Accelerating quantum instanton calculations of the kinetic isotope effects

Abstract

Path integral implementation of the quantum instanton approximation currently belongs among the most accurate methods for computing quantum rate constants and kinetic isotope effects, but its use has been limited due to the rather high computational cost. Here we demonstrate that the efficiency of quantum instanton calculations of the kinetic isotope effects can be increased by orders of magnitude by combining two approaches: The convergence to the quantum limit is accelerated by employing high-order path integral factorizations of the Boltzmann operator, while the statistical convergence is improved by implementing virial estimators for relevant quantities. After deriving several new virial estimators for the high-order factorization and evaluating the resulting increase in efficiency, using $\cdot {\mathrm{H}}_{\alpha }+{\mathrm{H}}_{\beta }{\mathrm{H}}_{\gamma }\to {\mathrm{H}}_{\alpha }{\mathrm{H}}_{\beta }+\cdot {\mathrm{H}}_{\gamma }$ reaction as an example, we apply the proposed method to obtain several kinetic isotope effects on $\mathrm{C}{\mathrm{H}}_4+\cdot \mathrm{H}\rightleftharpoons \cdot \mathrm{C}{\mathrm{H}}_3+{\mathrm{H}}_2$ forward and backward reactions.

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Cited by in corpus (4)

• Semiclassical analysis of the quantum instanton approximation
• Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems
• Accelerating equilibrium isotope effect calculations: I. Stochastic thermodynamic integration with respect to mass
• Accelerating equilibrium isotope effect calculations: II. Stochastic implementation of direct estimators