Molecular mechanics of organic halides

Journal of Molecular Structure, Elsevier

73 (1981)

145-157

ScientificPublishingCompany, Amsterdam-

MOLECULAR

MECHANICS

Part IV. Monobromides

and N.

A. Y. MEYER

Department (Received

OF ORGANIC

Printed

in The Netherlands

HALIDES

and non-gemrizaCdibromides

OHMICHI

of Organic

Chemistry,

Hebrew

University, Jerusalem (Israel)

24 July 1980)

ABSTRACT A molecular-mechanical hydrocarbon force field is extended to apply to saturated organic bromides, including non-geminal dibromides. Simultaneous calculation of molecular geometries, dipole moments, conformer energies and barriers to internal rotation is provided for. Results are reported for 34 molecules, acyclic and cyclic, representing altogether 78 structural variants. Variability in bond lengths and dihedral angles, and the “repulsive gauche effect”, are touched on in the discussion. INTRODUCTION

In previous publications we described the extension of Allinger’s 1973 force field (“MMl” [l] ) to organic chlorides and non-geminal polychlorides [ 21, fluorides, polyfluorides [ 31, and fluorinated olefins [ 41. Here we turn to bromides and consider geometries, relative energies, and dipole moments. To our knowledge, this is the first systematic force-field study of bromides. Preliminary attempts have been described [ 51, as well as exploratory calculations within the MM2 formalism [6]. Other reports on bromides [e.g., refs. 7-101 concern but few molecules or just one property, generally energies. The computed dipole moments and geometrical traits are on the whole representative. As for force-field energies, it has been noticed [ 111 that they are frequently of lower quality than the computed geometries. In fact, two notorious problems persist in this field: the a-g energy difference in lbromopropane and some of its homologues, and the ee-aa energy difference in trans-1,4-dibromocyclohexane (for notation, see Appendix). In 1-bromopropane [ 121, as in the chloro, fluoro, and cyan0 derivatives [13,14], gauche is more stable (not just more abundant) than anti. However, by torsional angles (XCCC and XCCH), g-CH3 CHz CH2 X resembles ax-C6H11 X, a-CH3CH&H2X resembles eq-C,H, ix, and in substituted cyclohexanes the equatorial conformer is always the more stable [ 151. Therefore, if the torsional constants in the force field are selected so as to favour eq-&Hi ix, they also make a-CH3CH&H2X more stable than gauche, and vice versa. We chose to fit to C6HIIX. 0022-2860/81/0000-0000/$02.50

0 1981

ElsevierScientificPublishingCompany

146

In anti-1,4-dibromocyclohexane, the di-axial conformer is as stable [ 163 as, or perhaps more stable [17] than, the di-equatorial. The field makes ee the more stable, even if by less than twice the calculated energy difference in C6HI ,Br (0.76 vs. 0.47 kcal mol-‘). It has been suggested [ 181 that aa is stabilized by the four 1,3-electrostatic ax-CBr/ax-CH interactions. It is indeed found that these interactions are responsible for the computed lowering (from 2 X 0.47 to 0.76), but that an unreasonable charge separation has to be assumed in axial C-H bonds in order to reverse the computed preference. Within the present formulation, therefore, this particular discrepancy is irremediable. The structure of cis-l-bromo-4-chlorocyclohexane must be considered an open question. Computation predicts close energies for the two conformers, eq-B--Cl and ax-Br-eq-Cl, in line with solution data [ 191. Yet, the radial distribution curve was interpreted as indicating an almost exclusive population of ax-Br-eq-Cl [20] . There is no evident reason for such an extreme equilibrium shift on passing to the vapour, inasmuch as the dipole and quadrupole moments [ 171 cannot be too different in the two conformers. Also, the geometries we computed differ appreciably from geometries assumed in the electron diffraction work, and the Br - - - Cl non-bonded distance comes out very close in the two forms. FORCE

FIELD

The formulation and constants of the basic hydrocarbon force field have been given [2]. Constants for bromides are listed in Table 1. Dipole moments are obtained as vectorial sums of bond moments at the optimized geometries. Electrostatic interaction is calculated by the point-dipole formula [ 231 and the local dielectric constant fixed at 4 [2]. The C-X and all C-H bonds are taken into account, as well as Cs--Ccl bonds (where C, carries the halogen). As justified elsewhere [4], calculation for dibromides is first performed with the listed value (~1~)of the C-Br bond moment. This furnishes a virtually final geometry, and the CBr/CBr electrostatic interaction (e:,) at that geemetry. The apparent C-Br bond moment (cl*) is then obtained from p*=pO-heo

es

*. The procedure works well both in cases and the calculation repeated with I_L of low and of high overall dipole moment. For example, in 2&3a-dibromo&-cholestane 1.35 D (cc* = 1.39) is obtained versus the experimental value of 1.39 D (CC14, 25°C [24] ); and in dihydrodibromocadinene 4.40 D is obtained (I-(* = 1.48) versus the experimental value of 4.20 D (C6H6, 25°C [25] ). The slight overestimation could be due to the accumulated effect of upwardrounding in our constants: in this molecule, the components in the dipole moment, owing to polarization in the C-Br, C-H and CP----Cabonds, are almost parallel. In gauche conformations of vicinal dihalides, w(BrCCBr) differs

147

TABLE

1

Force field for non-geminal bromidesa Exp. information used in fittingb Stretch C-Br

ks

10

Bend C-C-Br H-C-Br

kb 0.90 0.64

0, 108.8 105.6

Non-bonded=

E 0.30

r*

Br

Torsiond H-C-C-Br C-C-C-Br Br-C-C-Br

V, 0 0 1.31

Electrostntice e-G

IJo 0.33

b-k-

1.50

2.30

V, 0

V,

-0.40

0.05

1.943

(CH,),CBr

(G)

CH,CH,Br,

(CH,),CBr

(G)

2.04

C,H, , Br and its I-tertbutyi deriv. (E)

0.34

CH,CH,Br

1.36

C.$,

1.63 k

CH,CH,Br,

0.26

,Br WI

BrCH,CH,Br

(E) (E, G, DM)

Previous work CH,Br, ci~-1,2-C,H,~Br~, and 4-tert-butyl-trans-1,2dibromocyclohexane (DM) CH,CHICH ,Br (DM)

=For dimensions of constants see ref. 2. bG - geometry, E - relative energy of structural variants, DM - dipole moment. CHiIl equation [ 211 parameters, slightly different from the modified-Hill MM2 constants [S ] (0.32, 2.18). din the entire dihedral range (0 < w < 360” )_ =For the direction of p(CH) see ref. 22. Other bond moments obviously depend on this choice. For k, see main text.

significantly from 60” ; in di-axial cyclic structures, it is not 180’. Several data were therefore required in assigning the BrCCBr torsional constants. In a recent electron diffraction study of BrCH&H*Br [26], AE(g-a) was derived as ca. 2.2, higher than previous estimates, 1.6-l .7 kcal mol-’ [ 271. We chose to make the conformational energy come out in the range 1.81.9 kcal mol-’ _ The Br/H-syn barrier was assumed to be at 5.5-6.0 kcal mol-‘, in view of results from ultrasonic measurements on the liquid and in solution [28]. These choices, as well as w(BrCCBr) = 73” 1261 and the overall dipole moment

of the conformational

mixture,

are reproduced

by the listed

constants. We made an effort to detect and eliminate false minima. The technique developed, in default of literature antecedents, may be illustrated by reference to an extreme case. Optimization of a tial geometry for gg-BrCH&HzCHzBr led to a structure with E = 2.5590 kcal mol-’ , say I. The atomic coordinates of bromine and hydrogen atoms were then interchanged to produce a very distorted geometry of the enantiomer II. Re-optimization led to a new

148

geometry with a lower energy, 2.1497 kcal mol-’ , and back-iteration to I gave E = 2.1398 kcal mol-*. The components of the energy difference between the first and third minima are typical and instructive. In kcd mol-’ :

I

Stretch Bend and stretch-bend Non-bonded Torsion Electrostatic Total

II

E (first)-E -0.0028 -0.1568 0.0465 0.5582 -0.0199

(third)

0.42

Here, as in other cases encountered, the upper minimum is favoured by skeletal, the lower by non-bonded and torsional strain, and the passage incurs a rise in skeletal strain. Therefore, a standard trial geometry, with bond lengths and angles close to their expected values, is prone to converge into a false minimum. RESULTS

Computed energies, dipole moments and C-Br bond lengths are reproduced and compared with experiment in Tables 2 and 3. 1,6-Dibromo-1,5hexadiyne (Table 3, No. 34) was calculated by the alkyne force field [ 591, where L((C-H) = 0, p(=C-Br) = 0 (to reproduce the vanishing dipole moment of HCSZBr [60] ), p(C-C=) = 0.75 D, and local dielectric constant equals 1. This force field makes AE(g-a) in unsubstituted 1,5-hexadiyne equal to 0.66 kcal mol-’ , somewhat higher than in the dibromide. Judging by electron diffraction data [58,61], the trend is correct, but AE is somewhat underestimated in the hydrocarbon and somewhat overestimated in the dibromide. GEOMETRLES

Variability in the C-Br bond length has been noticed [35] but we are not aware of any systematic study. In CH&H2Br, I(CBr) - 1.950 A and B(CCBr) - 110.0” [30] ; in (CH&CBr, I(CBr) - 1.975 A [35]. To detect the cause for elongation, we adopted the strategy [62] of “turning off” various interactions one by one. With all interactions “on” in (CH,),CBr, I(CBr) comes out as 1.975 A and B(CCBr) = 108.4”. The sum of non-bonded H - - - Br interactions at this geometry is 0.7353 kcal mol-l , whereas it amounts to 0.1371 kcal mol-’ only in the optimized geometry of CH,CH2Br. When the non-bonded interactions of bromine were omitted (by setting to zero the

149

TABLE

2

Monobromides Molecule and structure=

Relative energyb

Dipole momentC

Calc.

talc.

Exp.

1. CH,Br 2. CH,CHZBr stg ccl

0 3.53

3. CH,CH,CH,Br g (70) a (180) 4. CH,CHBrCH, stg ccl

0 -0.24

0

Exp.

1.79

1.79

1.96

1.8-2.0

1.97

2.0-2.2

3.6 (MW)d

1.950 1.952 1.950 1.950

0

+O.l

Z(C-Br) talc.

(IR)=

f 0 1.84

5. CH,(CH,),B@ aa (180) ag (73) ga (175) gg (66) gg’ (92)

0.38 0.49

0

2.22 1.961 1.964 1.960

:.5 (IRP 0.6 2.19

2.21

1.99

1.99

4.31

-0.02

0.30 (IR) 2.19

0

0

0.29

1.4 (IR)

0

0

0.16 7.75 8.43

0.41 (NMR)

0

0

2.20

1.30 (NMR)“’

0 10.73 (NMR)”

1.975 1.977 1.951 1.950

0

k

0 11.26

1.961 1.964 1.950 1.951 1.950 1.950 1.952

2.10

8. (CH,),CHCH,Brj Br/Me-a (69, 168) Br/H-a (64)

12. (CH,),CBrC(CH,), stg (179, 62, 59) ccl (0,120,120)

2.17

0

0

11. (CH,),CCH,CH,Br Br/tert-Bu-a (180) Br/H-a (84)

1.97 0.37 0.60 0.86 2.66

7. (CH,),CBr’ stg ccl

10. (CH,),CBrCH(CH,),’ Br/H-a (66,63) Br/Me-a (166, 68) Br/H-syn (115,115) Br/Me-syn (0, 132)

2.21

0

6. CH,CHBrCH,CH, Me/Me-a (66) Me/Br-a (173) Me/H-a (66)

9. (CH,),CBrCH,CH, Br/H-a (64) Br/Me-a (179)

2.09

(2.27) 1.974 1.979

2.19

1.975 1.983 1.988 1.984

1.97

1.953 1.952

2.18

1.985 1.992

150 TABLE Molecule

2 (continued) and structure=

Relative talc.

energyb Exp.

13. C,H,Br (C, sym.) ax-Br (83) eq-Br (158)

0 0.77

0 0.61 (IR)p

14. C,H, ,Br eq-Br (178) ax-Br (73)

0 0.47

0 0.47 (NMR)q

15. 4-Tert-butyI-l-bromocyclohexane eq-Br (tram, 179) ax-Br (cis, 73)

0 0.39

16. 4,4-Dimethyl-lbromocyclohexane eq-Br (178) ax-Br (73)

0 0.48

Dipole talc. 2.12

momentC Exp.

I( C-Br talc.

)

2.21 1.959 1.954

2.10

(2.2) 1.961 1.961

2.13 2.16

(2.25) (2.19)

1.961 1.962

2.13 0 0.40 (NMR)=

1.960 1.961

=,(CCCBr) in parentheses. method in parentheses; bEnergies in kcal mol-’ . Experimental limits of accuracy not cited. cIn Debye. Experimental results from ref. 29 unless stated otherwise_ Solution values in parentheses. dRef. 30. By far-IR [31], barrier 3.72 kcal mol-’ _ eRef. 12 (10.2). See Introduction. fFor experimental geometry (MW) see ref. 32. sLeft symbol, butane conformation; right symbol, bromopropyl conformation; gg’ is BrlCY-syn. Computed populations (% at. 25°C): aa, 30; ag, 33; ga, 22; gg, 15; gg’, 0. Experimental (ED [33] ): 36, 24, 24, 16, 0, respectively. For solution data see ref. 34. hIn liquid [ 28 1. iFor recent work see ref. 35. ‘Br/Me-a (“gauche”) is calculated to be less stable but still more abundant (66% at 25°C) than Br/H-a. Experimental results from ref. 28 kCalculated energies correspond to 77% Br/H-a (“ga&ze”) at 25°C. Experimental res&s from ref. 36. ‘Calculated energies correspond to 61% Br/Me-a (“gaUche”) at 25°C. Experimental results from ref. 37. *Ref. 38. “Free energy 1391. Pin liquid [40 1. qIn solution [41]. ‘In CS, [42].

Hill equation 1211 parameter e(Br)), optimization of (CH3)&Br led to Z(CBr) = 1.947 A (too short) and B(CCBr) = 107.2” (probably too small). The sum of non-bonded interactions at this geometry would amount to 2.8021 kcal mol-’ , of which 2.2452 kcal mol-’ is due to H - - - Br. In a subsequent calculation, E(Br) was revived but the stretch-bend interaction eliminated. This gave I(CBr) = 1.972 (almost correct) and B(CCBr) = 108.4” (probably acceptable). One con/eludesthat the primary cause for C-Br stretching is non-bonded strain. Elongation in (CH&CBr alleviates repulsion by ca. 1.5 kcaI mol-’ , and even permits some further saving by a concomitant relaxation in HCH bond angles. This more than compensates for the stretching-strain incurred, ca. 0.15 kcal mol-‘. Data in Tables 2 and 3 suggest that I(CBr) is ca. 1.95 A for a primary carbon, 1.96 a for a secondary, 1.97-1.98 A for a tertiary; it is about

151 TABLE

3

Dibromides

17. BrCH,CH,Brd a(180.180) g (73.83) Br/H-sun Br/Br-syn

Relativeenergyb

Dipole moment=

talc.

talc.

Exp.

0.85 0 2.49

0.81 0 2.23

0

1.85 5.76 10.39

EXP.

0

1.6-2.2

X~.B~CH,CH~I-CH,~ Br/Br-a(170.171) Br/H-a(67.78) Br/Me-a 19_CH,CHBrCHBrCH,(meso a(180.180) g(68.79) Br/H-syn Br/Br-syn 20.CH,CHBrCHBrCH,
Br/H-a(62. 75) Br/Me-a(64. 74)

1.07 (25OC) 1.23 (81°C) 0.61 2.66 2.86

0 1.67 1.71

1.51 1.00 2.75 3.24

(1.62jg

0 1.07 1.82

0 1.73

1.09 (25OC) 1_27(8O"C) 0.58 3.00

1.4-1.5 (IR) 6.43(US)

21.
1.33 Aboveaa

23. Imns-1,2-Dibromocyclohexane aa(161. 162) ee(63.74)

0 0.82

24. trams-1.2-Dibromo4-tert-butylcyclohexane aa(161.162) ee(62.74)

0 0.89

for 2.3-dibromo5wcholestanek aa(149.151)

0

1.67 (IR)h

3.12

0

0.8 (NMR+

1.951

1.950.1.963 1.951. 1.960 1.952.1.963 (l-73+

0

1.949

1.13

1.05 0 2.96

0 1.57 8.60 13.57

Z(C-Br) talc.

1.966 1.962. 1.964 1.966 1.970 1,964 1.962 1.968 1.16 1.951. 1.982 1.952.1.976 (3.12)

1.960 (es) 1.964(H)

1.97(176°C) 1.09 3.24

2.00. 1.15? 3.28'

1.964 1.965

1.13 3.28

1.19 3.28

1.963 1.964

1.35 3.16

1.39 3.42

1.963.1.967 1.964.1.967

1.00

(1.36)

25. Model

ee(66.76)

0 -0.79

26. tram+1.2-Dlbromo1-methylcyclohexane aa<168.168) ee(65.76)

27.cis-1.3-Dibromocyclohexane ee(-, 110) aa+-. 27) 28.tmns-1.3-DibromocycIohexane(-,114) 29.cis-1,4Dlbromocyclohexane(-_.82)

0 1.73

0

3.08 0.39 Aboveee

(1.45)1

0 Largem

0.70 3.24 2.15 2.15

1.962. 1.966 1.982. 1.963

(2.17)" 1.960

3.86

1.960

2.40

(2.19)

1.961

2.71

(2.89)

1.960

152 TABLE

3 (continued)

Molecule

and structurea

Relatwe talc.

30. trons-1.4-Dibromocyclohexane aa (-. 180) ee (-. 180)

-0.76

31. cis-1-Bromo-4chlorocyclohexaneq eq-Br-ax-Cl (--_. 82) au-Br-eq-Cl (-_. 81)

-l-O.25

energyb EXP.

34. BrC=-CH,CH,GXBr a (-. 180) g (--. 77)

talc.

0 0

0.19 0.29 2.73 0

0.62

I(C-Br) talc,

Exp.

0 1.960 1.960

0 (IRjP

2.81 2.77

0

0

moment=

0

32. Dlhydrotibromocadinener (-_. 14) 33. BrCH,CH,CH,BS aa <-. 111) ag (-. 113) gg (-. 118) gfz’ (-. 30)

Dipole

(1.6) (1.0) (O-0) (Large) 0

(0.3-0.4)t

1.961 1.961

4.41

(4.20)

1.98 1.62 1.96 2.22 3.52

(1.96)

1.978. 1.951 1.950 1.950 1.950 1.789 1.789

0

1.70

=In parentheses w(BrCCBr) and x(CBr/CBr). bSee Table 2, footnote b. CSee Table 2, footnote c. dFor references and recent work see ref. 26. Dipole moment, calculated and experimental [43], at 66°C; estimate for gauche in ref. 44. For barriers, see refs. 28,45. eCalculated energies correspond to 11% of gauche forms (Br/H-a and Br/Me-a) at 25°C and 16% at 81°C. For experimental estimates and solution dipole moment see refs. 46, 47. Experimental moment from ref. 48, where AE(ga) is estimated as 1.25 kcal mol-’ . fExperimental energies [49]. gOf liquid, from dielectric constant [50]. hRef. 28. iExtrapolation of solution data [17, 183. For recent work see ref. 51. ‘Of corresponding dibromodecalin. kOnly rings A, B and 18-Me included in calculation. Experimental dipole moments (Ccl,, 25°C) from ref. 24. ‘Free energy from combined NMR and dipole-moment study [ 521. Experimental dipole moment in Ccl,. mRef. 53. “In heptane [54]. PRef. 16. Extrapolation of solution data [ 171 leads to large positive number. qSee Introduction. rExperimental [ 251. SOther calculations [55, 561. Experimental [55 ]. Critique (573. tEstimated roughly from electron diffraction populations in ref. 58. See Results.

1.95 A in l-bromoadamantane [35] (not reproduced by our field) and 1.93 A in bromomethane [63 1. One also notes a small difference between equatorial and axial C-Br bonds, the latter being more often longer. This is interesting, because the elongation of axial C-X bonds in Z-halotetrahydropyrans [64] has been taken as evidence for C-O/C-X interaction (anomeric effect [ 651); one now sees that some contribution to the effect may be more

fundamental. In cis-1,2-dibromocyclohexane

(No. 22), equatorial C-Br

is

calculated to be 1.960 A, the axial as 1.964 A, corresponding to a stretching energy of 0.048 + 0.070 = 0.118 kcal mol-‘; the Br - - - Br distance and nonbonded interaction are 3.480 A and 0.5483 kcal mol-’ , respectively. When bromine non-bonded interactions are suppressed, the axial bond shrinks to 1.945 A, and the equatorial to the reference value, 1.943 A ; the Br - - - Br distance is then 3.283 A. Elongation, here also, is mainly due to non-bonded repulsion.

1.981

153

As for dihedral angles, one notes that the value of 180” is adopted only if

imposed by symmetry, and that 60” is approached only occasionally. In the past it was taken for granted that the XCCY angle in di-axial trans-1,2-&H,,,XY is 180” [66] ; it was later realized, also from crystallography of cognate molecules [67],

that it must be lower [68], but the cause for deformation remained obscure [17]. The large XCCY angle in g-XCH2CH2Y has been interpreted as being due to X - - - Y non-bonded repulsion [69] . A large XCCY angle in di-equatorial trans-1,2-CdHloXY has been predicted for similar reasons [70], but this is not substantiated by calculation (nor expected on experimental grounds [67] )_ We performed molecular-mechanical optimizations, with “turned off” interactions, on three molecular species: g-BrCH,CH,Br, di-equatorial and di-axial trans-1,2dibromocyclohexane_ Results are shown in Table 4. The control calculations (b) and (c) are cited as a check that the results in (a) were not artificially imposed by the choice of the torsional or electrostatic formulations. It is calculation (d) that calls attention again to the interplay of non-bonded and skeletal strains. Strikingly, non-bonded Br - - - Br repulsion favours the closing, not the opening, of w (BrCCBr) in ax,ax-C,H,J3rz ; when repulsion is suppressed, the angle reverts to 174”, which is roughly the H(ax)CCH(ax) diheder in cyclohexane. Closing of BrCCBr makes C-Br bonds stretch (energy loss) and, consequently, the Br - - - Br non-bonded distance increases (energy gain). The balance set is obviously limited in range: for angles small enough, both the non-bonded and stretching strain would go up. Our non-bonded Br - - - Br energy function has a minimum at 4.11 a and becomes positive at 3.65 R. An estimation of dipolar angles, x, is sometimes required from the corresponding dihedral angles, w [71]. In Table 3 both w (BrCCBr) and x(CBr/CBr) are listed. A regression analysis yields cos x - 0.87 cos w - 0.13, which applies to within 1.5” throughout the range. The only exception is the highly distorted Br/Br-a conformer of (CH,),CBrCH2Br (No. 21), where B(CCBr) = 107” (tertiary) and 113” (primary). For comparison, the angles in mesoCH3CHBrCHBrCH3, Br/Br-a, are 108” (external) and 110” (internal). TABLE

4

Calculated geometrical parameters

(a) All interactions, w r(Br - - - Br) I( C-Br ) (b) No BrCCBr torsion, pi (c) No C-Br electrostatic, (d) No Br non-bonded, w r(Br - - - Br) I( C-Br )

W

@2-&Br,

ee-C,H, .Br2

aa-C,H,.Br,

73 3.660 1.951 72 73 76 3.586 1.943

63 3.511 1.965 62 62 68 3.466 1.943

161 4.654 1.964 161 161 174 4.604 1.943

154 ENERGIES

In many cases, the force field reproduces known conformational tendencies or barriers to internal rotation (Tables 2 and 3, Nos. 2, 5, 6, 10-14, 16, 17, 19, 21, 23, 26, 27, 34). In some cases, numbers are not available for comparison (Nos. 4, 7, 15, 18, 20, 24, 25). There are cases in which computation is at evident variance with experiment. Excepting No. 31, where the previous analysis could be at fault [19, 201, and No. 30 (see Introduction), ail discrepancies concern AE(g-a) in derivatives of l-bromopropane (Nos. 3, 8, 9, 33): in some instances, not all, gauche forms are more stable than calculated. This deficiency is not specific to this field [ 55, 561. It suggests the operation of “non-classical” [4] attractive gauche effects that have as yet eluded inclusion in the force-field formalism. We wondered why the d&axial conformer is preferred in trans-1,2dibromocyclohexane (No. 23), given that the equatorial form is the more stable in the monosubstituted six-membered ring [ 70]_ A “repulsive gauche effect” has been invoked to cover this and germane “counter-intuition” occurrences 1721. It seems to us that the relationship is puzzling only as long as one views C6H1,-,BrZas a superposition of two &H,,Br units. it ceases to be so if the molecule is viewed as a cyclic derivative of 1,2-dibromoethane. In the latter, the an fi conformer (which corresponds to di-axial) is far more stable than the gauche_ Cyclization affects the local geometry, as already discussed, and also the conformational energy, but cannot reverse the order of stability. This is because the primary preference of anti to gauche (that is, di-axial to d&equatorial) is strong with respect to the relative stabilization of equatorial in cyclic structures. Using numbers from Tables 2 and 3 (Nos. 14, 17) the ex~~odU?(ee-aa) value in C6H,,,Br2 is of the order of 1.8 - 2 X 0.5 = 0.8 _ This is roughly what we calculated (No. 23). Finaily, note again [6] that a tert-butyl grouping at position 4 on cyclohexane would stabilize an axial substituent at position 1. The conformational energy is consequently lower in case 15 than in case 14 (Table 2) and higher in case 24 than in case 23 (Table 3). Examination of the numbers indicates that this is yet another manifestation [ 581 of bromine non-bonded attraction. CONCLUSION

We have described a molecular-mechanical force field for monobrominated

and non-geminal dibrominated alkanes and cycloalkanes. The field provides conformational energies, geometries, and dipole moments. It is compatible with the basic hydrocarbon force field, and with previously reported fields for fluorides and chlorides. A survey of recent literature discloses that interest in the geometry and conformation of bromohydrocarbons is at the moment subsiding (see ref. 73!). Computation has led us to touch on several topics where knowledge is still fragmentary or inconclusive: variability in C-Br bond lengths and in

155

dihedral angles, manifestations of non-bonded attraction and repulsion, repulsive versus attractive “gauche effect”, conformational equilibria in unsymmetrical 1,4-cis-disubstituted cyclohexanes, and more. The foregoing discussion and numerical examples may serve to recall attention to these open su bjeck APPENDIX:

NOTATION

ax - Axial, eq - equatorial, aa - di-axial, ee - di-equatorial, g -gauche, a - anti (as distinct from gauche), stg - staggered, ccl - eclipsed. In preference to the “PST notation” 1743 conformations are codified by specifying groups crntito each other (e.g., the meso-conformer Br/Br-a in mesoCH3CHBrCHBrCH3), and eclipsed structures by specifying groups syn to each other (that is, eclipsing; e.g., the two barriers to internal rotation, Br/Br-syn and Br/H-syn, in BrCH2CH,Br). I- Bond length, r - non-bonded distance, 8 - valence angle, w - dihedral angle (between planes), x - dipole angle (between vectors), ,u - bond moment. ACKNOWLEDGEMENT

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