Symplectic algorithm for constant-pressure molecular dynamics using a Nosé–Poincaré thermostat

Abstract

We present a new algorithm for isothermal–isobaric molecular-dynamics simulation. The method uses an extended Hamiltonian with an Andersen piston combined with the Nosé–Poincaré thermostat, recently developed by Bond, Leimkuhler, and Laird [J. Comp. Phys. 151, 114 (1999)]. This Nosé–Poincaré–Andersen (NPA) formulation has advantages over the Nosé-Hoover-Andersen approach in that the NPA is Hamiltonian and can take advantage of symplectic integration schemes, which lead to enhanced stability for long-time simulations. The equations of motion are integrated using a generalized leapfrog algorithm (GLA) and the method is easy to implement, symplectic, explicit, and time reversible. To demonstrate the superior stability of the method we show results for test simulations using a model for aluminum and compare it to a recently developed time-reversible algorithm for Nosé–Hoover–Anderson. In addition, an extension of the NPA to multiple time steps is outlined and a symplectic and time-reversible integration algorithm, based on the GLA, is given.