Parallel multilevel preconditioned conjugate-gradient approach to variable-charge molecular dynamics

Abstract

Physical realism of molecular dynamics (MD) simulations is greatly enhanced by incorporating variable atomic charges which adapt to the local environment dynamically. In the electrostatic plus (ES+) model, atomic charges are determined to equalize electronegativity. However, this model involves costly minimization of the electrostatic energy at each MD step. A preconditioned conjugate-gradient method is developed for this minimization problem by splitting the Coulomb-interaction matrix into short- and long-range components; the computationally less intensive short-range matrix is used as a preconditioner. This preconditioning scheme is found to speed up the convergence significantly. Numerical tests involving up to 26.5 million atoms are performed on a parallel computer, and the preconditioner is shown to improve the parallel efficiency by increasing data locality. The computational cost is further amortized due to the algorithmic similarity to the multiple-time-scale MD.