A simple local expression for the prefactor in transition state theory

We present a simple and accurate computational technique to determine the frequency prefactor in harmonic transition state theory without necessitating full phonon density of states (DOS) calculations. The atoms in the system are partitioned into an "active region", where the kinetic process takes place, and an "environment" surrounding the active region. It is shown that the prefactor can be obtained by a partial phonon DOS calculation of the active region with a simple correction term accounting for the environment, under reasonable assumptions regarding atomic interactions. Convergence with respect to the size of the active region is investigated for different systems, as well as the reduction in computational costs when compared to full phonon DOS calculation. Additionally, we provide an open source implementation of the algorithm that can be added as an extension to LAMMPS software.