Optimized Verlet-like algorithms for molecular dynamics simulations

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.