Inclusion of quantum-mechanical vibrational energy in reactive potentials of mean force

Classical molecular dynamics and Monte Carlo simulations typically exclude quantum effects on the vibrations of reactants and transition states, and this may lead to significant errors in the computed potential of mean force. To correct this deficiency, a simple approximate procedure is proposed for the inclusion of quantum-mechanical vibrational energy in the computation of reactive potentials of mean force in condensed phases. The method is illustrated by a hydrogen atom transfer and a proton transfer reaction in water, in particular, the 1,5-sigmatropic shift in malonaldehyde and the intermolecular proton shift between ammonium ion and ammonia in an encounter complex. In both cases, quantum-mechanical vibrational energy makes significant contributions by reducing the free energy of activation by 2 to 3 kcal/mol. This finding has important implications in developing empirical potential functions for the study of enzyme reactions, and it is essential to quantize vibrational energy in the computed potential of mean force and free energy of activation in order to compare simulations quantitatively with experiment.