232.89850 4.37 - 232.89796

0.00

2.92

3.78 3.85 3.63 2.65

1.95 2.59 4.71

“See Table 1, footnotes a and b. bThe 4 values are 143.1’, 135.4’, 120.0” and 133.7’ for (E,E)-HD, (E,Z)-HD, (Z.-Z)-HD and 4-MPD, respectively. ‘The 4 values are 137.8’, 129.3”, 140.0° and 130.3’ for (E)-&MPD, (Z)-3-MPD, (E)-2-MPD and (Z)-2-MPD, respectively. dThe 4 value is 131.3’. “The geometrical parameters were fixed at the values of the trans conformation (see Appendix).

0 0 30 60 90 120 150 160

&a=) 4 (eta)

Fig. 4. The HF/6-31G AE curves for (E, E)-HD, (E, Z)-HD, (Z, Z)-HD and 4-MPD. (-.-.) (E, E)- HD; (p) (E, Z)-HD; (. . .) (Z, Z)-HD; (-- - -) 4-MPD.

1

0 0 30 80 90 120 150 180

b-4 4

(4

Fig. 5. The HF/6-31G AE curves for (E)-3-MPD, (2)3-MPD, (E)-P-MPD and (2)2-MPD. (-.-.) (E)-&MPD; (, . . .) (2)&MPD; (-) (E)-2-MPD; (----) (Z)-2-MPD.

crowded. The two (Z)-positioned methyl groups in (2, Z)-HD interact with each other very strongly around the s-cis conformation which leads to a large gauche( +)-gauche( -) barrier (about 8.5 kcalmol-‘) at $ = 0’. This repulsive interaction, which particularly destabilizes the gauche to s-cis region, also seems to be responsible for the relatively small gauche-s-trans barrier (about 1 vs. 3.3 kcal mol-l in butadiene) and for the decrease (about 25O) of the $I angle for the gauche conformer in going from butadiene (about 145O) to (2, Z)-HD (about 120’). The relatively small s-trans-gauche barrier (about 3.5 kcal mol-‘) in (2, Z)-HD is due to the C,H, . . . Hi and C: H, * . . H, interactions which increase the energy at the s-trans conformation; this was already noted in (2)PD.

As can be seen from Figs. 2 and 5, the potential functions for (E)-8MPD and (E)-2-MPD are close to that for MB as expected. The potential function of (2)8MPD is rather similar to the curve of (Z,Z)-HD in the region between 4 = 0” and 4 about 90°, and both molecules have a barrier of about 3.5 kcal mol-’ for the rotation from the s-trans to the gauche conformation. As we will see later, the similarity in the shapes of potential functions can be attributed to similar steric interactions in (Z)-8MPD and (Z,Z)-HD around the s-trans conformation. As is evident from Fig. 5, the most stable conformation for (Z)-2-MPD is no longer s-trans, in agreement with the conclusion of Werstiuk and Timmins [14] from PE spectroscopic studies and molecular mechanics and semi-empirical calculations; i.e. the ab initio energy at the gauche (4 = 130.3O) conformation is about 1.5 kcalmol-’

359

TABLE 4

HF/4-21G and HF/6-31G* energies for DMB”

d (deg.) HF/4-21G HF/6-31G*

E AE E BE

0.0 (trans) - 232.50636 0.00 - 232.99252 0.00 30.0 - 232.50442 1.22 - 232.99041 1.32 50.0 - 232.50263 2.34 - 232.98835 2.61 70.0 - 232.50224 2.59 - 232.98757 3.10 80.0 - 232.50253 2.40 - 232.98772 3.01 90.0 - 232.50301 2.10 - 232.98816 2.74

110.0 - 232.50409 1.42 - 232.98938 1.97 gaucheb - 232.50472 1.03 - 232.99017 1.47 150.0 - 232.50331 1.91 - 232.98876 2.36 180.0 (cis) - 232.49979 4.12 - 232.98506 4.68

“See Table 1, footnote b. Complete geometry optimization. b The 4 values are 127.4” and 129.0” from HF/4-21G and HF/6-31G* calculations, respectively.

lower than that at the s-trans conformation. It has been suggested that the existence of a global energy minimum at the gauche rather than the s-trans conformation for (Z)-2-MPD is a result of the strong steric repulsion between C,H3 and C:Hi groups around the s-trans conformation [2,14,17], and this suggestion seems to be supported by our analysis of the potential function (see below). As can be seen from Fig. 5, there is a second stable conformer at the s-trans conformation for (Z)-2-MPD, with an energy of 1.5 kcal mol-’ relative to the gauche form and a rotational barrier of about 1 kcal mol-’ from the s-trans to gauche conformation.

The HF/4-21G and HF/6-31G* energies of DMB are listed in Table 4, and the potential functions from different calculations are compared in Fig. 6. As can be seen from Fig. 6, the HF/6-31G potential function is closer to the HF/6-31G* potential function than that derived from the HF/4-21G calculations or from the HF/6-31G rigid rotation calculations. For instance, while the HF/421G s-trans-gauche barrier (about 2.6 kcal mol-l) is about 0.5 kcalmol-’ smaller than that from the HF/6-31G* calculations, the barrier (about 3.9 kcal mol-‘) from the HF/6-31G rigid rotation calculations is about 0.8 kcalmol-’ too large. In contrast, the HF/6-31G barrier determined with geometry optimization is only about 0.1 kcal mol-’ higher than that from the HF/6-31G* calculations. In agreement with previous ab initio calculations [25,27], the minor form of DMB is predicted to have a torsional angle 4 of about 130’ with a gauche to s-trans barrier of about 1.7 kcal mol-‘. The ab initio gauche-s-trans barrier is considerably smaller than the activation barrier (3.4 kcal mol-‘) for gauche to s-trans conversion estimated by Squillacote et al. [3] from a kinetic study.

360

8

0 30 60 90 120 150 180 (trans) (cis)

0

Fig. 6. Comparison of the AE curves for DMB. (-- --) 4-21G; (. . .) 6-31G with use of the fixed geometry of the s-trans conformation; (-.-.) 6-31G; (-) 6-31G*.

The HF/6-31G energies for six trimethyl- and tetramethyl-butadienes including 2,4-DMPD, (Z, Z)-8MHD, (2)2,3-DMPD, (E,E)-3,4-DMHD, (E, Z)-3,4-DMHD and (Z, Z)-3,4-DMHD are listed in Table 5, and the potential functions for the trimethylbutadienes (i.e. 2,4-DMPD, (2, Z)-&MHD and (Z)-2,3-DMPD) are plotted in Fig. 7. As is evident from Fig. 7, all the three trimethylbutadienes have a global potential minimum at the gauche

7

1

0 0 30 60 90 120 150 180

(t-4 *

(d

Fig. 7. The HF/6-31G AE curves for trimethylbutadienes. (-. - .) 2,4-DMPD; (-) (Z, .Z)-3- MHD; (. . .) (Z)-2,3-DMPD.

361

TABLE 5

Energetics of rotation about the central C-C bond for tri- and tetra-methylbutadienes”

4 (deg.) 2,4-DMPD’ (Z, Z)-3-MHD’ (Z)-2,3-DMPD”

E AE E AE E AE

0.0 (trans) - 271.92201 2.23 - 271.91857 3.14 - 271.91605 4.06 20.0 - 271.92174 2.40 - 271.91919 2.75 - 271.91674 3.63 40.0 - 271.92120 2.74 - 271.92000 2.25 - 271.91806 2.80 60.0 - 271.92217 1.91 - 271.92127 1.45 - 271.92050 1.27 80.0 - 271.92305 1.58 - 271.92205 0.96 - 271.92189 0.40

100.0 - 271.92420 0.86 - 271.92296 0.39 - 271.92243 0.05 gaucheb - 271.92557 0.00 - 271.92358 0.00 - 271.92252 0.00 120.0 - 271.92541 0.10 - 271.92248 0.02 140.0 - 271.92521 0.21 - 271.92092 1.67 - 271.92112 0.88 160.0 - 271.92312 1.54 - 271.91419 5.89 - 271.91722 3.32 180.0 (cis) - 271.92130 2.68 - 271.90638 10.79 - 271.91381 5.47

9 0%) (E, E)-3,4-DMHD (E, Z)-3,4-DMHD” (Z,Z)-3,4-DMHD

E AE E AE E BE

0.0 (trans) - 310.94143 20.0 - 310.94109 40.0 - 310.93958 60.0 - 310.93886 80.0 - 310.93938

100.0 - 310.94038 gaucheb - 310.94167 120.0 - 310.94153 140.0 - 310.94090 160.0 - 310.93701 180.0 (cis) - 310.93350

0.15 - 310.93320 0.36 - 310.93531 1.31 - 310.93743 1.76 - 310.93969 1.43 - 310.94127 0.81 0.09 - 310.94184 0.08 - 310.94175 0.48 - 310.93991 2.92 - 310.93492 5.12 - 310.93029

5.42 4.10 2.77 1.35 0.36

0.00

0.06

1.21 4.34 7.25

- 310.92426 12.25 - 310.92967 8.85 - 310.93582 4.99 - 310.94108 1.69 - 310.94341 0.23 - 310.94369 0.05 - 310.94377 0.00 - 310.94283 0.59 - 310.93871 3.17 - 310.92943 9.00 - 310.91649 17.12

“See Table 1, footnotes a and b. bThe 4 values are 128.0’, 116.7”, 115.4’, 126.4’=‘, 103.6O and 94.3’ for 2,4-DMPD, (.Z, Z)-3-MHD, (Z)-2,3-DMPD, (E, E)-3,4-DMHD, (E, Z)-3-4-DMHD and (Z, Z)-3,4-DMHD, respectively. ‘Certain geometrical parameters were fixed (see text).

conformation with a 4 angle between 115’ and 13OO. For 2,4-DMPD there is a second stable conformer at the s-trans conformation, and for (Z,Z)-3- MHD and (Z)-2,3-DMPD the gauche form is the only stable conformation. Although the general shapes of the potential functions for 2,4-DMPD and (Z)-2-MPD (see Fig. 5) are similar, there are some quantitative differences. For instance, the energy difference between the s-trans and gauche conformations increases by 0.7 kcal mol-’ in going from (Z)-2-MPD to 2,4-DMPD and the energy difference between the s-cis and gauche conformations increases by about 0.5 kcal mol-‘. The change of the potential function is

362

likely to be due to the introduction of some I$ dependent steric interactions as a result of the methyl substitution at the (E)-Cposition (see below).

2,4DMPD has been studied by different experimental methods including UV [2], ‘HNMR [18] and ion (He+ and Hi) impact [16] spectroscopies. Forbes et al. [2] have examined the UV spectra for a number of dienes and found that there is a hypsochromic shift of A,, in going from 4-MPD to 2,4-DMPD rather than the bathochromic shift as predicted by Woodward’s rules [l]. They interpreted such deviation from Woodward’s rules in terms of the steric interactions between C,H, and C:HG groups around the s-trans conformation. Moore et al. [16] have investigated the singlet-triplet transitions for butadiene and some of its methyl derivatives (MB, (E)-PD, DMB, (E, II)-HD, 4.MPD, 2,4-DMPD and 2,5-dimethylhexa-2,4-diene (2,5-DMHD)) from ion (He+ and H,’ ) impact spectroscopy. While the N + T, and N + T, transitions were found to be very insensitive to the methyl substitutions for almost all the dienes, a significant reduction in the N -+ T,-N + T, splitting in going from butadiene to 2,4-DMPD was observed and attributed to a non-planar conformation of 2,4-DMPD [16]. Cunliffe and Harris [18] studied the proton magnetic resonance spectra of 2,4-DMPD in a number of solution conditions and (in a CF,Cl, solution) over a range of temperatures. Based on the results for the 4J coupling constants, they suggested that the molecule exists predominantly in a single conformation with a 4 angle of 130 f 15’. This is inconsistent with the results of molecular mechanics calculations [19] which predicted that non-planar s-cis and s-trans forms are both present with an energy difference of only about 0.3 kcal mol-‘. As is evident from Table 5 and Fig. 7, the ab initio results are very different from those of the molecular mechanics calculations; i.e. the energy for the s-trans conformation was calculated to be about 2 kcal mol-’ higher than that of the gauche conformation. Furthermore, the trans conformation is expected to be unstable, since the s-trans-gauche barrier is only about 0.5 kcal mol-‘. Thus, in contrast to the molecular mechanics calculations, the ab initio results agree with the NMR analysis in that only one conformer should be populated. Both the molecular mechanics and ab initio calculations lead to a I#J angle of 128’ for the gauche conformation, in very good agreement with the NMR experiments (130’ + 15’) [18].

(2, 2).SMHD and (2).2,3-DMPD also have the global potential minimum at the gauche conformation from the ab initio calculations. But, the s-trans conformation is a local potential maximum for these two trimethylbutadienes rather than a local minimum as in 2,4-DMPD. The ab initio result for (Z,Z)-&MHD is significantly different from those for (2).2,3- dimethylhexa-2,4-diene and (2).2,4-dimethylhexa-2,4-diene determined from molecular mechanics and semi-empirical calculations [15] with use of the AM1 program [31]. For instance, while the ab initio potential function for (2, 2).&MHD has a minimum at 4 about 117’, the AM1 calculations predicted

363

30 60 20 120 150 180 (cis)

* Fig. 8. The HF/6-31G AE curves for tetramethylbutadienes. (E, Z)-3,4-DMHD; (p) (2, A’)-3,4-DMHD.

(-. -.) (E, E)-3,4-DMHD; (----)

that the (Z)-2,3-dimethylhexa-2,4diene has a twisted s-trans most stable conformation with a 4 angle of 45’ to 75’. Although the potential functions of (Z)-2,3-dimethylhexa-2,4-diene and (Z)-2,4-dimethylhexa-2,4-diene are not expected to be the same as that of (2, Z)-3-MHD due to the existence of an additional methyl group at the terminal E position (i.e. the C:Hj group for (2)-2,3-dimethylhexa-2,4-diene and the C,H, group for (Z)-2,4-dimethylhexa-2,4-diene), the differences seem too large to be accounted for by the interactions introduced by the terminal E methyl groups.

The potential functions for the tetramethylbutadienes (i.e. (E, E)-3,4- DMHD, (E, Z)-3,4-DMHD and (Z, Z)-3,4-DMHD) are plotted in Fig. 8. As is evident from Fig. 8, the potential function for (E,E)-3,4-DMHD has a similar shape to that of DMB (see Fig. 6). There are significant quantitative differences due to the additional methyl groups at the terminal E positions. For instance, while the s-trans conformation of DMB is about 1.5 kcal mol-’ more stable than the gauche conformation, the energies for the s-trans and gauche conformations of (E,E)-3,4-DMHD are almost the same with an energy difference of only 0.15 kcal mol-l. The differences are likely to be due to the fact that the existence of the two terminal E methyl groups in (E, E)-3,4-DMHD makes the molecule less flexible, which leads to higher interaction energies around the s-trans and s-cis conformations; the change in x conjugation as a result of the terminal E methyl substitutions may also affect the potential function (see below). The prediction from the ab initio calculations for the existence of a s-trans stable conformation for (E, E)-3,4-

364

DMHD is in agreement with the results [20] from a gas electron diffraction study where it was found that the diene has*a 4 angle of 26.63’. As was pointed out by Traetteberg [20], the 4 angle (26.63O) from the gas electron diffraction study may have no physical significance, as shrinkage effects [32] would influence the experimental data in much the same way as a torsional angle of the same magnitude. The ab initio results also agree with the PE spectroscopic study [12] which led to a 4 angle of 0 f 30’ for the stable conformation of (E,E)-3,4-DMHD. There is, however, no experimental evidence for a stable gauche conformation, even though it seems to have a similar energy to the s-trans conformation from the ab initio calculations.

As can be seen from Fig. 8, the potential functions for (E, Z)- and (Z,Z)- 3,4-DMHD are very different from that of (E,E)-3,4-DMHD, and there is only a single minimum for (E, Z)- and (Z, Z)-3,4-DMHD with the q5 angles at 104O and 94’, respectively. The values of the 4 angle for the (E,Z)- and (Z,Z)-3,4-DMHD stable conformations are about loo and 19” smaller, respectively, than those determined from the gas electron diffraction studies (i.e. 114.27’ for (E,Z)-3,4-DMHD and 113.31’ for (Z,Z)-3,4-DMHD) 1201. However, it is not clear whether the experimental structures or the theoretical results are more accurate because of the model dependent nature of interpreting the electron diffraction experiments. The structures of (E, Z)- and (Z, Z)-3,4-DMHD have also been studied by PE spectroscopy [12] which led to a 4 angle of about 80 f 15’ or about 110 f 15’ for (E, 2)-3,4- DMHD and a 4 angle of about 85-1O5o for (Z, Z)-3,4-DMHD. The ab initio stable conformations are within the error limits of these PE structures.

The existence of the potential minimum at the “orthogonal” conformation for (E, Z)- and (Z, Z)-3,4-DMHD is due to the strong steric repulsions at the s-trans and s-cis conformations. There are C,H,. . . ClHj and C,H,- . . Hi interactions for (E, Z)-3,4-DMHD and C,H, * * * C:HL and C;H; . . * C,H, interactions for (Z, Z)-3,4-DMHD. All these interactions reach the maximum at the s-trans conformation. The repulsions at 4 = O” are significantly greater than the stabilization energy of conjugation which makes the trans form a potential maximum.

(E, E)-, (E, Z)- and (Z, Z)-3,4-DMHD have been the subject of UV (VUV) spectroscopic studies [6]. Vaida and co-workers [5,6] studied the 1 ‘Bi t 1 lA; transition for a number of methylated butadienes and found that while MB, (E)-PD, DMB, (E, E)-HD and (E,E)-3,4-DMHD have absorptions similar to that of 1,3-butadiene with intense transitions at A,,, = 214 to 230 nm (A,,, about 210nm for butadiene), both (E, Z)-3,4-DMHD and (Z,Z)-3,4-DMHD have ethylene like spectra with the first A,,, at 171 and 168 nm, respectively. It has been suggested that while the UV spectrum for

(E, E)-3,4-DMHD arises from a transition from the planar ground state to the excited state, as is the case for butadiene, the spectra for (E,Z)- and

365

(Z,Z)-3,4-DMHD are due to transitions from non-planar ground states to highly twisted ‘B: excited states [4]. This is in good agreement with the ab initio results. There are observed absorptions at 209.1, 202.2, 198.3 and 194.9nm in the (E, E)-3,4-DMHD spectrum that are not assigned to the 1 ‘Bi t 1 ‘A; transition. They have been interpreted as the Rydberg transitions [4]. It would be interesting to examine if these additional features are related to the transitions for the gauche conformation of the ground state (E, E)-3,4-DMHD.

Although (E, 2) and (Z, Z)-3,4-DMHD both have an “orthogonal” conformation with a 4 angle close to 90°, they appear to have different properties in certain chemical reactions (e.g. the Diels-Alder reactions) in which the dienes are required to reach the s-cis conformation. Because of these differences, the experimental structures [20] for the two molecules have been called into question [17]. As we can see from Table 5, the barriers for the (Z,Z) isomer at the s-trans and s-cis conformations are considerably higher (about 10 kcal mall’) than those for the (E, 2) isomer. The large difference in the barrier near the cis conformation would be responsible for the differences in the reactivities for (E, Z)- and (Z, Z)-3,4-DMHD, because the very large barrier for the (2, 2) isomer makes it much more difficult to reach the s-cis conformation for the reactions than the (X,2) isomer.

Steric interactions

The stable conformations of 1,Bdienes and the shapes of potential functions are determined by the two basic interactions, conjugation and steric repulsion. While conjugation tends to stabilize the planar conformations (s-cis or s-trans), steric repulsion is normally strongest in the planar conformations and weakest in the orthogonal conformation (c$ about 90’). Although the shape of potential function for a methylated diene is determined by both conjugation and steric interaction, the change of potential function in going from one diene to another as a result of methyl substitutions is likely to arise mainly from the increase of steric interactions because methyl substitutions, especially at the terminal positions, seem to have relatively small effects on conjugation. This suggestion is supported by the present analysis of the potential function; i.e. dienes with similar steric interactions around the s-trans or s-cis conformation often have very similar potential functions in the corresponding region (see above). If we assume that the effects of methyl substitutions on conjugation are negligible, we can introduce an energy function, defined as

aE(4) = P(B, 4) - E(A, 4)l - VW4 4,) - HA, 4dl

for studying the change of the steric repulsion contribution as a result of methyl substitutions. Here A and B identify the dienes without and with

366

TABLE 6

HF/631G SE values for monomethylbutadiene”

4 (deg.) (E)-PD (Z)-PD MBb

0.0 (trans) - 0.07 1.25 0.96

20.0 -0.06 1.12 0.98 40.0 - 0.02 0.72 0.94

60.0 0.01 0.17 0.52 80.0 0.00 0.00 0.13

100.0 - 0.02 0.32 0.00 120.0 - 0.03 0.86 0.10 140.0 - 0.04 1.41 0.31 160.0 - 0.03 1.87 0.56 180.0 (cis) 0.00 2.17 0.69

“See Table 1, footnote a. In kilocalories per mole. See text for the definition of 6E. Except where otherwise noted, q$, = 80.0’ (see text). b$O = 100°.

methyl substitutions, respectively, and $,, is defined as

f& = 4(6E = min)

We choose A as butadiene, so that 6E(4) gives the value of the energy difference between a methylated butadiene and butadiene as a function of 4 angle. For the dienes studied in this work, $0 has a value near 90” (see below) at which the steric interactions are expected to be at a minimum. While the steric interactions within each ethylenic unit are only weakly dependent on the 4 angle (i.e. the distances between the atoms within each ethylenic unit remain nearly constant), the interactions between the atoms in the two different ethylenic units are expected to have a strong 4 depend- ence and make a major contribution to &Y(4). For convenience, we define US($) between 4 = 0’ and & as a&($) and that between $,-, and $J = 160° as 6E,(+). As we see later, the 6E,($) and N&(4) curves normally have different steric interactions and are independent of each other.

The 6E values at various angles from the HF/6-31G calculations for the monomethylbutadienes are listed in Table 6 and the 6E curves for (Z)-PD and MB are plotted in Fig. 9. For (E)- and (Z)-PD &, = 80’ and for MB $,, = 100’. As is evident from Table 6, the 6E values of (E)-PD are negligible at all r#~ angles, because the C,H, group does not interact significantly with the atoms in the other ethylenic unit. In contrast, the methyl substitution at the (Z)-4-position (i.e. in going from butadiene to (2)PD) gives rise to sizable 6E values (0-2.17kcalmolll) with two maxima of 1.25 and 2.17 kcalmoll’ at the s-trans and s-cis conformations, respectively. The d&(4) curve (see above for definition) for (2)PD apparently arises from the

367

30 60 90 120 150 180 (cis)

*

Fig. 9. The HF/6-31G 6E curves for (2)PD and MB. (. . . .) (Z)-PD; (-.-.) MB.

C,H, . . . H: interaction which replaces the original H, * * . Hi interaction in butadiene, while the &Y,(4) curve mainly reflects the steric repulsion between C,H, and Hi.

Comparison of the 6E curves in Fig. 9 shows that while the U,(4) curves for MB and (2)PD are significantly different, the L%,(4) curves for them are rather similar with a deviation of only 0.3 kcal mall’. The similarity in the 6E,($) curves is due to the similar interactions around the trans conformation for these two molecules (i.e. the C,H, * * * Hi for (Z)-PD and the C:H; . * *Hz for MB). The small difference in the MB and (Z)-PD SE,(c$) curves seems due to different orientations of the methyl groups for the C,H,- . + H: and C:Hi . - * H, interactions (see Appendix). Because methyl groups tend to have an orientation with one of the C-H bonds eclipsed to a C=C double bond, the H: atom in (Z)-PD mainly interacts with the hydrogen of the C,H, group with the eclipsed C-H bond. In contrast, the H, in MB interacts with the two hydrogens of the C:Hi group with the C’-H’ bonds staggered with respect to the C’-C single bond. As is expected from the interactions in MB, the 6E,(+) curve of MB remains almost constant in the region between 4 = 0” and 30° and is shifted toward larger angles by about 20-30’ from the (Z)-PD curve in the region between 4 = 30’ and 100°. It should be pointed out that methyl groups in methylated butadienes will move away from the preferred orientation (i.e. with one of the C-H bonds eclipsed to a C=C double bond) if strong steric interactions are present. For instance, the methyl group in the s-cis conformation of (Z)-PD has an orientation with two of the C-H bonds staggered with respect to the C=C

6

0 0 30 60 90 120 150 180

(tr=--) Cd e

Fig. 10. The HF/6-31G SE curves for (E, Z)-HD, (2, Z)-HD, 4-MPD and DMB. (-) (E, Z)-HD; (....) (Z,Z)-HD; (----) 4-MPD; (-.-.) DMB.

double bond to avoid the strong repulsion which would otherwise exist between the hydrogen of the C,H, group with the C-H bond eclipsed to the C=C double bond and the H: atom. For MB, the methyl substitution at the 2-position of butadiene replaces the original Hi. * - H, interaction by a C;H; . . . H, repulsion which leads to an increase in the 6E value of about 0.7 kcal mol-’ at the s-cis conformation.

The HF/6-31G 6E values for all the dimethylbutadienes are listed in Table 7. For (E)-&MPD and (E)-2-MPD for which the $J dependent steric interactions are similar to that in MB, & = 100°, and for the rest of the dienes in Tables 7 and 8 (see below), &, = 80’. The 6E values of (E, E)-HD are negligible at all 4 angles as expected. In Fig. 10, the 6E curves for (E,Z)-HD, (Z,Z)-HD, 4-MPD and DMB are plotted. As is evident from Fig. 10, the 6E curves for (E, Z)-HD and 4-MPD are close to each other and to that of (2)PD because of similar 4 dependent steric interactions involved in these systems.

There is an approximate additivity for the 6E, functions of (Z)-PD, (E, Z)- HD, 4-MPD and (Z,Z)-HD; i.e. the 6Et values for (2, Z)-HD which has the C,H, - . . H: and C:H; * * . H, repulsions in the region between 4 = 0” and 4 about & are about twice as large as that found for (Z)-PD, (E,Z)-HD or 4-MPD for which there is only one such interaction. The 6E value for (2, Z)-HD at the cis conformation is more than 10 kcal mall’ due to the very strong steric interaction between the two methyl groups. The DMB 6E, curve has a different shape compared with those for the other methylated butadienes in Figs. 9 and 10, because it has repulsions between the 2- and

369

TABLE 7

HF/6-31G SE values for dimethylbutadiene”

4 (deg.) (E, E)-HD (E, .Z)-HD (Z, Z)-HD I-MPD

0.0 (trans) 20.0 30.0 40.0 60.0 80.0

100.0 120.0 140.0 160.0 180.0

0.03 1.24 2.71

0.06

0.00 0.19 0.32 0.00 0.00 0.00

-0.03 0.31 0.49 -0.03 0.86 1.42 0.02 1.45 3.42 0.12 2.00 6.68 0.19 2.37 10.24

0.96 1.96

1.34 1.19

0.74 0.14 0.00 0.39 0.99 1.63 2.23 2.68

4 (deg.) (E)-3-MPDb (Z)-3-MPD (E)-2-MPDb (Z)-2-MPD

0.0 (trans) 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0 180.0

0.94

0.94

1.02 0.69 0.24 0.00 0.05

0.85 1.15

2.54 1.10 5.93

2.37 1.12 5.46 1.73 1.04 4.02 0.59 0.56 1.39 0.00 0.14 0.00 0.21 0.00 0.09 0.95 0.06 0.75 1.88 0.26 1.61 2.79 0.53 2.50 3.34 0.68 3.08

9 (deg.) DMB

0.0 (trans) 3.00 20.0 2.84 50.0 1.53 70.0 0.24 80.0 0.00 90.0 0.00 110.0 0.58 150.0 2.24 180.0 3.84

“See Table 1, footnote a. In kilocalories per mole. See text for the definition of 6E. Except where otherwise noted, C& = 80.0’ (see text). bl#J” = 100°.

3-positioned methyl groups in the region between C$ about 80’ and 4 = 180° that do not exist in the other systems.

The 6E curves for (E)-3-MPD, (2)&MPD, (E)-2-MPD and (Z)-2-MPD are plotted in Fig. 11. The shapes of the 6E curves for (E)-3-MPD and (E)-2-

370

TABLE 8

HF/6-31G SE values for tri- and tetra-methylbutadienes”

4~ (deg.) 2,4-DMPD (Z, Z)-3.MHD (2).2,3-DMPD

0.0 (trans) 6.82 8.35 9.83 20.0 6.21 7.18 8.62 40.0 4.48 4.61 5.72 60.0 1.28 1.44 1.82 80.0 0.00 0.00 0.00

100.0 0.15 0.30 0.52 120.0 0.89 1.99 140.0 1.86 3.94 3.71 160.0 2.96 7.93 5.92 180.0 (cis) 3.74 12.47 7.71

+ (deg.) (E, E)-3,4-DMHD (E, Z)-3,4-DMHD (Z, Z)-3,4-DMHD

0.0 (trans) 4.89 11.23 18.19 20.0 4.32 9.13 14.01 40.0 3.20 5.73 8.08 60.0 1.28 1.94 2.41 80.0 0.00 0.00 0.06

100.0 0.25 0.69 120.0 1.02 2.07 2.73 140.0 2.28 4.08 6.17 160.0 4.49 6.98 11.77 180.0 (cis) 6.33 9.53 19.53

“See Table 1, footnote a. In kilocalories per mole. See text for the definition of 6E. Except where otherwise noted, c#+, = 80.0” (see text).

MPD are generally close to the MB curve except that the 6E, curve for (E)-3.MPD is shifted to larger values in the region between 4 about 130’ and 4 = 180’ by about O-O.5 kcalmol-’ (see below). Because similar steric interactions are involved in (2).3-MPD and (Z,Z)-HD around the s-trans conformation, the shapes of the &I& curves for them (see Figs. 10 and 11) are similar; the small difference in the curves can be attributed to different methyl orientations for the C,H, * * . HI interaction in (2).&MPD and the C;H; . . . H, interaction in (Z,Z)-HD (see above). The 6E, curves for (2).3. MPD and (2).ZMPD are close to each other; because they represent similar interactions (the C,H, . * . HL and C,H, . . . Hi repulsions for (2).&MPD and the C,H,.. *HI and C:Hi*. . H, repulsions for (2).2.MPD) around the s-cis conformation. As can be seen from Fig. 11, the 6E value of (2).2.MPD at the s-trans conformation is about 6 kcalmol-’ which cancels almost all the conjugation energy at this conformation (e.g. for butadiene the energy difference between s-trans conformation and that at 4 = 80° is about

371

0 30 60 90 120 150 180

had 0 (cis)

Fig. 11. The HF/6-31G 6E curves for (E)-8MPD, (Z)-3-MPD, (E)d-MPD and (2)2-MPD. (-.-.) (E)-3-MPD; (. . .) (Z)-8MPD; (-) (E)-2-MPD; (----) (Z)-2-MPD.

6 kcal mol-‘, see Fig. 2) and, as a result, the gauche form becomes the most stable conformation (see above).

The 6E values for the tri- and tetra-methylbutadienes are listed in Table 8, and the 6E curves for the trimethylbutadienes are plotted in Fig. 12. As is evident from Figs. 11 and 12, although the 6E curves for (2)2-MPD and 2,4-DMPD have similar shapes, there are some quantitative

0 30 60 90 120 150 180

(trans) * (cis)

Fig. 12. The HF/6-31G 6E curves for trimethylbutadienes. (-.-.) 2,4-DMPD; (-) (Z, Z)-3- MHD; (. . .) (Z)-2,3-DMPD.

312

differences due to the existence of the (E)-4 positioned methyl group in 2,4-DMPD. For instance, the 6E increases by 0.9 and 0.7 kcal mall’ at the s-trans and s-cis conformations, respectively, in going from (Z)-2-MPD to 2,4-DMPD. This seems to be related to the fact that the steric interaction between the C,H, and C,H, groups in 2,4-DMPD (see Fig. 1) becomes 4 dependent due to the influence of the C, H, - * . C:Hg interaction. This suggestion is supported by a study of the 2,4-DMPD geometrical parameters [33] which shows that the C,-C,-C, angle in 2,4-DMPD increases from 112.3’ to 114.8O during the rotation from (b = 0” to 4 = 80’. By contrast, the C,-C,-C, angle in 4-MPD, which does not have the C:Hj group, remains almost constant (i.e. about 114.1-114.8’) when $I changes from 0” to 80”. The shift of the (E)-SMPD 6E, curve from that of MB (see above) in the region between 4 about 130’ and q5 = 180’ may have similar origins.

It is interesting to see that the 6E, curve of (Z)-2,3-DMPD is shifted to larger values from that of (Z,Z)-&MHD even though the two molecules appear to have similar steric interactions around the s-trans conformation (i.e. the C:HL - * * C,H, and C,H,* * * H: interactions for (2)2,3-DMPD and the C:H; *a-C,H,andC:HA * . . H, interactions for (Z, Z)-8MHD). The relatively large dE, values for (Z)-2,3-DMPD are probably due to the fact that the existence of the C,H, group in (2)2,3-DMPD has prevented the Ci-C,-C, angle from opening up to reduce the steric repulsion between the C:Hi and C,H, groups. This suggestion is supported by the structural results [33] which show that the Ci-C,-C, angle in (2, Z)-&MHD is 4.3O larger than that in (Z)-2,3-DMPD at 4 = O”, where the steric repulsion between the C:Hi and C,H, groups is most significant.

The 6E curves for three tetramethylbutadienes ((E, E)-, (E, Z)- and (2, Z)- 3,4-DMHD)) are plotted in Fig. 13. As is evident from Fig. 13, the 6E curve for (E, E)-3,4-DMHD is significantly different from that for DMB due to the existence of the terminal E methyl groups. For instance, the 6E values at 4 = 0’ and 180” for (E, E)-3,4-DMHD are about 2 kcal mall’ larger than the corresponding ones for DMB. There are C,H, . * * C:Hi and C,H, . . . H, interactions for (E, Z)-3,4-DMHD around the s-trans conformation which lead a SE value of ca. 11 kcalmol-’ at 4 = 0’. At s-cis conformation, the 6E value for (E, Z)-3,4-DMHD is about 9.5kcalmoll’, mainly arising from the

C,H, * *. C:HL and C,H, * 1. H: interactions. Comparison of the 6E curves for (E, Z)-3,4-DMHD and (Z)-2,3-DMPD shows that the methyl substitution at the (E)-l-position of (Z)-2,3-DMPD leads to an increase in the 6E of about 1-2 kcal mall’ at the s-trans and s-cis conformations. For (Z,Z)-3,4-DMHD, there are C,H, .** C:H& and C:Hi . - - C,H, repulsions around the s-trans conformation which lead to a 6E value of about 18 kcalmol-’ at 4 = 0”. At the s-cis conformation, the 6E value for (Z,Z)-3,4-DMHD is about 20 kcal mol-l, mainly arising from very strong C,H, . . * CLH; and

C,H, . - * C!:H; interactions.

373

0 30 60 90 120 150 180

(tr-) * (cis)

Fig. 13. The HF/6-31G 6E curves for tetramethylbutadienes. (-.-.) (E, E)-3,4-DMHD; (----) (E, Z)-3,4-DMHD; (-) (Z, Z)-3,4-DMHD.

The central C-C bond length

In Fig. 14, the central C-C single bond length as a function of 4 angle from the HF/6-31G calculations is plotted for the monomethylbutadienes along with the results for butadiene [23]. There is an increase in the C-C

151

x 3 150

P rl 149

148 [ I I I I I 1 0 30 60 QO 120 160 180

* Fig. 14. The HF/6-31G curves for the central C-C single bond length of monomethylbutadienes and butadiene. (----) Butadiene; (-) (E)-PD; (. . .) (Z)-PD; (-.-.) MB.

374

151

2

k 150 0)

P 0” 149

d

4 5

146

:, 147

Fig. 15. The HF/6-31G curves for the central C-C single bond length of (E, E)-HD, (E, Z)-HD, (Z,Z)-HD and 4-MPD. (-.-.) (E, E)-HD; (-) (E, Z)-HD; (. . .) (2, Z)-HD; (----) 4-MPD.

bond distance of the order of 0.02-0.03 A in going from $J = 0’ to 4 about 80’ for the three dienes due to loss of conjugation at about 80’. As is evident from Fig. 14, while the curves of the C-C bond distance for (E)-PD and (2)PD are very similar to each other and to that for butadiene, the curve for MB is shifted to larger values by about 0.005-0.015 A. Such an increase in the C-C single bond distance as a result of methyl substitution has also been found for the terminal C-C single bonds of some methylated butadienes (see Appendix) and for non-conjugated alkenes [34]; e.g. the C--C, ((Z-C,) bond length increases by ca. 0.009 A (0.006 A) in going from (E)-PD ((2)PD) to 4-MPD. It would be interesting to examine these effects of methyl substitutions experimentally. Unfortunately, the errors in experimental measurements are usually too large for such purposes. The change of the C-C bond length indicates that the x conjugation in the methylated butadienes with 2- and 3-positioned methyl groups may be different from that in butadiene which can lead to some errors in the estimate of steric interaction with use of the 6E function. However, the effect is expected to be small. As can be seen from Fig. 14, the effect of steric repulsion on the C-C bond length is reflected in the curve; there is a small deviation (about 0.005 A) of the (Z)-PD curve from that of butadiene in the region between 4 = 150’ and 180°, apparently due to the C,H, * * . H; interaction.

The HF/6-31G central C-C single bond lengths as functions of $J angle for the dimethylbutadienes are plotted in Figs. 15 and 16. As is evident from Fig. 15, the curve for (E, E)-HD is the same as that for butadiene, whilst those for (E, Z)-HD and 4-MPD are similar to each other and to that for

375

3 148 3

CL 147

146 ’ I I I I I I

0 30 60 90 120 150 180

a

Fig. 16. The HF/6-31G curves for the central C-C single bond length of (E)-3-MPD, (2)-3- MPD, (E)-2-MPD, (2)2-MPD and DMB. (-.-.) (E)-BMPD; (. . .) (Z)-8MPD; (-) (E)-P-MPD; (----) (2)2-MPD; (. - -) DMB.

(2)PD. It is interesting to see that while the C,H, * . . H: repulsion leads to a decrease in the C-C bond length in the region between 4 = 150’ and 180’ (see above), the C,H, * . . CiHi repulsion in (2, Z)-HD has little effect on the C-C bond length. As can be seen from Fig. 16, while the curves for (E)-2- MPD and (2)8MPD are close to each other (except for the region between 6 = 150’ and 180°, for the reason discussed above) and have shapes similar to that of MB, the curve for (E)-8MPD is shifted to larger values by about 0.002 A. It seems that the dienes with both 3- and (E)4-positioned (or 2- and (E)-l-positioned) methyl groups tend to have relatively longer central C-C bond length. Although the curve for (Z)-2-MPD has the same shape as that of (Z)-&MPD in the region between 4 = 60’ and 180°, it is shifted to larger values by about 0.005 A in the region between 4 = 0’ and 60’ as a result of the C,H, - . . C:Hi repulsion.

The curve of DMB is shifted to larger values by about 0.015-0.03A from that of butadiene. The C-C bond distance (1.501 A) for DMB at qS = 80’ is about 0.015 A longer than the corresponding bond length (1.487 A) in butadiene at the same conformation, but it is still about 0.03 A shorter than the C(sp,)-C(sp,) bond lengths in ethane (1.53OA) and propane (1.531 A) at the same level of calculation [33]. The shift is not likely to be due to a change in conjugation, because conjugation is lost at q!~ about 80’ for both butadiene and DMB. While some of the shift near the s-trans and s-cis conformations in going from butadiene to DMB may be ascribed to the steric repulsions involving the C:H; and C,H, groups (see above), the overall

376

up-shift for the curve cannot be attributed to such interactions and may arise from perturbations of the electronic structure by the methyl group(s), leading to a reduction of the C&C!, 0 bond order. Further Mulliken population analyses [33] at the HF/6-31G* level have shown that the overlap population (0.737e) between Ci and C3 atoms for DMB at 4 = 80’ is 0.027 smaller than that (0.764e) for butadiene at the same conformation, though it is still larger than the populations for the C-C bond in ethane, propane and t-butane, which are about 0.650 e-O.700 e.

The PE spectra for a number of planar methylated butadienes have been studied by Sustmann and Schubert [35] and by Heilbronner and co-workers [36,37]. Although the methyl substitutions at the terminal ((E) or (2)) positions were found to have little effect on the 7t+, x_ splitting, significant effects have been observed for methyl substitution at the 2- or 3-position. For instance, while butadiene, (E)-PD, (Z)-PD, (E, E)-HD, (E, Z)-HD, (Z,Z)- HD, 4-MPD and 2,5-dimethylhexa-2,4-diene all have a x, , n_ splitting of about 2.42.5eV, the splitting decreases along the series butadiene (2.43 eV) --) MB (2.05 eV) + DMB (1.58 eV). Sustmann and Schubert interpreted the effect of methyl substitutions at the 2- and 3-position by assuming that the orbital sequence in the diene systems is II, u, ‘II rather than 71, x, r_r as widely accepted, and Heilbronner and co-workers [12,36,37] suggested that the effect is a result of a “long range through space interaction” between the double bond x orbital and non-bonded pseudo-x orbital of the methyl group [38,39]. It is interesting to see that the effect of the methyl substitutions at the 2- and 3-position on the ‘II, , R_ splitting in the

Fig. 17. The HF/6-31G curves for the central C-C single bond length of trimethylbutadienes. (-.-.) 2,4-DMPD; (-) (Z, Z)-3-MHD; c.. .) (Z)-2,3-DMPD.

377

3 k 150 I

if “0 149

6

‘g E 148

t: 147

146 0 30 80 90 120 150 180

Fig. 18. The HF/6-31G curves for the central C-C single bond length of tetramethylbutadienes. (-. - .) (E, E)-3,4-DMHD; (- -- -) (E, Z)-3,4-DMHD; (-) (Z, Z)-3,4-DMHD.

PE spectra seems to correlate with the changes in the C-C bond length; i.e. the splitting decreases by about 0.4-0.5 eV after the methyl substitution at the 2- or 3-position while the C-C bond length increases by about 0.005 0.015 A.

The HF/6-31G central C-C single bond lengths as functions of 4 angle for the tri- and tetra-methylbutadienes are plotted in Figs. 17 and 18, respectively. While the curves for 2,4-DMPD and (Z, Z)-3-MHD are similar to each other and to that for (2)2-MPD, the curve for (Z)-2,3-DMPD has a shape similar to that for DMB with some deviations around the s-trans and s-cis conformations. As is evident from Figs. 16 and 18, the curves for (E, E)-3,4- DMHD and (E, Z)-3,4-DMHD are shifted to larger values from that of DMB due to the existence of the (E) positioned methyl group(s) (see the dis- cussion for (E)-8MPD given above). The curve of (Z,Z)-DMHD deviates considerably from that of DMB in the region between 4 = 0’ and 60’ probably due to the C,H, * * . CiHi and the C!,H,. * . C!:Hb interactions around the s-trans conformation.

CONCLUSION

The potential energy function (AE) about the central C-C single bond was determined for 18 different methylated butadienes using the HF/6-31G method with geometry optimization. It was found that the methyl substitutions at the 2(3)- and terminal-Z positions of butadiene can have significant effects on the shape of the potential function. Although the

378

terminal E methyl group in the mono- and di-methylbutadienes does not affect the shape of the potential function, sizable effects of the @)-methyl group were observed in the tri- and tetra-methylbutadienes. While the most stable conformation is s-trans for most (11) of the dienes from the ab initio calculations, the major form for all the dienes with both (2)4- and 2-positioned (or (2)-l- and 3-positioned) methyl groups (i.e. (2)2-MPD, 2,4- DMPD, (Z, Z)-8MHD, (Z)-2,3-DMPD, (E, Z)-DMHD and (2, QDMHD) was predicted to have a gauche or “orthogonal” structure with a 4 angle between 90° and 130’. For (2 )-2-MPD the ab initio calculations confirmed the earlier results from PE spectroscopic studies and molecular mechanics and semi-empirical calculations that the most stable conformation is no longer s-trans. The ab initio results for 2,4-DMPD agree with NMR analysis in that only one conformer should be populated; i.e. the energy for the s-trans conformation was calculated to be about 2 kcalmolll higher than that of the gauche conformation. In contrast, previous molecular mechanics calculations suggested that non-planar s-cis and s-trans forms were both present with an energy difference of only about 0.3 kcal mall’. Furthermore, the ab initio structure (4 = 128’) for 2,4-DMPD is also very close to that from the NMR experiments (130 + 15’). For (E, E)-DMHD the two stable conformations (s-trans and gauche) were calculated to have similar energies. The prediction for the existence of a s-trans stable conformation for (E, E)-DMHD is in agreement with gas electron diffraction and PE spectroscopic studies, but there is no experimental evidence for a stable gauche conformation of (E, E)-DMHD. For (E, Z)-DMHD and (2, Z)-DMHD the ab initio conformations are similar to those determined experimentally, and it was found that the barriers for the (2, 2) isomer at the s-trans and s-cis conformations are considerably higher (about 10 kcal mall’) than those for the (E, 2) isomer. It was suggested that the large difference in the barrier near the cis conformation would be responsible for the differences in certain chemical reactions (e.g. the Die&Alder reactions) for the two molecules, Furthermore, the ab initio gauche-s-trans barrier for DMB is considerably smaller than the activation barrier (3.4 kcal malll) for gauche to s-trans conversion estimated from a kinetic study.

An energy function (6E) defined as the energy difference between a methylated butadiene and butadiene was proposed. Such energy function gives mainly the potential energy contribution from the steric interactions involving methyl group(s) and can be used to estimate the increase of the steric interactions as a result of methyl substitutions. It was found that at the s-trans conformation each C,H, . . . C:HL (or C,H,. * . C:Hi) repulsion leads to an increases in the 6E value by about 6-9 kcal mol-’ which cancels all the conjugation energy at this conformation. And as a result, the gauche or iio&hogonal” form becomes the most stable conformation for the dienes with the C,H;.-CiHi (or C,H,e. . Cl Hi) interaction(s). Furthermore, each

379

C,H, . . * Hi repulsion or a similar interaction (e.g. the C:Hi.. - H,, C,H,.. * H; or C:H; * . . H, interaction) leads to an increase in the 6E value of ca. l-2 kcal mall’ at the s-trans conformation. At the s-cis conformation, the C!,H,.* . C;Hj, C,H, . ..C.H;, C,H, - . . HL and C: HA. . . H, interactions increase the 6E value by about 10-15, 4-6, 2-3.5 and 0.7-1.5 kcal mall’, respectively.

The central C-C single bond length as a function of the torsional angle was examined for each of the methylated butadienes. It was found that the C-C bond distance is shifted to larger values at all the angles by about 0.005-0.015 A after a methyl substitution at the 2- or 3-position. In contrast, much smaller effects on the central C-C bond were observed for the methyl substitution at the terminal positions. It was suggested that the overall up-shift for the C-C bond length may arise from perturbations of the electronic structure by the methyl group(s) which lead to a reduction in the Cl-C, CT bond order.

ACKNOWLEDGMENTS

We are grateful to Cray Research for providing the CRAY X-MP time used for these calculations. We thank Drs. Eric Wimmer, John Mertz and John Carpenter for their assistance in making this calculation possible. We are also indebted to Professor V. Vaida for making results available prior to publication. The work reported here was supported in part by a grant from the National Science Foundation.

REFERENCES

5

6 7 8 9

10 11 12

R.B. Woodward, J. Am. Chem. Sot., 64 (1942) 72. W.F. Forbes, R. Shilton and A. Balasubramanian, J. Org. Chem., 29 (1964) 3527. M.E. Squillacote, T.C. Semple and P.W. Mui, J. Am. Chem. Sot., 107 (1985) 6842. W.R. Roth, H.-W. Lennartz, W.V.E. Doering, Jr., W.R. Dolbier and J.C. Schmidhauser, J. Am. Chem. Sot., 110 (1988) 1883. D.G. Leopold, R.D. Pendley, J.L. Roebber, R. J. Hemley and V. Vaida, J. Chem. Phys., 81 (1984) 4218. V. Vaida, personal communication. U. Dinur and B. Honig. J. Am. Chem. Sot., 101 (1979) 4453. J.A. Pople and M. Gordon, J. Am. Chem. Sot., 89 (1967) 4253. L. Radom, W.A. Lathan, W.J. Hehre and J.A. Pople, J. Am. Chem. Sot., 93 (1971) 5339. M.D. Newton and W.N. Lipscomb, J. Am. Chem. Sot., 89 (1967) 4261. L. Libit and R. Hoffmann, J. Am. Chem. Sot., 96 (1974) 1370. E. Honegger, Z. Yang, E. Heilbronner, W.V.E. Doering and J.C. Schmidhauser, Helv. Chim. Acta, 67 (1984) 640.

13 P. Masclet, G. Mouvier and J.F. Bocquet, J. Chim. Phys., 78 (1981) 99. 14 N.H. Werstiuk and G. Timmins, Can. J. Chem., 66 (1988) 2954. 15 N.H. Werstiuk, K.B. Clark and W.J. Leigh, Can. J. Chem., 68 (1990) 2078. 16 J.H. Moore, Y. Sato and S.W. Staley, J. Chem. Phys., 69 (1978) 1092.

17 J.C. Schmidhaueer, Ph.D. thesis, Harvard University, Cambridge, MA, 1985. 18 A.V. Cunliffe and R.K. Harris, Org. Mag. Resonance, 6 (1974) 121. 19 N.L. Allinger and J.C. Tai, J. Am. Chem. Sot., 99 (1917) 4256. 20 M. Traetteberg, Acta Chem. Stand., 24 (1970) 2295. 21 W. von E. Doering and W.R. Dolbier, unpublished work. 22 W. Reeve and D.M. Reichel, J. Org. Chem., 37 (1972) 68. 23 H. Guo and M. Karplus, J. Chem. Phys., 94 (1991) 3679, and references cited therein. 24 Yu. N. Panchenko, V.I. Pupyshev and A.V. Abramenkov, J. Mol. Struct., 130 (1985) 355. 25 K. Kavana-Saebq S. Saebcl and J.E. Boggs, J. Mol Struct., 106 (1984) 259. 26 C.W. Bock, P. George and M. Trachtman, Theor. Chim. Acta, 64 (1984) 293. 27 C.W. Bock and Y.N. Panchenko, J. Mol. Struct., 187 (1989) 69. 28 M. Traetteberg, G. Paulen, S.J. Cyvin, Yu.N. Panchenko and V.I. Mochalov, J. Mol.

StNCt., 116 (1984) 141. 29 J.S. Binkley, R.A. Whiteside, K. Raghavachari, R. Seeger, D.J. DeFreea, H.B. Schlegel,

M.J. Frisch, E.M. Fluder and J.A. Pople, GAUSSIAN 82, Carnegie-Mellon University, Pittsburgh, PA, 1982.

30 B. Gelin and M. Karplus, Proc. Natl. Acad. Sci., USA, 72 (1975) 2002. 31 Dewar Research Group and J.J.P. Stewart, QCPE Bull., 6 (1986) 2. 32 Y. Morino, J. Nakamura and P.W. Moore, J. Chem. Phye., 36 (1962) 1050. 33 H. Guo and M. Karplus, unpublished work, 1990. 34 H. Guo and M. Karplua, J. Chem. Phys., 91(1989) 1719. 35 R. Sustmann and R. Schubert, Tetrahedron Lett., (1972) 2739. 36 M. Beez, G. Bieri, H. Bock and E. Heilbronner, Helv. Chim. Acta, 56 (1973) 1028. 37 G. Bieri, F. Burger, E. Heilbronner and J.P. Maier, Helv. Chim. Acta, 60 (1977) 2213. 38 R. Hoffmann and R.A. Olofson, J. Am. Chem. Sot., 88 (1966) 943. 39 R. Hoffmann, Ch. Levine and R.A. Moss, J. Am. Chem. Sot., 95 (1973) 629.

APPENDIX

In Table Al, the HF/6-31G optimized geometries for the stable conformations of monomethylbutadienes and DMB are listed along with the HF/6-31G* results for MB and DMB. The HF/6-31G geometries for the rest of the dimethylbutadienes are given in Tables A2 and A3 and those for the tri- and tetra-methylbutadienes are listed in Table A4.

TA

BL

E A

l

Opt

imiz

ed g

eom

etri

es f

or t

he

stab

le c

onfo

rmat

ion

s of

mon

omet

hyl

buta

dien

es

and

DM

B”

UW

’D

(Z)-PD

M

B

s-tr

an

s gauche

s-tr

an

s gauche

s-tr

am

gauche

DM

Bb

s-tr

am

3

gauche

AE

0.

0 2.9

4

0.0

3.0

8

O.O

(O.0

) 2.

29(2

.37)

d

0.0

- 144.3

0.

0 -

136.5

O

.O(O

.0)

- 140.3

(- 1

37.0

)

Die

m

part

r(

c;

=c;

,

Jc-

C,)

d

C,=

C,)

tic;

-H;)

ti

c;-H

:)

C&

-H;)

r(

C,H

,)

dC

,H,

) ti

c,-H

,)

w;q

qJ

L c

c;c,

c,

) L

(C

;C;H

;)

L(C

bC

;H,)

L(C

;C;H

,)

UC

&H

,)

W&

H,)

UC

&H

,)

r(se

c;c

;c,)

r(H

;C;C

;C,)

r(H

bC

;C;H

;)

7(H

eC

,C&

) dH

,C,C

,C;)

‘(H

,C,C

,H,)

dH

,C,C

,H,)

1.32

79

1.3

273

1.4

635

1.4

729

1.3

291

1.3

284

1.0

726

1.0

732

1.0

748

1.0

740

1.0

771

1.0

773

1.0

776

1.0

779

1.3

284

1.3

274

1.4

646

1.4

735

1.3

316

1.3

309

1.0

727

1.0

734

1.0

748

1.0

731

1.0

744

1.0

779

1.0

767

1.0

773

1.0

767

1.0

769

1.3

3O

q1.3

258)

1.3

290(1

.3235)

1.3

316(1

.3264)

1.3

286(1

.3232)

1.4

750(1

.4773)

1.4

815(1

.4845)

1.4

896(1

.4913)

1.4

936Q

.4947)

1.3

277(1

.3228)

1.3

261(1

.3210)

1.3

316(1

.3264)

1.3

m1.3

232)

1.0

731(1

.0753)

1.0

737(1

.0759)

1.0

731(1

.0753)

1.0

74q1.0

762)

1.0

74q1.0

760)

1.0

729(1

.0749)

1.0

71q1.0

732)

1.0

727(1

.0747)

1.0

783

1.0

772

124.5

9

125.9

2

124.1

7

125.4

9

121.7

7

121.4

7

121.8

6

122.0

3

119.3

0

118.6

8

123.6

5

126.7

4

127.2

2

128.2

1

121.7

7

121.3

2

121.8

7

122.2

4

118.7

2

118.3

7

117.3

7

117.0

6

1.0

764(1

.0777)

1.0

779(1

.0796)

1.0

728(1

.0750)

1.0

732(1

.0754)

1.0

730(1

.0749)

1.0

737(1

.0756)

119.8

q119.6

5)

122.4

q122.1

6)

126.1

8(1

26.1

8)

125.6

6(1

25.4

8)

121.9

5(1

21.9

0)

121.6

2(1

21.5

5)

121.7

q121.6

8)

121.8

3(1

21.7

0)

118.9

2

119.5

2

180.0

0.0

180.0

0.0

180.0

119.0

4

118.9

1

178.7

5

- 2.1

3

176.9

8

117.8

1

117.3

5

180.0

-

179.3

6

0.0

-

0.7

4

180.0

176.9

2

180.0

179.8

8

121.1

4(1

20.9

9)

121.4

9(1

21.3

6)

122.8

4(1

22.7

6)

121.9

6(1

21.8

6)

118.8

2(1

18.6

0)

118.9

2(1

18.8

4)

179.9

2(1

80.0

) 178.8

8(1

78.9

4)

- 0.0

2(0

.0)

- 2.0

3( -

1.8

6)

1.7

6

177.1

1

179.8

6(1

80.0

)

~ O

.l(O

.0)

0.0

180.0

179.6

2(1

79.7

6)

- 1.1

9( -

0.8

3)

0.0

-

1.9

0

O.O

(O.0

) O

.O(O

.0)

1.0

731(1

.0753)

1.0

740(1

.0762)

1.0

71q1.0

732)

1.0

727(1

.0747)

121.9

0(1

21.7

7)

121.4

6(1

21.3

2)

121.9

0(1

21.7

7)

121.4

6(1

21.3

2)

121.1

4(1

21.0

9)

121.6

2(1

21.5

6)

123.0

9(1

23.0

1)

121.7

q121.6

8)

121.1

4(1

21.0

9)

121.6

2(1

21.5

6)

123.0

9(1

23.0

1)

121.7

8(1

21x8)

18O

.ql8

0.0

) O

.O(O

.0)

180.0

(180.0

)

O.O

(O.0

)

179.0

3(1

79.0

0)

- 1.5

6( -

1.6

9)

179.0

3(1

79.0

0)

- 1.5

6( -

1.6

9)

1.4

8(1

.47)

- 131.3

( - 129.4

)

TA

BL

E A

l (c

onti

nu

ed)

(E>

PD

s-tr

am

gau

che

(OP

D

s-tr

ans

gau

che

MB

s-tr

am

gau

che

DM

Bb

s-tr

am

gau

che

(E)-

Met

hyl

on

C,

tic,

-C,)

r(

C,H

l)’

dC,-

H2)

r(

C,H

3)

UC

,C,C

,)

L(C

,C,H

l)’

UC

,C,H

2)

W,C

,H3)

~

W,C

,C&

) T

(C&

,C,H

~)~

dC,C

,C,H

2)

G&

,C,H

3)

(2)~

Met

hyl

on C

,

dC,-

c,)

r(C

,Hl)

r(C

,-H

2)

dC,H

3)

UC

,C,C

,)

L(C

,C,H

1)C

UC

,C,H

2)

UC

,C,H

3)

r(C

,C,C

,C;)

r(

C,C

,C,H

l)

dC,C

,C,H

2)

G,C

,C,H

3)

1.49

96

1.03

33

1.03

62

1.03

62

125.

13

111.

55

111.

09

111.

99

180.

0 0.

00

120.

52

- 12

0.52

1.50

06

1.03

34

1.08

60

1.08

62

124.

95

111.

30

111.

13

111.

01

179.

03

- 0.

02

lM).

l%

120.

41

1.50

18

1.50

20

1.03

07

1.09

13

1.09

61

1.08

70

1.03

61

1.03

49

129.

04

127.

94

113.

18

112.

07

110.

52

111.

24

110.

52

110.

39

0.0

- 1.

44

0.0

- 17

.75

120.

93

102.

93

120.

93

- 13

8.56

C2-

Met

hyl

r(w

G)

r(C

;-H

’l)

r(c:

-H’2

) r(

c;-H

’3)

L(c

:c;c

;)

L (C

;C; H

’l)

L (C

;C; H

’2)

L (C

;C:H

’3)

r(C

:C;C

;H:)

t(

C:C

;C;H

;)

r(C

;C;C

:H’l)

r(

C;C

;C:H

’2)

r(C

;C;C

;H’3

)

1.50

82(1

.508

3)

1.08

17(1

.082

9)

1.08

51(1

.086

1)

1.08

51(1

.086

1)

121.

73(1

21.8

0)

110.

98(1

10.9

3)

111.

05(1

11.0

3)

111.

10(1

11.0

1)

O.O

(O.0

) lS

O.O

(l80

.0)

O.O

(O.0

) 12

0.39

C20

.32)

12

0.10

( -

120.

31)

-

1.51

03(1

.510

1)

1.08

20(1

.083

2)

1.08

54(1

.086

6)

1.08

65(1

.087

4)

122.

27(1

22.3

9)

111.

49(1

11.5

1)

110.

94(1

10.8

6)

110.

75(1

10.7

2)

- 1.

85( -

1.

87)

177.

24C

77.3

4)

- 0.

22(0

.03)

12

0.58

(120

.92)

12

0.54

( -

120.

40)

-

1.51

18(1

.511

4)

1.08

16(1

.082

8)

1.08

47(1

.085

6)

1.08

47(1

.085

6)

120.

08(1

20.0

2)

110.

64(1

10.6

2)

111.

30(1

11.3

0)

111.

30(1

11.3

0)

O.O

(O.0

) 18

0.0(

180.

0)

O.O

(O.0

) 12

0.03

(120

.08)

.1

20.0

5( -

120.

08)

-

1.51

20(1

.512

2)

1.08

20(1

.083

2)

1.08

55(1

.086

6)

1.08

51(1

.086

3)

121.

66(1

21.7

0)

110.

88(1

10.9

7)

110.

95(1

10.9

1)

111.

53(1

11.3

8)

- 1.

34( -

1.

48)

177.

89(1

77.8

2)

5.92

(6.3

8)

126.

21(1

26.8

6)

114.

18( -

11

3.79

)

“See

Fig

. 1

for

the

mol

ecu

les.

B

ond

len

gth

s in

an

gstr

oms

and

angl

es a

nd

tors

ion

al

angl

es (

4) i

n d

egre

es.

Exc

ept

wh

ere

oth

erw

ise

not

ed,

the

valu

es a

re f

rom

HF

/6-3

1G c

alcu

lati

ons.

T

he

nu

mbe

rs i

n p

aren

thes

es a

re f

rom

HF

/6-3

1G*

calc

ula

tion

s.

Th

ere

is a

ph

ase

diff

eren

ce (

- 1)

fo

r $I

giv

en h

ere

and

that

giv

en i

n t

he

text

for

th

e ga

uch

e co

nfo

rmat

ion

. T

he

rela

tive

en

ergy

(A

E)

at t

he

tran

s co

nfo

rmat

ion

is

tak

en a

s th

e ze

ro.

b Wit

h C

, sy

mm

etry

. ‘C

-H

bon

d ec

lips

ing

C=

C d

oubl

e bo

nd.

TA

BL

E A

2

Opt

imiz

ed g

eom

etri

es f

or t

he

stab

le c

onfo

rmat

ion

s of

dim

eth

ylbu

tadi

enes

w

ith

tw

o te

rmin

al m

eth

yls”

(E, E

)-H

Db

s-tr

ans

gau

che

(E, Z

)-H

D

s-tr

ans

gau

che

(2,

Z)-

HD

b

s-tr

ans

gau

che

4-M

PD

s-tr

ans

gau

che

AE

4 Die

ne

part

r(

c; =

c;)

r(G

C,)

@

,=C

,)

G-H

: )

r(C

fHI)

r(

Ck

f-f:

)

r(C

,H,)

r(

C,-

H,

) r(

C,-

Hz

) U

XC

,)

L (C

SX

,)

L (C

;C;H

:)

L(C

;C;H

;)

L (

C;C

;H;)

L(C

,C,H

,)

WY

XZ

) L

(C,C

,H,)

r(

H:C

;C;C

,)

r(H

;C;C

;C,)

r(

H:C

;C;

H:)

r(

H:C

;C;H

;)

r(H

,C,C

,C;)

0.0

2.92

0.0

- 14

3.1

0.0

3.12

0.

0 -

135.

4 0.

0 0.

0 2.

51

0.0

3.18

-

120.

0 0.

0 -

133.

7

1.32

92

1.32

86

1.33

90

1.32

87

1.46

33

1.47

28

1.46

40

1.47

37

1.32

92

1.32

86

1.33

16

1.33

10

1.33

26

1.46

45

1.33

26

1.07

69

1.32

97

1.32

89

1.47

84

1.46

37

1.32

97

1.33

47

1.07

72

1.07

27

1.07

49

1.07

83

1.07

42

1.07

83

1.07

71

1.07

72

1.32

75

1.47

36

1.33

37

1.07

35

1.07

33

1.07

83

1.07

80

1.07

83

1.07

73

1.07

79

1.07

82

1.07

79

1.07

82

1.07

83

1.07

65

1.07

53

1.07

89

1.07

71

1.07

76

1.07

67

1.07

70

1.07

42

1.07

42

1.07

69

1.07

83

1.07

73

124.

46

125.

80

124.

46

125.

80

123.

55

126.

59

127.

44

128.

41

126.

65

126.

65

117.

29 .

127.

83

123.

67

127.

83

127.

70

117.

52

121.

75

117.

53

121.

90

118.

47

117.

52

127.

09

128.

72

121.

33

122.

24

118.

16

118.

96

119.

09

119.

28

118.

70

119.

90

119.

27

118.

74

118.

40

117.

41

117.

13

116.

95

117.

29

118.

96

119.

09

119.

28

118.

70

117.

65

117.

20

116.

95

180.

0 11

7.53

11

7.73

-

179.

16

179.

99

0.04

-

1.94

-

179.

95

- 17

9.16

117.

34

- 17

8.96

0.

02

0.0

- 2.

12

0.0

- 0.

45

0.0

180.

0 17

6.88

18

0.0

176.

99

180.

0 17

9.64

17

7.16

18

0.0

4H,W

,C;)

#L

C,C

, H

e)

dH,C

,C, I-

4)

7U-L

W,W

(E)-

Met

hyl

on

C;

q-c;

) r(

C:-

H’l)

r(

C:-

H’2

) r(

C;-

H’3

) L

(c:c

;c;)

L

(C;C

;H’l)

L

(C;C

:H’S

) L

(C;C

:H’3

) T

(c:c

;c;c

;)

r(C

;C;C

;H’l)

r(

C;C

;C;H

’2)

r(C

;C;C

:H’3

)

(E)-

Met

hyl

on C

, ti

c*-C

,) r(

C,H

l)

r(C

,H2)

ti

t--H

3)

L (C

&C

,)

L(C

,C,H

l)

L(C

,C,H

2)

L (C

A

H3)

c$

,C,C

;)

r(C

,C,C

,Hl)

GC

,C,H

2)

GC

,C,H

3)

0.0

180.

0 17

6.88

1.50

01

1.50

11

1.49

99

1.50

14

1.08

36

1.08

35

1.08

35

1.08

35

1.08

63

1.06

61

1.08

63

1.08

61

1.08

63

1.08

63

1.08

63

1.08

62

125.

14

124.

94

125.

22

124.

79

111.

51

111.

56

111.

54

111.

54

111.

16

111.

16

111.

14

111.

10

111.

16

111.

09

111.

14

111.

11

180.

0 17

8.76

18

0.0

- 17

9.21

0.

0 0.

06

0.0

- 0.

41

120.

49

120.

70

120.

51

120.

17

- 12

0.49

- -

120.

34

- 12

0.51

-

120.

88

- 2.

12

0.0

- 1.

89

0.0

- 1.

94

179.

90

176.

66

1.50

88

1.50

98

1.08

22

1.08

22

1.08

68

1.08

66

1.08

68

1.08

67

120.

77

120.

66

111.

89

112.

00

110.

85

110.

79

110.

84

110.

70

179.

94

179.

39

0.04

-

1.79

12

0.75

11

9.13

-

120.

67

_ 12

2.45

TA

BL

E A

2 (c

onti

nu

ed)

(E, E

)-H

Db

s-tr

ans

gau

che

(E, Z

)-H

D

s-tr

ans

gau

che

(2,

Z)-

HD

b

s-tr

ans

gau

che

4-M

PD

s-tr

ans

gau

che

(Z)-

Met

hyl

on

C,

tic,c

, 1 r(

C,H

l)’

r(C

,H2)

r(

C,H

3)

L (W

&J

L (C

,C,H

l)

L (C

,C,H

2)

L (C

,C,H

B)

+Y

xC;)

r(

C,C

,C,H

l)

GC

,C,H

2)

GW

H3)

-

1.50

20

1.50

22

1.50

19

1.50

14

1.50

82

1.50

82

1.08

09

1.08

14

1.08

05

1.08

99

1.07

93

1.07

95

1.08

63

1.08

71

1.08

63

1.08

68

1.08

65

1.08

72

1.08

63

1.08

50

1.08

63

1.08

56

1.08

66

1.08

59

127.

91

127.

88

128.

27

127.

28

125.

15

125.

01

113.

13

111.

99

113.

26

111.

90

113.

55

112.

43

110.

59

111.

36

110.

51

111.

19

110.

29

110.

87

110.

60

110.

32

110.

51

110.

36

110.

28

110.

10

0.0

- 1.

79

0.0

- 0.

82

- 0.

19

- 1.

71

0.0

- 17

.36

0.0

- 9.

54

0.99

-

13.5

1 12

0.88

10

3.43

12

0.94

11

1.36

12

2.07

10

7.52

12

0.87

-

138.

04

- 12

0.94

-

130.

14

- 12

0.10

-

134.

45

“See

foo

tnot

e a

to T

able

Al.

bSee

foo

tnot

e b

to T

able

Al.

“See

foo

tnot

e c

to T

able

Al.

TA

BL

E A

3

Opt

imiz

ed g

eom

etri

es

for

the

stab

le c

onfo

rmat

ion

s of

dim

eth

ylbu

tadi

enes

w

ith

on

e te

rmin

al

met

hyl

”

(E)-

BM

PD

(Z

)-8M

PD

(I

I)-2

-MP

D

(Z)-

2-M

PD

s-tr

ans

gau

che

s-tr

ans

gau

che

s-tr

ans

gau

che

s-tr

ans

gau

che

AE

4 Die

ne

part

r(

c; =

c;)

G-C

,)

r(C

,=C

,)

r(C

;-H

:)

r(C

;-H

I)

@G

-H:

) r&

H,)

r(

C,-

H,)

r&

H,

) L

(CG

C,)

L

(GG

C,)

L

(C;C

;H:)

L

(C;C

;H;)

L

(C;C

;H:)

L (C

,C,H

,)

L(C

,C,H

,)

L(C

,C,H

,)

r(H

$;C

;C,)

-

r(H

;C;C

;C,)

r(

H:C

;C;H

;)

~(H

,C,C

,C;)

r(

H,C

,C,C

;)

r(H

,C,C

, H

,)

r(H

,C,C

, H

z)

0.0

0.0

2.36

0.

0 2.

07

- 13

7.7

0.0

- 12

9.3

1.32

81

1.32

64

1.32

90

1.32

62

1.47

67

1.48

38

1.47

46

1.48

22

1.33

54

1.33

29

1.33

58

1.33

25

1.07

29

1.07

34

1.07

30

1.07

36

1.07

27

1.07

38

1.07

25

1.07

35

1.07

68

1.07

83

1.07

32

1.07

87

1.07

71

1.07

76

1.07

80

1.07

67

126.

69

126.

03

118.

29

120.

80

120.

98

121.

48

123.

02

121.

99

118.

32

118.

67

125.

84

126.

50

122.

96

124.

97

120.

96

121.

35

123.

07

122.

17

117.

66

118.

55

117.

18

117.

18

117.

14

117.

23

179.

05

179.

23

0.34

-

1.52

18

0.27

17

6.98

179.

99

- 17

8.51

0.

22

0.51

18

0.25

17

7.29

18

0.16

17

9.59

-

0.34

-

2.08

0.0

0.0

-

2.10

14

0.0

0.0

0.0

- 1.

53

- 13

0.0

1.33

13

1.32

94

1.33

29

1.32

92

1.47

45

1.48

09

1.47

87

1.48

24

1.32

90

1.32

76

1.33

29

1.33

00

1.07

31

1.07

38

1.07

30

1.07

41

1.07

40

1.07

30

1.07

38

1.07

26

1.07

73

1.07

88

1.07

67

1.07

82

1.07

76

1.07

72

1.07

61

1.07

70

120.

12

122.

71

126.

33

125.

59

121.

95

121.

63

121.

73

121.

85

118.

26

123.

17

132.

57

128.

25

121.

89

121.

58

121.

87

121.

93

115.

25

117.

07

119.

89

119.

01

118.

66

118.

89

180.

0 17

8.62

-

0.03

-

2.26

115.

29

- 17

9.55

0.

51

117.

43

- 17

9.14

-

0.19

- 17

9.65

-

179.

83

- 0.

03

- 1.

37

0.26

-

1.81

%

17

9.97

17

6.94

TA

BL

E A

3 (c

onti

nu

ed)

(E)-

BM

PD

s-tr

am3

gau

che

(Z)-

8MP

D

s-tr

ans

gau

che

(E>

2-M

PD

s-tr

ans

gau

che

b?

(Z)-

2-M

PD

s-tr

am

gau

che

(E)-

Met

hyl

on

C,

r(C

,C,

) r(

C,-

Hl)

” r(

C,H

2)

r(C

,H3)

L

(C&

C,)

L

(C,C

,Hl)

b

L (C

,C,H

2)

L (C

,C,H

3)

GC

,Cm

T

(C,C

,C,H

~)~

GC

,C,H

2)

t(C

,C,C

,H3)

(Z)-

Met

hyl

on

C,

r(C

,-C

, )

I(C

,H~

)~

r(C

z-H

2)

r(C

z-H

3)

L (C

*C,C

,)

L(C

,C,H

l)b

L (W

zH2)

L

(WH

3)

r(C

,C,C

,C;)

T

(C,C

,C,H

~)~

+W

,C,H

2)

S,C

,C,H

3)

C$M

eth

yl

r(C

TW

_

1.50

04

1.50

19

1.08

01

1.08

04

1.08

65

1.08

63

1.08

65

1.08

66

128.

99

128.

49

113.

50

113.

41

110.

51

110.

64

110.

45

110.

38

179.

68

178.

47

0.25

0.

15

121.

34

121.

40

120.

68

- .12

0.57

1.50

24

1.50

26

1.50

34

1.50

22

1.07

99

1.08

07

1.07

65

1.08

06

1.08

66

1.08

71

1.08

54

1.08

68

1.08

61

1.08

54

1.08

74

1.08

53

129.

11

128.

26

131.

92

128.

08

113.

83

112.

30

114.

26

112.

20

110.

36

111.

34

109.

70

111.

10

110.

36

110.

17

110.

30

110.

24

0.75

-

1.85

1.

08

- 1.

17

- 3.

62

- 14

.88

13.0

4 -

13.7

0 11

7.46

10

6.05

13

4.08

10

7.07

12

4.68

-

135.

60

‘108

.64

- 13

4.63

1.50

08

1.50

09

1.08

33

1.08

34

1.08

62

1.08

61

1.08

62

1.08

61

124.

60

124.

92

111.

58

111.

60

111.

07

111.

10

111.

11

111.

01

180.

0 17

9.63

0.

04

- 1.

08

120.

55

119.

57

120.

51

- 12

1.51

-

1.50

89

1.51

07

1.51

00

1.51

14

r(C

;-H

’l)b

1.0

817

1.0

820

1.0

820

1.0

822

r(C

:-H

’2)

1.0

852

1.0

856

1.0

845

1.0

855

r(C

IH’3

) 1.0

852

1.0

864

1.0

836

1.0

865

L (c

:c;c

;)

121.4

1

122.0

3

120.0

5

121.9

2

L(C

;C;H

’l)b

110.9

4

111.5

5

110.3

7

111.5

6

L (C

;C; H

’2)

111.1

2

110.8

7

111.3

1

110.8

2

L(C

;C:H

’3)

111.1

2

110.7

5

111.5

8

110.7

6

r(C

;C;C

;H;)

179.9

7

177.0

6

- 179.9

5

177.6

2

7(C

;C;C

:H’1

)b

0.0

0

- 0.6

4

- 3.4

9

- 0.5

7

r(C

;C;C

;H’2

) 120.2

2

120.2

0

116.0

5

120.2

7

s(C

;C;C

:H’3

) -

120.2

3

_ 120.9

9

- 123.4

8

- .121.0

0

C,-

Met

hyl

r(C

,C,)

r(

C,H

Qb

r(G

H2)

r(

C,H

3)

L (C

&C

,)

L (C

,C, H

l)b

L (C

,C,H

2)

L (C

,C,H

3)

7(C

,C,C

,C,)

7(C

,C,C

,C,)

T(C

,C,C

,H~)~

GC

,C,H

2)

7(C

,C,C

,H3)

-

1.5

086

1.5

115

1.0

789

1.0

794

1.0

856

1.0

860

1.0

849

1.0

863

124.6

6

125.2

4

112.6

1

113.1

0

110.6

5

110.5

8

110.6

6

110.3

0

0.2

7

- 2.1

4

1.5

118

1.5

134

1.0

820

1.0

824

1.0

854

1.0

856

1.0

853

1.0

868

120.0

2

121.0

8

111.0

3

111.5

4

111.1

6

111.0

1

111.2

5

110.8

9

- 4.4

7

- 5.6

6

116.2

5

115.6

0

124.9

7

126.2

3

- 17

9.27

176.8

3

- 0.7

0

0.0

8

119.4

8

120.8

4

- 120.9

4

- 120.2

4

“See

foo

tnot

e a

to T

able

Al.

bSee

foo

tnot

e c

to T

able

Al.

iz

0 T

AB

LE

A4

Opt

imiz

ed g

eom

etri

es f

or t

he

stab

le c

onfo

rmat

ion

s of

tri

met

hyl

- an

d te

tram

eth

yl-b

uta

dien

es”

2,4-

DM

PD

(2

, .Z

)-3-

MH

D

(Z)-

2,3-

DM

PD

(E

, E)-

3,4-

DM

HD

b (E

, Z)-

3,4-

DM

HD

(Z

, Z)-

3,4-

DM

HD

b

s-tr

ans

gau

che

gau

che

gau

che

s-tr

ans

gau

che

gau

che

gau

che

AE

0.

0 -

2.23

4

0.0

- 12

8.0

Die

m p

art

$2;

=c;

)

r(w

A)

r(C

,=C

,)

rK3-

U

r(W

-C

) r(

W-L

)

r(W

-0

rV3-

L)

~w

;G)

L G

GC

,)

L(C

;C;H

:)

L(C

;C;H

;)

L (C

&H

,)

L (C

&H

,)

L(C

,C,H

,)

r(H

:C;C

;C,)

T

(H$;

C;C

,)

r(H

,C,C

,CH

) r(

H,C

,C,C

;)

r(H

,C,C

,C,)

r(

H,C

,C,C

,)

1.33

36

1.32

92

1.47

96

1.48

24

1.33

61

1.33

27

1.07

3Od

1.07

3od

1.07

38

1.07

38

1.07

67

1.07

88

117.

94

123.

44

133.

41

128.

68

121.

89

121.

61

121.

92

121.

89

- 11

5.20

17

9.37

0.

61

0.54

117.

43

- 17

9.03

-

0.05

- 2.

22

- 11

6.7

- 11

5.4

1.33

15

1.48

58

1.32

88

1.07

7od

1.32

78

1.49

65

1.33

12

1.07

7od

1.07

32

1.07

89

1.07

70

1.07

80

1.07

81

1.07

80

124.

77

127.

92

117.

55

117.

52

117.

60

- 17

9.20

- 17

8.33

121.

84

123.

89

121.

68

121.

77

117.

29

- 17

8.99

0.

58

177.

00

0.0

0.0

1.33

66

1.33

25

1.33

08

1.49

99

1.49

97

1.50

22

1.33

66

1.33

25

1.33

04

1.07

31

1.07

66

1.07

76

1.07

31

1.07

66

120.

67

120.

25

120.

67

120.

25

118.

38

118.

38

0.04

0.04

- 0.

15

- 12

6.4

117.

14

117.

14

- 1.

47

- 1.

47

- 10

3.6

- 94

.3

120.

11

123.

69

117.

15

117.

64

1.05

17

9.73

1.32

96

1.50

04

1.32

96

1.07

80

123.

57

123.

57

117.

87

117.

87

- 17

8.25

- 17

8.25

(E)-

Met

hyl

on

C,

r(c,

-c,

) 1.

5133

r(

C,H

l)

1.08

18

r(C

,H2)

1.

0869

r(

GH

3)

1.08

66

L(C

,C,C

,)

119.

19

L(C

,C,H

l)

112.

11

L (C

,C,H

2)

110.

71

L(C

,C,H

3)

110.

82

GC

,C,C

I)

- 17

8.48

r(

C,C

,C,H

l)

1.49

G

C,C

,H2)

12

2.19

~

(C,C

,C,H

3)

- 11

9.36

(Z)-

Met

hyl

on

C,

r(w

a 1.

5096

r(

C,H

l)

1.07

44

r(C

,H2)

1.

0861

r(

C,H

3)

1.08

75

~(C

,C,C

,)

128.

48

L(C

,C,H

l)

114.

46

L(C

,C,H

2)

109.

71

L(C

,C,H

3)

110.

04

GC

,C,C

;)

0.83

r(

C,C

,C,H

l)

11.0

2 G

GC

zH2)

13

2.12

G

C,C

, H

3)

- 11

0.76

Ci-

Met

hyl

r(

C1-

C;)

1.

5107

r(

C;-

H’l)

1.

0820

r(

c!-H

’2)

1.08

40

@-H

/3)

1.08

38

L (c

:c;c

;)

119.

46

L(C

;C:H

’l)

110.

18

L(C

gH’2

) 11

1.62

1.51

03

1.08

23

1.08

65

1.08

67

120.

63

111.

95

110.

87

110.

72

179.

80

- 1.

59

119.

31

- 12

2.18

1.50

85

1.50

15

1.50

27

1.07

93

1.08

09

1.08

02

1.08

71

1.08

67

1.08

69

1.08

60

1.08

57

1.08

61

125.

07

127.

29

128.

20

112.

46

111.

97

121.

45

110.

77

111.

03

110.

95

110.

11

110.

43

110.

30

- 1.

11

0.46

-

1.37

-

12.0

1 -

8.24

-

8.10

10

8.90

11

2.53

11

2.69

-

133.

11

- 12

9.02

-

129.

11

1.51

18

1.51

37

1.51

27

1.51

34

1.51

37

1.51

23

1.08

23

1.08

28

1.08

24

1.07

78

1.07

94

1.08

00

1.08

54

1.08

56

1.08

54

1.08

47

1.08

54

1.08

59

1.08

64

1.08

69

1.08

51

1.08

47

1.08

56

1.08

52

121.

75

121.

20

121.

74

122.

27

124.

51

125.

14

111.

60

111.

61

111.

04

112.

15

112.

50

112.

86

110.

78

110.

92

110.

70

111.

07

110.

33

110.

08

1.50

32

1.50

30

1.07

93

1.08

04

1.08

68

1.08

65

1.08

68

1.08

66

129.

09

128.

70

114.

14

113.

57

110.

28

110.

48

110.

30

110.

51

.179

.91

179.

35

0.02

-

0.59

12

1.21

12

0.36

12

1.20

- ‘

121.

67

_

1.50

24

1.50

24

1.08

08

1.08

13

1.08

67

1.08

66

1.08

64

1.08

64

127.

65

127.

12

112.

25

112.

14

110.

86

110.

83

110.

59

110.

78

- 0.

64

1.37

-

3.27

-

0.79

11

7.40

11

9.71

.1

24.3

4 -

121.

85

1.51

36

1.08

30

1.08

57

1.08

59

121.

46

111.

39

110.

69

s

TA

BL

E A

4 (c

onti

nu

ed)

%

h3

2,4D

MP

D

(Z,Z

)-3-

MH

D

(Z)-

2,3-

DM

PD

(E

, E)-

3,4-

DM

HD

b (E

, Z)-

3,4-

DM

HD

(2

, Z

)-3,

4-D

MH

Db

s-tr

ans

gau

che

gau

che

gau

che

s-tr

ans

gau

che

gau

che

gau

che

L (c

;c:

H’3

) r(

C$;

C;H

;)

r(C

:C;C

;H:)

r(

c:c;

c;c;

) t(

c:c;

c;c:

) r(C;C;C:wly

r(C

;C;C

:H’2

) r(

C;C

;C:H

’3)

-

&M

eth

yl

r(C

,C,)

r(

C,H

l)

r(G

H2)

r(

GH

3)

L (q

&C

,)

L(C

,C,H

l)

L (C

,C,H

2)

L (G

GH

3)

~(W

-GW

,)

W,W

,G)

r(C

,C,C

,Hl)

G’X

H2)

G

W,H

3)

(E)-

Met

hyl

on

C;

tic;

-Cl

) r(

C;-

Hl)

r(

C;-

H2)

r(

CfH

3)

L (C

:w;)

111.

62

110.

75

110.

80

111.

52

111.

08

179.

93

177.

40

- 0.

62

176.

97

0.11

-

2.35

-

0.71

-

1.23

5.

57

- 0.

13

117.

15

120.

19

119.

70

125.

93

120.

09

122.

10

- 12

1.16

-

121.

60

- 11

4.71

-

120.

25

1.51

49

1.51

39

1.08

26

1.08

30

1.08

55

1.08

56

1.08

55

1.08

55

120.

86

121.

11

111.

04

111.

33

110.

81

110.

57

111.

69

111.

65

178.

18

179.

36

5.61

-

0.42

12

5.85

12

0.00

-

114.

59

- 12

0.91

_

111.

33

111.

02

111.

36

179.

81

-0.9

9 0.

0 10

.08

- 0.

9 -

1.66

13

0.44

11

9.90

11

8.87

11

0.56

-

121.

82

- 12

2.28

1.50

3od

1.08

OO

d l.O

W

1.08

7od

128.

7od

Ab initio studies of methylated 1,3-butadienes

Documents

Transcript of Ab initio studies of methylated 1,3-butadienes