Optimized Verlet-like algorithms for molecular dynamics simulations

Abstract

Explicit velocity- and position-Verlet-like algorithms of the second order are proposed to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an extended decomposition scheme at the presence of a free parameter. The nonzero value for this parameter is obtained by reducing the influence of truncated terms to a minimum. As a result, the proposed algorithms appear to be more efficient than the original Verlet versions that correspond to a particular case when the introduced parameter is equal to zero. Like the original versions, the extended counterparts are symplectic and time reversible, but lead to an improved accuracy in the generated solutions at the same overall computational costs. The advantages of the optimized algorithms are demonstrated in molecular dynamics simulations of a Lennard-Jones fluid.

Quasi-normal modes from non-commutative matrix dynamics

“…14) 15) supplemented by the constraint (2.11): I [P I , X I ] = 0. The integral form of the equations of motion defines the Hamiltonian flow ϕ : I × P → P, where I ⊂ R is a interval of time, and ϕ is a map such that for each initial point X (0) in phase space, the path γ(t) := ϕ t (X (0) ) is the unique curve with initial condition γ(0) = X (0) .…”

Multiscale modeling and simulation of rolling contact fatigue

“…Eq.2.1, to obtain the atomic trajectories. In this chapter, the Velocity Verlet algorithm is employed as the time integration algorithm since it achieves a considerable accuracy [49].…”

Modeling tabular icebergs submerged in the ocean

“…The traditional velocity Verlet algorithm is commonly used in molecular dynamics, as it is simple to implement, second-order accurate and computationally efficient [Swope et al, 1982;Omelyan et al, 2002]. Here we modify the traditional scheme to allow for the drag forces to be modeled implicitly, which prevents large accelerations for elements whose mass approaches zero.…”