Calculation of quantum mechanical rate constants directly from ab initio atomic forces

Abstract

Harmonic quantum transition state theory (HQTST), sometimes referred to as ’instanton theory’ or ’ImF theory’, has been implemented in an efficient way and tested. HQTST is analogous to the more familiar classical harmonic transition state theory (HTST), where the rate is estimated from the energy difference between a reactant state minimum and a first order saddle point on the potential energy surface ridge that separates reactants and the products, along with a prefactor derived from harmonic expansion of the potential around both the minimum and the saddle point. The method described here makes use of a generalized minimum mode following method to locate saddle points on the effective quantum mechanical energy surface for discretized Feynman path integrals (FPI). The overall computational cost of estimating rate constants with this method is relatively low and it is possible to use directly atomic forces obtained from first principle calculations. The method is also well suited for systems containing many degrees of freedom, on the order of a few hundred. Usually, a well converged results is achieved with 500 - 700 force calls per system replica used to represent the FPI. The method has been tested on several one- and two-dimensional systems where more accurate (or even analytical) solutions for the rate constant can be obtained. Not only is it found to robust and fast, but accurate as well, yielding results within a factor of 2-3 from the exact values, indicating that the approximations inherent in the procedure are well justified for chemically relevant systems. In addition, the method has been used for calculating the rate of various transitions involving hydrogen atoms or molecules where the atomic forces are derived from empirical, semi-empirical or first principle calculations. Calculations presented here include the rate of hydrogen abstraction from gas phase H3BN3, hydrogen atom diffusion in Ta and Pd, adsorption/desorption of H2 onto/from Cu(100) and Cu(110) surfaces and hydrogenation of N on Ru(0001) surface. Comparison is made with either higher level theoretical calculations or experimental results when available, and the agreement is found to be good in all instances.