Time reversible and phase-space conserving molecular dynamics at constant temperature

Algorithms for constant temperature molecular dynamics simulations are presented. The basic equations of motion, keeping the temperature constant, are derived by an extension of phase space. Time reversible integration algorithms are obtained for these equations of motion by a factorization of the classical Liouville propagator. In particular an algorithm is derived which includes the phase-space conservation property of the equations of motion. This algorithm is compared with the Nosé–Hoover approach for systems of a single degree of freedom. It is demonstrated that the derived equations of motion generate canonical distributions. In addition, a comparison with various isothermal integration algorithms for the Nosé–Hoover equations is presented for a system of Lennard-Jones particles.