Efficient recursive Adams–Bashforth methods in molecular dynamics simulations of N-body systems interacting through pairwise potentials

ABSTRACT

A recursive multistep Adams–Bashforth method applied to the Molecular Dynamics simulations of N-body systems interacting through pairwise force fields is introduced and analysed. Equations of motion are obtained using a set of Cartesian coordinates solved by means of an Adams–Bashforth numerical integration scheme of order s, which requires the iterative computation of function time derivatives. The proposed algorithm has been implemented using a programming approach that makes it possible to re-use a source code resulting in small codes, easy to maintain. Practical examples and benchmarks that illustrate the performance of these implementations are included. The study of its performance gives clues to evaluate its efficiency and precision. Numerical tests for a N-particle system are made on the equilibrium configuration of liquid argon near its triple point at 86.5 K and 0.021 Å${}^{-3}$. In most cases, the algorithms here presented outperform those implemented traditionally as the Gear corrector-predictor or the Verlet family, leading to important savings in terms of total computation times and significantly increasing the numerical precision obtained with standard algorithms.

KEYWORDS:

• Recursive formulation
• Adams–Bashforth methods
• integration Algorithms
• molecular dynamics

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

JM gratefully acknowledges financial support from Spanish Ministry of Science, Innovation and Universities (project number PGC2018-099277-B-C21, funds MCIU/AEI/FEDER, UE).