Strain and structural effects on rates of formation and stability of tertiary carbenium ions in the light of molecular mechanics calculations

Abstract

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.

Gas-phase stability of tertiary carbenium ions and rates of solvolysis of tertiary derivatives

“…They refer to average values for bromides. 3,4 Figure 1 shows that the ICR data collected from olefin protonation (filled circles) are in reasonable agreement with the DPA line, although there is some scatter. 7 The ICR data for bromide exchange are in column 4.…”

“…2,4 In addition, the tertiary neopentyl derivative 5, which should be far less subject to nucleophilic solvent assistance, 13,14 solvolyses also at an enhanced rate, although the deviation is much less pronounced than in the case of tert-butyl (9). The rate ratio for solvolysis of 1-adamantyl vs. tert-butyl (2-methyl-2-propyl) derivatives varies from ca 1:5000 in EtOH 10 to 1600 in MeOH 11 and 1:2.4 12 in 97% aqueous HFIP.…”

“…Early empirical force-field calculations have been used to rationalize the structural effects on the rate constants of solvolysis in terms of strain changes between the bridgehead compound and the developing carbenium ion, which was assumed to be close to the transition state of the reaction in terms of energy and structure. 3,4 The observation of rearrangements occurring during the ICR experiments casts doubt on the entire set of data obtained by this method. In order to remedy this situation, we determined the stability of bridgehead-and bridgehead-like tertiary carbenium ions by ion cyclotron resonance (ICR) techniques.…”

“…The data are collected in Table 1. 4 The equilibrium data for olefin protonation afford gas-phase basicities (GB) from which proton affinities (PA) may be derived. (1).…”

“…All energies are expressed as Gibbs free energies in kcal mol À1 (1 kcal = 4.184 kJ) relative to 1-adamantyl according to Eqn. Enthalpies of formation of the carbenium ions can be calculated provided the enthalpies of formation of the olefins are known [DH f o (MH ) 3,4 Originally, the ICR data were reported as enthalpies and are, therefore, not strictly comparable to the DPA results in column 3. The DPA data in column 3 are from Ref.…”