Symmetric, explicit numerical integrator for molecular dynamics equations of motion with a generalized friction

A general mathematical scheme to construct symmetric, explicit numerical integrators of Newtonian equations of motion endowed with a generalized friction is provided for molecular dynamics (MD) study. The exact integrations are done for all the decomposed vector fields, including the one that contains the friction term. On the basis of the symmetric composition scheme with the adjoint for the resulting maps, integrators with any local order of accuracy can be systematically constructed. Among them, the second order P2S1 integrator gives the least evaluation of atomic force and potential, which are most time consuming in MD simulations. As examples of the friction function, three functional types are considered: constant, Laurent polynomial, and exponential with respect to the kinetic energy. Several MD equations of motion fall into these categories, and the numerical examinations of their integrators using a basic model system give positive results on the accuracy and efficiency. The extended phase-space scheme also presents an invariant function, which allows to easily detect numerical errors in the integration process by monitoring the function value.