Calculations of induced dipole moments: adamantane derivatives

Journal of Molecular Structure, 197 (1989) 361-366

361

Elsevier SciencePublishersB.V., Amsterdam-- Printed in The Netherlands Short communication

C A L C U L A T I O N S OF I N D U C E D D I P O L E M O M E N T S : ADAMANTANE DERIVATIVES

LJIIAANA DOSEN-MICOVIC Institute of Chemistry, Faculty of Science, University of Belgrade, P.O. Box 550, YU-11001 Belgrade (Yugoslavia)

OTTO EXNER Institute of Organic Chemistry and Biochemistry, Czechoslovak Academy of Sciences, 166 10 Prague 6 (Czechoslovakia)

(Received29 September1988)

Electron distribution on a given bond is to a first approximation independent of its environment as expressed, for example, in the concept of natural bond orbitals [ 1 ] or in empirical calculations of dipole moments from bond moments [2]. However, deviations from this principle are observed even in nonconjugated compounds [2 ] and are explained in terms of electrostatic induction [2-6 ]: a polar bond induces a m o m e n t within the hydrocarbon residue and the observed dipole moment increases. When two polar bonds are present, they influence each other and the total dipole moment is usually reduced. Calculations of these effects were attempted on several levels. The classical SmithEyring (SE) approach [3,4] takes into account only polarization by adjacent atoms, when the charge distribution is controlled solely by molecular topology. Allinger's Modified Smith-Eyring (MSE) procedure [5,6 ] also includes polarization by non-adjacent dipoles through space. The Induced Dipole Moment and Energy (IDME) method [7] considers, in addition to longitudinal polarizability, transversal and vertical polarizabilities. For this reason charge distribution must be represented in terms of bond moments instead of atomic charges. When the dipole m o m e n t has been measured in solution, the reaction-field theory [ 6,8-10 ] may be applied. A dissolved molecule is treated [ 11 ] as a point dipole located in the centre of a spherical cavity ( radius a) within a continuous dielectric medium. The dipole polarizes the surrounding matter, producing the reaction field R which in turn polarizes the solute molecule. The modified di-

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362

pole/~* is given by eqn. (1) where c~ is the average molecular polarizability. The theory was extended to the eccentric position of the dipole within the cavity [12,13], eqn. (2). Here k=o~/aa= ( n 2 - 1 ) / ( n 2 + 2 ) , where n is the refraction index and x can be calculated [12,13 ] according to eqn. (3), from the dipole position (distance from the centre s, angle 0) [26] and from the permittivities e and Eo outside and inside the cavity, respectively

/~*= ~+ ~R

(1)

~*=~/(1-kx)

(2)

e-Co eo(2e+eo)

~ eolWe(l+l) cos 20 2e+eo 2 l=o

+ ( 1 - c o s 2 0) ~ t = o

col+e(/+1)

(3)

The goal of the present communication is to apply the above theories to adamantane derivatives whose rigid system is advantageous for both calculations and experiments [14-17]. In particular the following two facts are to be interpreted. Firstly, the experimental dipole moments of 1,3-dihaloadamantanes (II) and 1, 3, 5-trihaloadamantanes (III) are somewhat smaller than expected according to the additivity rule starting from adamantane mono derivatives {I). This effect, observed for the first time for such a long distance [14], was of course much smaller than in gem-dihalo- or trihalo-derivatives [2], and even smaller than in aromatic meta derivatives [ 18 ]. Nevertheless, it was measured on four compounds (IIa, b and IIIa, b) in two solvents. In a previous paper it was suggested [ 14 ] that the controlling factor is electrostatic induction rather than distortion of geometry. Secondly, the dipole moments of adamantane mono derivatives themselves (not only with halogens) were consistently larger [15,16] than those of corresponding aliphatic derivatives, including tert-butyl. This is understandable in terms of polarization, but the still larger dipole moments of diamantane derivatives IV and V can hardly be explained by polarization over such a long distance. It was suggested tentatively [16 ] that the fundamental theoretical assumption of the dipole in the centre of a cavity is no longer valid for such large molecules. However, the author has been unable to find additional examples [19,20].

363

X

I

X

X

~

X

~

IW

V-

~:

x=

CI

b:

x=

Br

B e f o r e a p p l y i n g t h e I D M E m e t h o d to m o l e c u l e s I - I V it w a s n e c e s s a r y to obtain their geometry by molecular mechanics. Here, the extensively used MM2 force field [21] was applied. As a r e s u l t o f t h e s e c a l c u l a t i o n s b o n d angles were o b t a i n e d w h i c h differed o n l y i n s i g n i f i c a n t l y f r o m t e t r a h e d r a l . T h e l a r g e s t dev i a t i o n ( + 0.15 ° ) was on t h e s e c o n d a r y c a r b o n of I I , b e t w e e n t h e t w o t e r t i a r y c a r b o n s b e a r i n g C1. T h i s c o n f i r m e d t h e a u t h o r s ' o p i n i o n [16] t h a t a n g l e def o r m a t i o n s are n o t r e s p o n s i b l e for t h e o b s e r v e d effects. Actually, c a l c u l a t i o n s w i t h t h e M M 2 g e o m e t r y , b u t still b a s e d on t h e p r i n c i p l e o f c o n s t a n t b o n d m o m e n t s , differ quite i n s i g n i f i c a n t l y f r o m t h o s e w i t h t e t r a h e d r a l g e o m e t r y ( T a ble 1, t h e first t w o lines): t h e t r e n d of e x p e r i m e n t a l values is n o t r e p r o d u c e d . O n t h e o t h e r h a n d , all m e t h o d s b a s e d o n e l e c t r o s t a t i c i n d u c t i o n reflect t h i s t r e n d at l e a s t q u a l i t a t i v e l y ( T a b l e 1, lines 3 to 5). P a r t i c u l a r l y s i g n i f i c a n t is t h e d i f f e r e n c e b e t w e e n I a n d I I I , t h e dipole m o m e n t s o f w h i c h s h o u l d be e q u a l a c c o r d i n g to t h e b o n d m o m e n t s c h e m e . B e s t r e s u l t s w e r e o b t a i n e d w i t h t h e TABLE 1 Comparison of calculated and experimental dipole moments of adamantane chloro derivatives Ia-IIIa

Method of calculation

Geometry

Bond moments Tetrahedral Bond moments MM2 SE Tetrahedral IDME c MM2 IDME a MM2 Experimental in CC14e Experimental in benzene e

Dipole moment of

Moment of one C-C1 bond" in

Ia

IIa

IIIa

IIa

IIIa

1.94 1.94 2.42b 2.47 2.32 2.40 2.49

2.24 2.24 2.77b 2.77 2.60 2.70 2.82

1.94 1.94 2.37b 2.36 2.19 2.25 2.37

0 0 -0.02 -0.08 -0.07 -0.06 - 0.05

0 - 0.01 -0.05 -0.16 -0.13 -0.15 - 0.12

"Relative values with reference to the C-C1 bond moment in Ia calculated by the same method; contributions from the induced dipole moments are included, bRef. 16. cParameter Vc_c~= 0.56, as in ref. 7. aWith the improved parameter Vc c~--0.6, eRef. 14.

364

IDME approach when the parameter Vc-c~ was slightly corrected to 0.6, replacing the original value [7] of 0.56. This correction has been substantiated by other examples [22]. Most striking is a comparison of relative values: the dipole moments were recalculated to the idealized dipole of one C-C1 bond, including all induced contributions, and these values were referred to the C-C1 bond moment of 1-chloroadamantane (Ia), always calculated by the same method. The results are given in the last two columns of Table 1. For the improved version of IDME they agree extremely well with experiment and reveal that this approach is about to reproduce even quite small effects if relative values are compared. The dipole moments of monohaloadamantanes and diamantanes are best compared in a broader context (Table 2). Both SE and IDME reproduce the general trend well, although SE particularly overestimates the tertiary derivatives. Dipole moments generally increase with the size of molecule but its shape is also of importance: vicinal C-H bonds seem to increase the C-C1 dipole in the gauche orientation but decrease it in anti. A more detailed examination is prevented by two facts: the experimental values were measured in solution and some of them are suspected of containing errors (e.g. AdC (CH3)2C1 compared to AdCH (CH3) Cl). Excluding two compounds, AdC (CH3) 2C1 and TABLE 2 Calculated dipole m o m e n t s a n d their increase in solution Compound

CH3C1 C2H~C1 (CH3)2CHC1 (CH~)3CC1 (CH~)3CCH2CI [ (CH3)3C]2CHC1 c-C6HllCl(e) AdC1 ( l a ) AdCH2C1 AdCH (CH3)CI AdC (CH3)2C1 IVa Va

~tc,lc. SE a

IDME b

1.86 2.02 2.15 2.25 2.12 2.31 f 2.27 2.42 2.08 2.19 2.29 2.47 2.43

1.85 1.99 2.05 2.07 1.97 1.87 2.25 2.32 2.05 2.01 1.95 2.18 2.43

s/a

tt* / tt c

#exp. a

#exp. corrected e

0.147 0.202 0.174 0.147 0.333 0.204 0.360 0.350 0.455 0.428 0.399 0.322 0.457

1.04 1.04 1.05 1.04 1.07 1.05 1.08 1.10 1.15 1.12 1.12 1.11 1.19

1.69, 1.88 1.89 2.06, 2.12 2.14 1.97 1.89 f (2.18) g 2.55 a 2.02 2.16 1.75 2.76" 2.79"

1.63, 1.81 1.82 1.96,2.02 2.06 1.84 1.84 (2.02) g 2.32 1.76 1.93 1.56 2.49 2.34

"Ref. 16. bWith Vc cl =0.6. t i n benzene, e = 2.27. din benzene, ref. 23. eThe experimental value divided by the factor tt*//~, f T h i s work, the experimental value determined in benzene by the H a l v e r s t a d t - K u m l e r m e t h o d (ref. 24), o~--2.30, fl= - 0 . 0 3 1 , po = 124.3 cm 3, RD (calc) = 4 8 . 7 cm 3, PA 5%. gDipole m o m e n t of a conformational mixture.

365 IVa, the I D M E dipole moments depend reasonably linearly on the experimental values with a slope of 0.6 which is, however, determined essentially by the compounds I a and Va. To explain the behaviour of a d a m a n t a n e and diamantane derivatives in particular reference is made to reaction-field theory with the eccentric dipole [12,13 ]. In Table 2 this eccentricity is represented by the ratio s/a and the results according to eqns. (3) and (2) are given by the ratio #*/#. Since #* represents merely an apparent dipole m o m e n t as obtained by measurements in solution, the "corrected" values were calculated (Table 2, last column) to be compared with the I D M E calculations. The comparison suffers from deviations for the same compounds as in the case of uncorrected values but the slope has increased from 0.6 to 0.9, approaching the required value of unity. It follows t h a t the theory describes at least qualitatively the effect of the eccentric dipole in solution measurements. Also, the view [16] was corroborated t h a t the unusually large dipole moments of compounds IV and V, possibly also of I, are essentially artifacts, due to the size and shape of the molecules which are not strictly compatible with the assumptions of Debye theory. A search is underway for further examples of this behaviour [25 ]. ACKNOWLEDGEMENTS T h a n k s are due to Dr. H.-D. Beckhaus, Freiburg i. Br., for making available the M M results on the geometry of I I and III, essentially identical with the present ones.

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