Quantum-instanton evaluation of the kinetic isotope effects

摘要

A general quantum-mechanical method for computing kinetic isotope effects is presented.The method is based on the quantum-instanton approximation for the rate constant and on the path-integral Metropolis-Monte Carlo evaluation of the Boltzmann operator matrix elements.It computes the kinetic isotope effect directly,using a thermodynamic integration with respect to the mass of the isotope,thus avoiding the more computationally expensive process of computing the individual rate constants.The method should be more accurate than variational transition-state theories or the semiclassical instanton method since it does not assume a single tunneling path and does not use a semiclassical approximation of the Boltzmann operator.While the general Monte Carlo implementation makes the method accessible to systems with a large number of atoms,we present numerical results for the Eckart barrier and for the collinear and full three-dimensional isotope variants of the hydrogen exchange reaction H + H_2->H_2+H.In all seven test cases,for temperatures between 250 and 600 K,the error of the quantum instanton approximation for the kinetic isotope effects is less than ~10%.