Quantum instanton approximation for thermal rate constants of chemical reactions

A quantum mechanical theory for chemical reaction rates is presented which is modeled after the semiclassical (SC) instanton approximation. It incorporates the desirable aspects of the instanton picture, which involves only properties of the (SC approximation to the) Boltzmann operator, but corrects its quantitative deficiencies by replacing the SC approximation for the Boltzmann operator by the quantum Boltzmann operator, exp(−βĤ). Since a calculation of the quantum Boltzmann operator is feasible for quite complex molecular systems (by Monte Carlo path integral methods), having an accurate rate theory that involves only the Boltzmann operator could be quite useful. The application of this quantum instanton approximation to several one- and two-dimensional model problems illustrates its potential; e.g., it is able to describe thermal rate constants accurately (∼10–20% error) from high to low temperatures deep in the tunneling regime, and applies equally well to asymmetric and symmetric potentials.