Semi-empirical calculation of rates of S_N2 Finkelstein reactions in solution by a quasi-thermodynamic cycle

Abstract

Free energies of activation for the reactions:

              Nu^-+MeX → MeNu+X^- (Nu = nucleophile, X = halogen)

are calculated by a quasi-thermodynamic cycle. The six steps involved are: (i) desolvation and escape into the gas phase of MeX; (ii) desolvation and escape of Nu^- ; (iii) loss of an electron from Nu^-; (iv) combination of Nu^.(g) with MeX(g) to form a methyl radical transfer 'transition state'; (v) placement of an electron on the 'transition state'; (vi) transfer of the anionic transition state from the gas phase to the solvent. The BEBO method is used to calculate the energetics of step (iv), and the BEBO exponents for various Nu and X are calculated from the measured or estimated rates of the symmetrical halide exchanges X^-+MeX and Nu^-+ MeNu. The energy of the system is plotted as a function of the fractional bond orders of the Nu...C and C...X partial bonds, and ΔG^‡ is identified with the maximum value of this energy. An excellent correlation of calculated against experimental results is found for reactions in water and methanol, whilst interactions between polarizable HCONMe₂ and polarizable S_N2 transition states lead to small but regular discrepancies in HCONMe₂. Observed nucleophilic and leaving group orders of reactivity are reproduced, as is the lack of a correlation between reactivity and selectivity. The computed transition state bond orders do not concur with predictions based on the Hammond postulate.