An empirical MM2 force-field was developed for the calculation of steric or strain energies of carbenium ions, and applied to the rationalization of the rates of solvolysis of bridgehead derivatives. The latter constitute a homogeneous series of model compounds for solvolysis, spanning a rate range of ca 20 log units. Their rate constants correlate with the calculated steric energy differences between bridgehead bromides and the corresponding carbenium ions. The rate constants of tertiary derivatives of general structure may similarly be rationalized in terms of strain changes, although the correlation exhibits more scatter than that for the bridgehead derivatives alone. In the bridgehead series, the relative free energies of activation for solvolysis correlate with the heterolytic bond dissociation energies D"(R + -Br-) in the gas phase. However, this correlation breaks down when simple mono-and acyclic substrates are included. This is attributed in part to the proximity of the leaving group in the transition state of solvolysis, which stabilizes the developing positive charge at the cationic centre in comparison with the charge of the free ion. The significance of the force-field calculations with respect to the structure of bridgehead carbenium ions was tested by comparison of structural data obtained from ab initio calculations. The structures of cations suffering strong distortions owing to C-C hyperconjugation are poorly reproduced by the molecular mechanics calculations, the parameters of which are based on solvolytic reactivity and not on carbenium ions.

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(1 6.VIII.91) Force-field parameters have been developed for the molecular-mechanics calculation of tertiary carbenium ions with tricyclane structure, for tertiary cyclobutyl and cubyl cations. The cyclobutyl parameters are also applicable to tertiary 7-norbornyl cations. Satisfactory plots are obtained for correlation of the rates of solvolysis with the differences in steric energies between carbenium ions and the corresponding bromides.Introduction. -Bridgehead derivatives constitute a mechanistically homogeneous series in solvolysis reactions. Their solvolytic reactivity has been investigated systematically by Schleyer and coworkers [I-31. The reactions were found to be dominated by strain changes upon change of hybridization of the reacting C-atom from sp3 to sp2 in going to the transition state. These strain changes were calculated by molecular mechanics [3], and they were successfully correlated with the experimental rate constants (log k ) for solvolysis of bridgehead chlorides, bromides, p -toluenesulfonates, and trifluoromethane sulfonates. The solvolytic reactivity of bridgehead derivatives varies enormously with the structure of the substrate, and it is impossible to measure the rate constants with one and the same leaving group and under identical experimental conditions. For quantitative strain-reactivity correlations, a uniform reactivity scale is a prerequisite. Such a reactivity scale has been set up. Bentley and Roberts [4] have critically established rate constants for several bridgehead derivatives with different leaving groups. It was found that relative rate constants in the series are almost independent from the leaving group and the solvent, and subsequently to this observation, correction factors for solvent and leaving group changes (chlorides, bromides, p-toluenesulfonates, and trifluoromethane sulfonates) have been proposed. A reactivity scale for standard conditions (TsO leaving group solvolyzing at 70°in 80 % aq. EtOH) spanning a rate range of 22 log units was established. Similarly, conversion factors for p -nitrobenzoate solvolysis and for acid-catalyzed dehydration of tertiary alcohols in the bridgehead and nonbridgehead series have been determined by using linear free-energy relationships [5]. The extrapolated rate constants, when taken from different conditions, agree in general within 0.5 log units.The original strain-reactivity calculations for bridgehead derivatives were carried out with a preliminary force field which was later abandoned. More recently the strain calculations of Schleyer have been repeated with a carbenium ion force field similar

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