Conformational energy analysis of substituted diphenylethanes

Journal of Molecular Structure, 38 (1977) 259-267 @Elsevkr Scientific Publishing Company, Amsterdam -

CONFORMATIONAL DIPHENYLETHANES

ENERGY

ANALYSIS

Printed in The Netherlands

OF SUI3STITUTED

Part II. Empirical energy calculations on stiIbene dihalogenides

P. IVANOV

and I. POJARLIEFF

Institute of Organic Chemistry.

Bulgarbn Academy

of Sciences.

I I 13. Sofia (Bulgaria)

(First received 7 June 1976; in revised form 15 December 1976)

ABSTRACT The geometry and energy of the stable conformations of the isomer-k forms of 1.2-haiogeno-1,2-diphenylethanes have been obtained by means of empiricai energy functions. A minimization of the conformationai energy with respect to the torsion angles and the valence angles around the asymmetrically substituted carbon atoms has been carried out. The evaluated populations of the stable conformations showed good agreement with available experimental data. CNDOIP calculations on the lowsnergy conformations of the isomeric forms of 1,2difluoro-, 1.2~fluorochioro-. and 1,2dichiorodiphenylethane have been carried out. These yielded improved estimates of the dipole moments for the dichloro isomers. INTRODUCTION

The experimental studies on the conformations of 1,2dihaiogeno-1,2diphenylethanes mainly concern the dichloro and dibromo derivatives and are of a quahtative nature [l-11]. No systematic a priori treatment of these compounds has been described, and we hope that the results obtained here provide some insight into the intramolecular interactions governing the conformational equilibria. The RS (threo) (a) and the meso (erythro) (b) forms of the ten possible stilbene dihalogenides of the type X,-CH(C,&)CH(CaH5)--X2 were investigated, where X, X.

I

XI

ID

IV

v

VI

VII

VU1

IX

x

F

Cl

Br

F

Ci

Br

I I

F Cl

F Br

F I

Ci Br

Cl I

Br I

Throughout this paper the terms ‘*syncIinaI” and “antiperiphmar” conformation are used in reference to the rotational isomerism, defined by the two phenyl substituents with respect to the mti bond as illustrated in Fig. 1.

260

Fig. 1. Designation

+SC

OP

-St

of conformations

THE CALCULATIONAL

in the FI.S-(threo) and me.so-(erythro-)

series.

METHOD

The molecular force field of Dashevsky [12-161 was used and for the compounds treated here, it includes the following energy terms: nonbonded interactions, angle bending, electrostatic interactions and torsional potentials. The potential function accounting for the nonbonded interactions is of “6-exp” form *. The total energy of the nonbonded interactions is a sum over the pairwise interactions between all atoms separated by two or more covalent bonds. For the estimation of the energy of angle deformations only the force constant k,, = 30 kcal mol-’ rad-‘, was used. The electrostatic interactions were estimated with a dielectric constant of 1. The charges on F, Cl, Br, I and HI’ were taken from ref. 17 and the charge distribution on the phenyl substituents (Fig. 2) was selected from that of the corresponding fragment of N-acetyl W-methyl phenylalanyl amide [ 181. The partial charges on CY’ were determined from the condition of electroneutrality of the whole molecule. For the rotation around the cwti bond an ethane-like potential with a barrier of 2.8 kcal mol-’ was used. The assessment of the populations of the various conformations followed the approach of Scheraga and co-workers [18]. To this purpose we calculated the statistical weights by accounting the librational entropy contribution under conditions where only the torsion angles are varied. The following geometry [ 17,19,20] for the compounds under .consideration was selected: Cw = 1.53 A, C*Lc” = 1.40 A; @-CY =,I.51 A, c”LHa’ = 1.09 A , C-H”= 1.08 A, C-F =,1.36 A, C-Cl = 1.77& *The parametersfor the “6-exp” potential together with &he re&a ftim the force field calculations havebeen deposited with the British Library at Ba&ton Spa;Y&kshir&i U.K. _ as Supplementary PublicationNo. SUP. 26060 (10 pages).

261

Fig. 2. Description of the molecular geometry. A, B - numbers of the valence bonds, necessary for the description of the corresponding valence (0) and torsion (w ) angles. The partial atomic charges (in electronic units X 1000) are given in parentheses.

C-Br = 1.93 A, C-I = 2.13 A, LH%alY = 109.47” (Y = Cal, Car), LCa’Ca’Y = LCUC?‘Y = LCO’C?CU = 111.0” (Y = F, Cl, Br, I). The phenyl substituents were treated as rigid parts of the molecules with ideal benzene geometry. The three torsion angles and the valence angles around the two asymmetrically substituted carbon atoms were variable geometric parameters (Fig. 2). The conformation is described in terms of the three torsion angles w , , o 1 and 03, with o = 0” in the eclipsed conformation. The calculations were carried out in two stages. At first assuming constant bond lengths and valence angles, and starting from the conformations (go”, 60”, go”), (go”, 180”. 90”) and (go”, -6O”, go”), the potential energy was minimized with respect to the three torsion angles, until its fast derivatives were reduced to <10e4 kcal mol-’ deg-‘. The second derivatives matrix and the statistical’weight [18] were computed for the conformers thus obtained. In the second stage starting from these local minima, the conformational energy was minimizedwith respect to the torsion angles and the valence angles around the asymmetricaIIy substituted carbon atoms (13 independent variables). Critdia for finding a 1ocaI minimum-in this subspace of the configurational space of the molecule, were the stability of the varied

262

structural parameters and the energy difference diminution, supposed to be ~10~~ kcal mol-‘. RESULTS

AND

DISCUSSION

The smaller dipoIe moments of meso-stilbene dichloride and dibromide (IIb and IIIb) [ 1,241 compared to the corresponding RS-isomers, suggest an antiperiplanar disposition of the halogen atoms in the meso-forms, and a synchnat arrangement of these atoms in IIa and IIIa. Another source of information, albeit rather qualitative, comes from the data for the molecular optical rotation. The corresponding experimental data for IIa, IIIa and VIIIa [ 10 ] is close to that for the (+ )-synclinal conformation, calculated by the method of Brewster [Zl]. On the same basis the antiperiplanar conformation for the meso-chlorobromo compound (VIIIb) is referred to as the preferred one. The IR and Raman spectral analysis of the dichloride (II) and dibromide (III) showed favouring of the antiperiplanar conformation for the meso-isomer both in the crystaf state and in solution [ 5,8). In the case of the racemie form, synchnal position of the halogen atoms was observed in the crystal state. In solution, besides this conformation, that with tmns halogens is also populated to some extent. From the integrated intensities of the bands it has been concluded that the above preferred conformations of IIIa and IIIb are more populated than those of IIa and IIb, respectively.

Empirical energy calculations The two stage procedure outlined above for minimization of the conformation& energy was adopted in order to estimate the librational entropy terms from the curvature of the energy surface around the local minima with a reasonable amount of computer time. The data for the local minima obtained after the first and second stage of minimization (see the footnote on p. 2). include torsion angles, energies, librational entropy terms and statistical weights at 300 K, and valence angles around the asymmetric carbon atoms obtained after the second minimization stage. The data obtained after minimization with respect to the torsion angles only were mcluded in order to assess the effect of varying the valence angles. These data should be considered with some constraint as they have been obtained under conditions, Le. at constant valence angles, where the internal consistency of Dashevsky’s procedure is probably not preserved The RS- Ithreo-) series. After variation of thg torsion and valence angles three minima for the potential energy were obtained corresponding to the three conformations depicted in Fig. 1. In all cases the (-)-synclinal conformation with anti halogen atoms is of the lowest energy mainly due to the most favourable electrostatic interactioris, Next in ene%y is the (+ )-synclinal conformation and the antiperiplan~ donfo*a$i_on- is 6f the highest energy with most unfavourable nonbond_ed and_eIectrost@c

263

interactions. The computed energy difference between +sc- and SC- conformations is largest with the lightest atoms: 1.18 kcal for the difluoride (Ia) and 0.85 kcal for the fluorochloro derivative (Va) and drops gradually to 0.10 kcal for the diiodo (IVa) and 0.11 kcal for the bromoiodo derivative. With respect to the various energy terms this effect is due to the decrease in the electrostatic repulsion with the larger halogen atoms, the nonbonded interactions being practically the same for the two conformations. In the more crowded se-conformation the angle bending strain is greater and becomes up to 0.6 kcal higher than that of the +scconformation in IVa. It is noteworthy that after the first stage of minimization (before varying the valence angles) the lowest energy is calculated for the +sc-conformation (with the exception of the difluoride (Ia)) because of most favourable nonbonded interactions. Upon the second minimization an opening of the angles between the heavy atoms (Cl, Br, I, Cal, Car) takes place with a release of strain which is greatest in the sc-conformation. A significant contribution is gained by attractive interactions between the phenyl groups which can take up more advantageous orientations after the widening of the valence angles. As far as the predicted populations at 300 K are concerned, however, the most populated conformations are the (+ )-synclinal ones due to the most favourable entropy of libration contribution which outweighs the energy difference. Stilbene difluoride (Ia) is the only exception, as, due to the smaller size of the fluorine atoms, the entropy difference favouring the +sc-conformation is less appreciable. The following fractions were computed for the + SC- and -sc-conformation, respectively: Ia: 0.22, 0.76; Ha: 0.71, 0.29; IIIa: 0.80, 0.20; IVa: 0.82.0.18. In the derivatives with two different halogen atoms the populations are similar ranging from O-53,0.44 for the +sc- and se-conformation, respectively, in the fluorochloro derivative (Va) to 0.83,0.17 in the bromoiodo derivative (Xa). The apconformation is appreciably (2-3s) populated in the fluorine compounds. The following comments can be made concerning the geometry of the conformer at the local minima. As regards the rotation of the phenyl groups, the optimum value for w , and w 3 appears as a balance between the repulsions of the geminal and the opposing vicinal groups. In the +sc-conformation these work in the same direction and the phenyl groups are strongly twisted from the initial position (0, = w3 = 90”) perpendicular to the w1 bond. From 78.5” in the difluoride (Ia) wI and w3 are reduced to 58.5” in the diiodide (IVa). In the sc-conformation the phenyl groups are flanked by two vi&al heavy atoms and the torsion angles of the phenyl groups remain close to 90” - the largest deviations being o, = w I) = 82.0” in IVa and oI = 88.6” and w3 = 80.8” in VIIa. These angles remain close to 90” in the ap-conformation when the two halogens are equal. When they are different the phenyl geminal to the heavier halogen atom is strongly twisted towards the lighter one. Thus in the threo-fluorochloro compound (Va) wI = 95.8” and 03 = 74.6”. and in the fluoroiodo compound (VIIa)

264

W, = 103.2O and a3 = 68.9”. With respect to the torsion angle about the etbane bond, ~2, noteworthy is the preponderance of the repulsions between the halogens in the +soconformation as compared to that of the two phenyl groups. w2 is 53.3” in Ia and drops to 46.6” in IVa. On the contrary the interaction between the larger halogens appears a weaker place in the ap-conformation and o2 decreases gradually with the size of the halogen from 180.6” in Ia to 165.0” in IVa. In the se-conformation wz remains close to -60”. Release of strain in the difluoro compound (Ia) is achieved mainly by opening of the CY-C~’ angle, the effect being greatest in the se-conformation (8, = 6, = 112.8”). With the heavier halogens usually, but not always, the bond angles involving halogen atoms are strongly opened, e.g. for an extreme case, the diiodide (IVa), the following angles were obtained: in ap e1 = 87= 112.2q & = f& = 115.3’, 95= es = 113.4”, and in SC 8, = 0, = 114.0”, & = & = 112.69 85 = 08= 113.5”. The meso- (erythro-) series. In meso-compounds with two equal halogen atoms the two synclinal forms are enantiomeric~ in the erythro series with two different halogens according to the notation adopted in the +sc-conformation the heavier halogen is vicinal to a phenyl group and a lighter one in the ~c-confo~ation. In all cases the lowest energy is computed for the ap-conformation. This conformation is with most favourable electrostatic interactions. In meso-stilbene difluoride (Ib) these are almost outweighted by the lower energy of nonbonded interactions of the synclinal conformation. Similarly in the case of dibenzyl [ 19, 2Uf an important contribution is an attractive interaction in the synclinal conformation of 1.3 kcal mol-’ between the gauche phenyl groups with respect to the ap-conformation. The net energy difference between the SC- and ap-conformations is 0.18 kcal mol-‘. This difference gradually increases in the meso compounds: O-63,*1.05, and 1.61 kcal in IIb, IIIb, and IVb, respectively. This is due to the gradual increase in steric strain (nonbonded and angle bending) in the more congested synclinal conformation. In the erytbro-compounds with a fluorine atom the energy difference between the se-conformation andthe apconformation is quite insignificant: 0.20,0.08, and 0.15 kcal in Vb, Vfb, and VIIb, respectively. The entropy of libration is greatest in the apconformation and this enhances its preference. The calculated polAations for the zip-copformation at 300 K are 0.68, 0.86, 0.92, 0.98 for Ib, IIb, IIIb, and IVb;‘mspectively._ For the fluorine-containing erythro-compounds,~ Vb, VIb; andVII6, considerable populations, 28-35%, were obt&ned for the -c-conformationtogether with 3-5% for the Csc-conforniation due t;iithe s&lI steric hindrance of the fhorine at&n.

are strongly rotated, e.g. in Ib and IVb U, is 78.3” and 59.43 and w3 is 101.5” and 120.6”) respectively. Strain is also released by broadening of angles between bonds to heavy atoms. The congruence of our results with the experimental data is quite satisfactory. (1) The calculated averaged values of the dipole moments (&c” = (~~ni(P~~c)2)‘P~ where ni is the population of the ith local minimum) for IIa, b and IIIa, b are in such relation to each other, as are those determined experimentally (Table 1). In the case of II, the agreement becomes even TABLE

1

A comparison of calculated values for the dipole moments’ rotation with experimental data Conformation

9,talc

(D)

cak @av

(D)

RS-1.2-dichloro-l.2-diphenyiethane (+=I 2.59 2.20 (3.56) (3.10) tap) 2.46 (3.66) (-cl 0.53 (1.48) Meso-l.O-dichloro-1.2-diphenylethane (=) 2.57 0.96 (ap)

(3.36) 0.00

exv

:D) (Ilo) 2.75b

-249

-183

-259b

-401

-57 5d

-281

-396d

-106

-69d

-750 -21 (Ilb) 1.27b

(1.26)

RS-Z.2-dibromo-1.2-diphenylethane (+sc) 2.53 2.27 tap) 2.44 (-=J) 0.52

(Illa) 2.81=

Meso-l.P-dibromo-1.2-diphenylethane 0.00 2.54 0.72

(IIIb) 0.4-0.9=

I:P))

-563 -752 +249

Threo-I-chloroJ-bromo-1.2.diphenylethane (+sc) tap) (--8c)

(Villa) 406 -751 +114

Erythro-I-chloro-I-bromo-I.2-diphenylethane (+=c) tap)

(VIIib) -364

(-)

and the molecular optical

-149 + 490

Vhe charge distribution adopted for the estimation of the electrostatic interactions and the geometries obtained after minimization of the conformational potential energy with respext to the torsion and valence angles were used in the calculation of the dipole moments. In parentheses are given the values obtained by the CNDO/2 procedure. %ef. 1. %ef. 4, dref. 10.

quantitatively better when the -dipole moments determined byethe CNDO/Z procedure are used. (2) The calculated averaged values for the-molecular optical rotation of IIIa, VIIIa and IIa ([M,,coleIn = Mini [;M,‘d”4]n)folloti the. relation 2.21-1.5:1.0. This is exactly the relation the corresponding experimental quantities satisfy (Table 1). (3) From-NMR measurements (at room. temperature) in meso-l,2-dichloro-l-(2-fluorophenyl)-2-(4-fluorophenyl) ethane, the population of the:conformation with antiperiplanar chlorine atoms has been estimated to be about 82% [ 22 1. Here the population of .the corresponding conformation of IIb is evaluated to be 86%. All these coincidences are good evidence for the capability of predicting correct molecular geometries and relative energies on the basis of empirical potentials. Quantum chemiazl calculations The basic purpose of our CNDO/B calculations on Ia, b, ?a, b and Va, b

was to check the correctness of using the adopted partial charges (Fig. 2) for the estimation of the electrostatic interactions. The calculations were carried out for all local minima of these compounds. Averaged values for the partial charges on the atoms are shown in Table 2. C* designates the a-Car atom. The partial charges on the other atoms of the phenyl substituents are insignificant and could be chosen in some suitable way, following the condition of electroneutrality of the molecule. It is seen that the CNDO/B partial charges do not differ considerably from those used in our calculations. Only the partial charges on the HP’ atoms of Ia, b differ even in sign. The same is true for the corresponding atoms of Va, b. A detailed analysis of the intramolecular electrostatic interactions, including these atoms, showed that they are not of importance for the calculated conformational preference. TABLE Partial

F

2 atomic

Cl

charges

(electronic

Hal=

plb

units X 1000)

CaP

C”‘b

C*“c

C*b.c

1.2-Difluoro-1.2-diphenylethane -215

195

-15

15

1.2-Dichloro-1.2-diphenytethane -155

15

1 -Fluoro-2-chloro-1.2-diphenylethane -220 -150 -20 20

.85 230

‘Atoms attached to the fluorine be-a&g bAtoms attached to the chloriqebearing =C* designates the &? atom. _

50

45

10

carbon at_om. carbon atom_.

46

267 ACKNOWLEDGEMENTS

We thank Dr. J. Kaneti for making his CNDO/B program available to us and Dr. B. Jordanov for some stimulating discussions and remarks during the preparation of this paper. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

A. Weissberger and H. Bach, Ber., 64B (1931) 1095. K. Higasi, Bull. Chem. Sot. Jpn., 13 (1938) 158. J. D. McCullough, J. Am. Chem. Sot.. 62 (1940) 480. A. Weissberger. J. Am. Chem. Sot., 67 (1945) 778. G. Drefahl and G. Heublein, J. Prakt. Chem.. 21 (1963) 18. G. Heublein, 2. Chem., 6 (1966) 221. G. Heublein, J. Prakt. Chem.. 31 (1966) 84. G. Hublein. R. Kuehmstedt and H. Dawczynski, Tetrahedron, 25 (1969) 329. C. J. Devlin and B. J. Walker, J. Chem. Sot., Perkin Trans. 1, (1972) 1249. L. Stoev and Yu. Stefanovsky. unpublished results. E. Baciocchi and C. Liilocci. J. Chem. Sot., Perkin Trans. 2, (1973) 38. V. G. Dashevsky, 2. Strukt. Khim., 7 (1966) 93. A I. Kitaygorodsky and V. G. Dashevsky, Theor. Exp. Chem. (U.S.S.R.), 3 (1967) 35. V. G. Dashevsky and A. I. Kitaygorodsky. Theor. Exp. Chem. (U.S.S.R.). 3 (1967) 43. V. G. Dashevsky, Z. Strukt. Khim.. 9 (1968) 289. V. G. Dashevsky, Z. Strukt. Khim., 11 (1970) 912. R. J. Abraham and K. Parry, J. Chem. Sot. B (1970) 539. P. N. Lewis, F. A. Momany and H. A. Scheraga, kr. J. Chem., 11 (1973) 121. P. Ivanov, I. Pojariieff and N. Tyutyulkov, Commun. Dept. Chem. Buig. Acad. Sci., 9 (1976) 516. 20 P. Ivanov, I. Pojarlieff and N. Tyutyulkov, Tetrahedron Lett.. (1976) 775. 21 J. H. Brewster, J. Am. Chem. Sot., 81 (1959) 5475. 22 M. G. Voronkov, E. Liepins, E. P. Popova and V. A Pestunovich. Latv. PSR Zinat. Acad. Vestis. Kim. Ser., 1973, p. 339.