Rate-determining cooperative effects of bimolecular reactions in solution

An expression for the rate constant of condensed-phase bimolecular reactions is derived. The key feature of the proposed model is the formulation of the energy-dependent rate constant in terms of the diffusion rate and the ratio of the volume in phase space that leads to product over the total volume. The dependence of the bimolecular rate constant by the reduced barrier x = E thermod/kT is given in explicit form in terms of the incomplete and the complete gamma functions of Euler. The performance of the proposed model is tested against the experimental rate constants for the Menschutkin reaction by fitting the parameters of the expression for the rate constant to experimental data at various temperatures. The potential energy barrier obtained from the regression (16.75 kcal mol-1) is close to the independently computed value at the CPCM B3LYP/CRENBL.6-311(+)G(d) level of theory (16.84 kcal mol-1). The corresponding fitting to the transition state theory expression affords the lower value of 14.65 kcal mol-1.