Robust and efficient configurational molecular sampling via Langevin dynamics

Abstract

A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian motions in some combination. The Baker-Campbell-Hausdorff expansion is used to study sampling accuracy following recent work by the authors, which allows determination of the stepsize-dependent bias in configurational averaging. For harmonic oscillators, configurational averaging is exact for certain schemes, which may result in improved performance in the modelling of biomolecules where bond stretches play a prominent role. For general systems, an optimal method can be identified that has very low bias compared to alternatives. In simulations of the alanine dipeptide reported here (both solvated and unsolvated), higher accuracy is obtained without loss of computational efficiency, while allowing large timestep, and with no impairment of the conformational exploration rate (the effective diffusion rate observed in simulation).The optimal scheme is a uniformly better performing algorithm for molecular sampling, with overall efficiency improvements of 25% or more in practical timestep size achievable in vacuum, and with reductions in the error of configurational averages of a factor of ten or more attainable in solvated simulations at large timestep.

Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems

“…Compared with other prevailing splitting methods for the Lagevin dynamics, the BAOAB scheme has demonstrated higher accuracy without sacrificing computational efficiency. Also, it is also demonstrated [44] the BAOAB scheme enables using larger time steps in the simulation while keeping the stability of the integrator.…”

“…To numerically integrate the Langevin dynamics, we apply the BAOAB splitting scheme [44] developed in the context of Langevin thermostat for classical molecular dynamics. The BAOAB scheme has been applied to and analyzed for conventional PIMD simulations (for single energy surface) recently and exhibit advantageous numerical performance over other numerical integrators [45] [46].…”

Nonequilibrium processes from generalized Langevin equations: Realistic nanoscale systems connected to two thermal baths

“…Such a decomposition has been shown to provide a more appropriate description of the velocity correlation functions [50].…”

Applications of the generalized Langevin equation: Towards a realistic description of the baths

“…[45], we use the following algorithm for a single time step t. The algorithm is derived, in a Verlet style, from a different splitting and a Trotter-type decomposition of the total Liouvillian for the extended Langevin dynamics of the system DOF r iα and the virtual DOF s (k) 1,2 . Such a decomposition has been shown to provide a more appropriate description of the velocity correlation functions [39].…”