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 •H α + H β H γ → H α H β + •H γ reaction as an example, we apply the proposed method to obtain several kinetic isotope effects on CH 4 + •H ⇋ •CH 3 + H 2 forward and backward reactions.

Semiclassical analysis of the quantum instanton approximation

“…Eqs. (32) and (33) can thus be used to obtain the semiclassical limit of the QI and 2OCE approximations. Using the known expressions (for the 1D case) 49…”

Accelerating equilibrium isotope effect calculations. I. Stochastic thermodynamic integration with respect to mass

“…The combination of higher-order path integral splittings with standard thermodynamic integration has been discussed elsewhere; 21,[57][58][59] as for the extension to stochastic thermodynamic integration, the main additional change consists in replacing the potential V in the acceptance probability in Eq. (27) with an effective potential depending on mass and, in the case of the fourth-order Suzuki splitting, in an additional factor depending on the imaginary time-slice index s. …”

Kinetic isotope effects and how to describe them

“…(For details, see Ref. 67.) The table shows that the accelerated methodology can obtain the results with the same accuracy as much as 100 times faster than the original path-integral implementation from Ref.…”

“…In Ref. 67, these two strategies were combined; the resulting method was tested on the model $·{\mathrm{normalH}}_{\alpha }{+\mathrm{H}}_{\beta }{\mathrm{normalH}}_{\gamma }\to {\mathrm{normalH}}_{\alpha }{\mathrm{normalH}}_{\beta }+·{\mathrm{normalH}}_{\gamma }$ rearrangement and on the reaction ${\text{CH}}_4+·\mathrm{H}\to ·{\text{CH}}_3{+\mathrm{H}}_2$, a process whose kinetic isotope effects have been studied in detail both experimentally and theoretically, with classical transition-state theory, several of its corrected versions, 75,76 reduced dimensionality quantum dynamics, 77 and RPMD 78 …”