Pressure and temperature control in molecular dynamics simulation: a unitary approach in discrete time

New dynamical equations for both classical and quantum mechanical molecular dynamics simulations in the canonical and Gibbs free-enthalpy ensemble are presented. It is proved that these equations sample the appropriate phase-space distribution functions of statistical mechanics correctly. Based on a generalization of the Liouville theorem, numerical integration schemes are constructed, which respect the fundamental symmetries of the dynamical equations. This approach to molecular dynamics simulations is then applied to liquid silicon in a tight-binding description, resulting in a high numerical stability in terms of a conservation law.