Efficient <i>ab initio</i> path integral hybrid Monte Carlo based on the fourth-order Trotter expansion: Application to fluoride ion-water cluster

We propose an efficient path integral hybrid Monte Carlo (PIHMC) method based on fourth-order Trotter expansion. Here, the second-order effective force is employed to generate short trial trajectories to avoid computationally expensive Hessian matrix, while the final acceptance is judged based on fourth-order effective potential. The computational performance of our PIHMC scheme is compared with that of conventional PIHMC and PIMD methods based on second- and fourth-order Trotter expansions. Our method is applied to on-the-fly ab initio PIHMC calculation of fluoride ion-water complexes, F(-)(H(2)O) and F(-)(D(2)O), at ambient temperature, particularly focusing on the geometrical isotope effect.