Abstract
In harmonic quantum transition state theory (HQTST) based on Feynman Path integrals (FPI), the identification of transition mechanism and estimation of rate constants involves finding a first-order saddle point on the temperature-dependent, NPdimensional, effective potential energy surface, where N is the number of classical degrees of freedom and P is the number of system replicas in the FPIs. The saddle point corresponds to the so-called ‘instanton’. Once the relevant saddle points have been found, the rate can be estimated by using harmonic approximation to the partition functions at the initial and transition states. We have implemented a method to locate instantons in complex, high-dimensional systems using atomic forces from either empirical potential functions or directly from ab initio estimates, without the need for second derivatives of the energy. The method is a quantum mechanical extension of the minimum mode following method of Henkelman and Jónsson.We have applied the HQTST method as well as the quantum wavepacket MCTDH method to the gas phase H+CH4 reaction using an analytic potential energy surface.This forms the first real test between instanton theory and in principle exact quantum dynamics for a multidimensional molecular system. Results are very encouraging since a typical deviation of only about 30% in the calculated rate constants is found, if the anharmonicity of the reactants is properly treated.HQTST has also been interfaced with the plane-wave DFT code VASP to provide ab initio forces. Application to steps in the formation of ammonia on the Ru(0001) surface will be presented, where all degrees of freedom in the motion of N and H atoms are included and some of the metal atoms. It is found that the motion of the topmost surface layer has a small, but nonnegligible, effect on the quantum rate constants.
