Nuclear quantum effects in chemical reactions via higher-order path-integral calculations

A practical approach to treat nuclear quantum mechanical effects in simulations of condensed phases, such as enzymes, is via Feynman path integral (PI) formulations. Typically, the standard primitive approximation (PA) is employed in enzymatic PI simulations. Nonetheless, these PI simulations are computationally demanding due to the large number of beads required to obtain converged results. The efficiency of PI simulations may be greatly improved if higher-order factorizations of the density matrix operator are employed. Herein, we compare the results of model calculations obtained employing the standard PA, the improved operator of Takahashi and Imada (TI), and a gradient-based forward corrector algorithm due to Chin (CH). The quantum transmission coefficient is computed for the Eckart potential while the partition functions and rate constant are computed for the H₂ + H hydrogen transfer reaction. These potentials are simple models for chemical reactions. The study of the different factorization methods reveals that in most cases the higher-order action converges faster than the PA and TI approaches, at a moderate computational cost.