Ensemble simulations with discrete classical dynamics

For discrete classical Molecular Dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment h there exists (for sufficiently small h) a shadow Hamiltonian (H) over tilde with energy <()over tilde>(h), for which the discrete particle positions lie on the analytic trajectories for (H) over tilde. The first order estimate of (E) over tilde (h) is employed to determine the relation with the corresponding energy, E, for the analytic dynamics with h = 0 and the zero-order estimate E-0(h) of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics for the (NV (T) over tilde (h)) ensemble and determine the relations between the energies and temperatures for the different ensembles, including the (NVE0(h)) and (NVT0(h)) ensembles. The differences in the energies and temperatures are proportional with h(2) and they are of the order of a few tenths of a percent for a traditional value of h. The relations between (NV (E) over tilde (h)) and (NVE), and (NV (T) over tilde (h)) and (NVE) are easily determined for a given density and temperature, and allow for using larger time increments in MD. The accurate determinations of the energies are used to determine the kinetic degrees of freedom in a system of N particles. It is 3N - 3 for a three dimensional system. The knowledge of the degrees of freedom is necessary when simulating small system, e.g., at nucleation. (C) 2013 AIP Publishing LLC.