Implementation of the self-consistent phonons method with ab initio potentials (AI-SCP).

The self-consistent phonon (SCP) method allows one to include anharmonic effects when treating a many-body quantum system at thermal equilibrium. The system is then described by an effective temperature-dependent harmonic Hamiltonian, which can be used to estimate its various dynamic and static properties. In this paper, we combine SCP with ab initio (AI) potential energy evaluation in which case the numerical bottleneck of AI-SCP is the evaluation of Gaussian averages of the AI potential energy and its derivatives. These averages are computed efficiently by the quasi-Monte Carlo method utilizing low-discrepancy sequences leading to a fast convergence with respect to the number, S, of the AI energy evaluations. Moreover, a further substantial (an-order-of-magnitude) improvement in efficiency is achieved once a numerically cheap approximation of the AI potential is available. This is based on using a perturbation theory-like (the two-grid) approach in which it is the average of the difference between the AI and the approximate potential that is computed. The corresponding codes and scripts are provided.

Surface hopping with cumulative probabilities: Even sampling and improved reproducibility.

Trajectory surface hopping simulations of photochemical reactions are a powerful and increasingly important tool to unravel complex photochemical reactivity. Within surface hopping, electronic transitions are mimicked by stochastic hops between electronic potential surfaces. Thus, statistical sampling is an inescapable component of trajectory-surface-hopping-based nonadiabatic molecular dynamics methods. However, the standard sampling strategy inhibits computational reproducibility, limits predictability, and results in trajectories that are overly sensitive to numerical parameters like the time step. We describe an equivalent approach to sampling electronic transitions within fewest switches surface hopping (FSSH) in which hops are decided in terms of the cumulative probability (FSSH-c) as opposed to the usual prescription, which is in terms of the instantaneous conditional probability (FSSH-i). FSSH-c is statistically equivalent to FSSH-i and can be implemented from trivial modifications to an existing surface hopping algorithm but has several key advantages: (i) a single trajectory is fully specified by just a handful of random numbers, (ii) all hopping decisions are independent of the time step such that the convergence behavior of individual trajectories can be explored, and (iii) alternative integral-based sampling schemes are enabled. In addition, we show that the conventional hopping probability overestimates the hopping rate and propose a simple scaling correction as a fix. Finally, we demonstrate these advantages numerically on model scattering problems.