Conformational energy analysis of substituted diphenylethanes

Journal of Molecular Structure, 64 (1980) 67-7 3 o Elsevier Scientific Publishing Company, Amsterdam

CONFORMATIONAL DH’HENYLETHANES

ENERGY

ANALYSIS

-

Printed in The Netherlands

OF SUBSTITUTED

Part VI. Calculations equilibria

of the solvent dependence of the conformational in stilbene dihalogenides. Intramolecular interactions in the

PClLO framework*

PETKO

M. IVANOV

and IVAN

Institute of Organic Chemistry, (Received

G. POJARLIEFF Bulgarian Academy

of Sciences, Sofia 1113

24 April 1979; in final form 18 September

(Bulgaria)

1979)

ABSTRACT As partof a theoretical analysis of the conformational equilibria of stilbene dihalogenides, the free energy at 300 K of each stable conformational isomer of these molecules has been estimated for a solvent of dielectric constant 3.5. Classical empirical potential functions were used. interaction with the solvent was considered only in termsof a continuous dielectric medium interacting with the local dipoles and quadrupoles of the molecule. Simulation of the experimental conditions (i.e. appropriate values for the dielectric constant of the solvent) yielded better agreement with the available experimental data, which were mainly dipole moments and optical rotation values. The quadrupole energy term has a very small influence on the calculated conformational populations and can be neglected when dibenzyl derivatives are considered. The mechanism of the intramolecular interactions is discussed within the PCILO framework. INTRODUCTION

The main features of the conformational behaviour of isomeric 1,2-disubstituted-1,2diphenylethanes have been satisfactorily reproduced by means of molecular force-field and CNDO/B calculations on simpler representatives of this series [l-4]. To progress with the modelling of larger systems it seems essential to review some deficiencies in the empirical-energy and SCF-MO procedures used in these earlier studies. Firstly, in the moIecular mechanics approach used, the effect of the solvent was simply reflected in an “effective dielectric constant” of the medium whenever intramolecular electrostatic interactions were estimated [3,4]. For this reason a comparison with a reaction-field theory (RFT) treatment [ 5,6] of stilbene dihalogenides is presented here. Secondly, correlation-energy effects lie beyond the scope of the SCF process and to solve this problem a perturbative treatment t.nthe PCILO framework [7] has been attempted.‘PCILO-CNDO has *For a previous communication

see ref. 1.

68

several advantages over the CNDO-SCF method [S] : firstly, it is much less expensive, and secondly, the method allows an analysis of the energy changes. The latter feature makes PCILO-CNDO particularly well suited for discussion of the mechanisms of inter- and intra-molecular interactions in terms of the individual energy contributions. IWETHOD

For calculations of the solvation energy [(E, - E,), where E, and E, are the energy of the molecule in vapour and solution, respectively] the RFT model of Abraham and Bretschneider [5,6] was adopted with the following additional parameters: a value of 1.00 X lo- 3o C m for the dipole moments of the phenyl groups (from the CNDO/B charge distribution for the fluoroand chloro-derivatives with a positive pole on *the phenyl rings), a radius for the spherical cavity of R0 = 0.69 nm (2Ro = the distance between the most widely separated aromatic protons when the phenyl rings are in the trans position plus the Van der Waal’s radius of H), and a macroscopic dielectric constant for the medium of E = 3.5. Solute refractive indexes were estimated on the basis of experimental data [9] for dibenzyl, haloethanes and halotoluenes. For the estimation of E, the approach of ref. 2 was followed with partial atomic charges from CNDO/Z calculations [Z] and a minimization with respect to the three torsion angles only. As suggested by V. G. Dashevsky (private communication) we adopted independently-determined parameters for the C---H interaction, instead of the C---H potential cme (a combination of those for C-.-C and H--OH) previously used. This alters the value for the coefficient before rm6 (see the supplementary material to ref. 2) to 506.22 X 10e60 kJ mol-’ m6_ The calculations were carried out (in both the RFT and the PCILO treatments) with the force-field geometries (valence bonds and angles) presented in the supplementary material to ref. 2. The PCILO results were obtained after a stepwise search (step-size 0.035 rad) around the force-field local minima described in ref. 2, with polarities of the localized MO optimized for the first conformation only. Additional optimiiation was carried out in the case of the meso-difluoro compound to find the lowest-energy combination of Kekule structures for the two phenyl rings in each local minimum. The different combinations of Kekule structures only slightly influence the calculated total energies, and to save computer time this sort of minimization was not performed for the other compounds. RESULTS

AND DISCUSSION

The RS(threo) (a) and the meso(elythro) (b) forms of 1,2difluoro-(I), l-fluoro-2chloro-(II) and 1,2-dicbloro-(III) 1,adiphenylethane were investigated. The RFT calculations yielded the torsional angles, energies [E,, (E, -ES) as a sum of a dipole and a quadrupole term], conformational entropies [lo] and relative populations at 300 K for the local energy minima*. *The results of the RFT and PCILO calculations have been deposited with B.L.L.D. Sup. Pub. No. SUP 26139 (6 pages).

as

69

Fig. 1. Designation of conformations

Salvation-energy

in the RS(threo)

and meso(erythro)

series.

calculations

The previous empirical energy calculations on stilbene dihalogenides [ 21 showed that the -SC conformation for the Z&series and the ap conformation for the meso-series are those of lowest energy (where SCdenotes synclinal and ap antiperiplanar). The conformations are shown in Fig. 1. The re-estimation of the electrostatic interactions on the basis of the CNDO/B partial atomic charges, and the new parameters for the C---H interaction do not alter this general picture. Again the --SC and the ap conformations are of lowest energy for the RS(threo) and meso(erythro) series, respectively (see Table 1). The inclusion of the salvation-energy term favours the conformations with larger dipole moments [namely +sc and ap for RS(threo) and +sc for meso (erythro)] . The slight ch ange in the torsion angles for rotation around the bond joining the two aliphatic carbon atoms, Q-C,, parallels the increase in dipole moment, i.e. the better solvation of the molecule. When compared with similar results for haloethanes [ 51 and phenylhaloethanes [ 111 the E,,--E, values calculated here are very small, i.e. the solvent only slightly favours the conformations with larger dipole moments and the conformational preferences are mainly determined by the intramolecular interactions. Even for a polar solvent (E = 25) the value of E, -E, for the conformations with gauche halogen atoms does not exceed 2.09 kJ mol-‘. The calculated quadrupole terms are very small and cannot compete with the dipole terms, contrary to findings for haloethanes [5]. Consequently it is not necessary to include the quadrupole energy term in the RFT model when dibenzyl derivatives are considered, due to the larger R,, value in the case of stilbene dihalogenides (the dipole and quadrupole terms are proportional to Ri3 and R$, respectively). It is a commonly held view (see for example Gounelle et al. [12] for the case of three-1-fluoro-2-chloro-1,2diphenylethane) that the ap conformation is preferred for the threo-isomers because of its higher dipole moment and the relative reactivity of RS(threo)--meso(erythro) pairs. Irrespective of the favourable solute--solvent interactions, our estimates of the populations of the ap conformations for the RS(threo) isomers are actually the lowest ones,

70 TABLE

1

Solvationenergy(E, - E,) at E = 3.5 potentialenergyminima(kJ mof’) Comoound

(in parentheses)

values for the local

Conformation +sc

Ia Ik

and AE,

ap

-SC

0.63(8.99)

O-71(7.78) 0.79(9.50)

0.13(0.00)

IIIa

1.21(4.10) 1.30(2.01)

ib Ifi XIIb

0.92(0.92) 1.05(1.13) l-17(2.68)

0.08(0.00) 0_17(0.00) 0.17(0.00)

1.05(0.88)

l.Og(6.40)

0.21(0.00) 0.25(0.00)

namely, approximately 6, 6, and 1% for compounds la, IIa and IIIa, respectively at E = 3.5. This is due to severe steric hindrance in the ap conformation, in which the two skew halogen atoms are flanked by the phenyl groups. According to model considerations the two synclinal conformations are preferred. The inclusion of the solvation-energy term only slightly enhances the population of the (+ )-synclinal conformation with respect to the (--)synclinal form, and the calculated fractions for the two conformations are, respectively: Ia: 0.17, 0.78; IIa: 0.41, 0.53; IIIa: 0.64, 0.34. In all cases in the meso(erythro) series the fractional populations are calculated to be greater for the ap conformation, namely, approximately 0.73, 0.54, and 0.83 for Ib, IIb and IIIb, respectively. The favourable solutesolvent interactions in the synclinal conformations cannot compete with the more advantageous intramolecular interactions and the greater conformational entropy contribution for the ap conformation. As the experimental data are mainly for the chloro- and bromo-derivatives, solvation-energy calculations were also carried out for 1-chloro-2-bromo-(IV) and 1,2-dibromo-(V) 1,2-diphenylethane. The results for these compounds are close to those for the dichloro derivative. The following fractions were computed for the fsc-, ap and -SC- conformations, respectively (E = 3.5): IVa: 0.72,,0.01,0.27; Va: 0.76,0.003,0,23; IVb: 0.08, 0.77,0.16;and for Vb: 0.07 (SC), 0.93 (ap). Calculated averaged values for the dipole moments and the molecular optical rotation of compounds IIa, b-Va, b are compared in Table 2 with the corresponding experimental findings. In all cases a simulation of the experimental conditions is included; i-e_ &v and rqp1 n values were obtained using relative conformer populations from RFT calculations which refer to the solvent used in the experimental dipolemoment and molecular optical-rotation measurements. For [Mz?], , E values of 25 (solvent ethanol for IIIa, I,Va, and Va) [ 13,141 and 4.7 (solvent chloroform for IVb) 1131, were used. The dipole moments measured for are compared with RFT dipole-moment solutions in benzene [12,14-161

72

TABLE

3

Energy contributions (kJ mol-*)

Conformation

to the conformational

Zerofh-order +sc ap -sc

energy

Second-order

energy

IIa

(A&‘,)~ 1.92 2.01 0.00

2.84 18.20 0.00

0.00

0.00

20.46 0.00

21.96 6.11

0.00 13.76 0.00

9.87

11.76 0.00 5.91

8.62 0.00 8.62

5.06 0.00 1.34

(A&,)

0.00 9.25 1.59

(a&)

ap

19.37 0.00

SC

14.68 = 4(2,

6.02 0.00 6.02

4.31 0.00 4.31

0.00

(3)

mb

6.36 5.52

10.88 1.84 energy

IIb

Ib

0.00

aP

-sc

IIIa

0.00 1.51 3.93

+sc

a*g0(2)

framework

Compound la

Third-order i-SC

energies calculated in the PCILO

(3) -

(t”,,2,

19.12 0.00 13.09 (3&z?

23.34 0.00 18.37

where (CT), is bat

the global

0.00 9.87

minimum.

local minima (with E = 3.5) have been made. These yielded conformational energies similar to the RFT values (at E = 3.5). For the sake of simplicity it is better to follow this approach in the case of dibenzyl derivatives, instead of using the more complicated RFT model. This is particularly true for molecules with a greater number of intramolecular rotational degrees of freedom and more complex electrostatics than the halogenodibenzyl derivatives. Intramolecular in teractions in tke PCILO framework 71, the PCILO-CNDO results generally parallel the CNDOSCF values [ 11. Here again the conformational energies of the conformations with antiperiplanar phenyl groups of the RS(threo) and nzeso(erythro) forms are respectively lowered and raised (see ref. 1). The following comments may be made concerning the influence of the individual PCILO energy contributions upon conformational preference when gauche or anti phenyl substituents are present (Table 3). fn all cases studied for the meso(erythro) forms, the contribution of the zeroth-order energy g0 (involving the short-range repulsion and the electrostatic interaction) is disadvantageous for the synclinal conformations, in which gauche-halogen/halogen and gauche-phenyljphenyl interactions are present. In the RS(threo) series, the competition between the latter two interactions and the different skew-phenyl/halogen interactions favours (as regards Co) the conformations with trans-halogen (Ia) and transhydrogen (IIa, IIIa) atoms respectively. The second-order energy contribuAs expected

[

73

tion g2, determined mainly by the delocalization interaction, and also by the interbond correlation, enhances the conformations with skew-phenyl groups in all cases. The interbond correlation, which contributes to g2, reflects the intramolecular dispersion interactions. As regards the small third-order energy contribution &, this opposes (and for the RS(threo) forms even outweighs) the delocalization and the interbond-correlation stabilization of the conformations with gauche-phenyl groups. Thus the mechanism of the intramolecular interactions is reasonably well reflected by the individual PCILO energy contributions. ACKNOWLEDGEMENTS

We thank Prof. R. J. Abraham from the Robert Robinson Laboratories, University of Liverpool, for making available his DIPQUADMOMS program. We are also pleased to acknowledge the skilful assistance of Dr. J. Kaneti in some aspects of the PCILO computer adaptation. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

P. M. Ivanov, Commun. Dept. Chem. Bulg. Acad. Sci., 11 (1978) 249. P. M. Ivanov and I. G. Pojarlieff, J. Mol. Struct., 38 (1977 ) 259. P. M. Ivanov and I. G. Pojarlieff, J. Mol. Struct., 38 (1977) 269. P. M. Ivanov and I. G. Pojarlieff, C. R. Acad. Buig. Sci., 3 1 (1978) 201. R. J. Abraham and E. Bretschneider in W. J. Orville-Thomas (Ed.), Internal Rotation in Molecules, Academic Press, London, 1974, Chap. 13. R. J. Abraham, in B. Pullman (Ed.), Environmental Effects on Molecular Structure and Properties, D. Reidel, Dordrecht, 1976. p. 41. J. P. Malrieu, in G. A. Segal (Ed,), Semiempirical Methods of Electronic Structure Calculation, Part A, Plenum Press, New York. 1977. p. 69. G. Trinquier and J. P. Mahieu, J. Mol. Struct., 49 (1978) 155. R. C. Weast (Ed.), Handbook of Chemistry and Physics, 56th edn., CRC Press, 1975. S. S. Zimmerman, M. S. Pottle, G. Nemethy and H. A. Scheraga, Macromolecules, 10 (1977) 1. W. F. Reynolds and D. J. Wood, Can. J. Chem., 51 (1973) 2659. Y. Gouneile, J. Juiiien and C. Minot, Buii. Sot. Chim. Fr., (1972) 2760. L. Stoev and Yu. Stefanovsky, Commun. Dept. Chem. Bulg. Acad. Sci., 10 (1977) 587. A. Weissberger and H. Bach, Ber., 64B (1931) 1095. A. Weissberger, J. Am. Chem. Sot., 67 (1945) 778. K. Higasi, Bull. Chem. Sot. Jpn., 13 (1938) 158. J. H. Brewster, J. Am. Chem. Sot., 81 (1959) 5475. M. G. Voronkov, E. Liepins, E. P. Popova and V. A. Pestunovich, Latv. PSR Zinat. Acad. Vestis. Kim. Ser., (1973) 339.