Direct Dynamics for Free Radical Kinetics in Solution:  Solvent Effect on the Rate Constant for the Reaction of Methanol with Atomic Hydrogen

We calculate the rate constant for the reaction •H + CH3OH → H2 + •CH2OH both in the gas phase and in aqueous solution at 298 K. To accomplish this, we apply two different methods to estimate the electronic energies along the reaction path. First, we use specific reaction parameters (SRP) to mix the exchange and correlation energies in Becke's adiabatic connection theory (AC-SRP) to optimize the model for the specific bond-breaking, bond-making combination under consideration. Second, we obtain the potential energy using a linear combination of the Hartree−Fock method and AM1 with specific reaction parameters (HF||AM1-SRP); in this linear mixing method, eight NDDO parameters and the linear mixing parameter are simultaneously optimized by a genetic algorithm. To calculate the reaction rate constants in solution, the solute atomic charges are represented by class IV charges, the electric polarization of the solvent is determined from the electronic charge distribution of the solute self-consistently, and the solute electronic, solvent electric polarization terms are augmented by first-solvation-shell terms calculated by the SM5.42 solvation model. Reaction rate constants of the hydrogen transfer reaction and the kinetic isotope effects are studied both in the gas phase at 200−2400 K and in aqueous solution at 298 K. The AC-SRP and HF||AM1-SRP methods, although quite different, give qualitatively similar pictures of the reaction at the separable equilibrium solvation level; however, it is found that a full equilibrium solvation path (ESP) calculation, which involves optimization of structures along the reaction path in the presence of solvent, is essential to reproduce the speedup of the reaction due to solvation. The final calculation, based on the HF||AM1-SRP electronic structure calculations and ESP dynamics with variational transition state theory in curvilinear coordinates with the microcanonical optimized multidimensional tunneling approximation, agrees well with experiment not only for the speedup due to the solvation but also for the •D + CH3OH and •H + CD3OH kinetic isotope effects.