Split Integration Symplectic Method for Molecular Dynamics Integration

Abstract

An explicit Split Integration Symplectic Method (SISM) for molecular dynamics (MD) simulations is described. This work is an extension of an efficient symplectic integration algorithm introduced by Janežič and Merzel (J. Chem. Inf. Comput. Sci. 1995, 35, 321−326). SISM is based on splitting of the total Hamiltonian of the system into a harmonic part and the remaining part in such a way that both parts can be efficiently computed. The Hamilton equations of motion are then solved using the second order generalized leap-frog integration scheme in which the high-frequency motions are treated analytically by the normal mode analysis which is carried out only once, at the beginning of the calculation. SISM requires only one force evaluation per integration step; the computation cost per integration step is approximately the same as that of the standard leap-frog-Verlet (LFV) method, and it allows an integration time step up to an order of magnitude larger than can be used by other methods of the same order and complexity. The simulation results of selected examplesMD simulations of a model system of linear chain molecules of the form H-(-C⋮C-)2-H and a model system of flexible CO2 moleculesshow that the SISM posses long term stability and the ability to use long time steps. The approach for MD simulations described here is general and applicable to any complex system.

Recent advances in molecular dynamics simulation towards the realistic representation of biomolecules in solution

“…Empirical (pairwise) MM potential functions are necessary due to the large number of energy and force evaluations required since small integration time steps are typically applied to properly represent the high-frequency motions and allow stable integration (for a good review, see Schlick et al [22]). Integration steps in the 1±2 fs range are routine, although more recently various groups are starting to apply slightly longer time steps (in the 2±6 fs range) through the application of multiple time-step methods [23] such as RESPA [24], Langevin-Newton, Implicit-Euler [22], or split integration symplectic methods [25]. Due to their stability, reversibility, and reasonable representation of the Hamiltonian, RESPA methods are the most promising to increase the speed of these calculations.…”

Symplectic molecular dynamics integration using normal mode analysis

“…This treatment of high‐frequency terms in the Hamiltonian permits the SISM proposed in Eqs. (10)–(16) to use a much larger integration step size Δ t than the standard methods 12–14.…”

“…Although the harmonic model may be incomplete because of the contribution of anharmonic terms to the potential energy, it is nevertheless of considerable importance because it serves as a first approximation for which the theory is highly developed. This model is also useful in the split integration symplectic method (SISM), which uses normal mode analysis 12–14.…”

Parallel programming library for molecular dynamics simulations

“…Potential parameters were the same as in Ref. 12, and the periodic boundary conditions were imposed to overcome the problem of surface effects.…”

“…We recently introduced an efficient split integration symplectic method (SISM) 10–12 for MD integration. The method allows the use of a time‐step up to an order of magnitude larger than the commonly used LFV algorithm, which is of the same order and computational complexity as SISM.…”