Symplectic molecular dynamics integration

The survey of our past and present work on symplectic integration algorithms for numerical solution of molecular dynamics (MD) equation is presented. Symplectic integrators are numerical integration methods for Hamiltonian systems which are designed to conserve the symplectic structure exactly as the original flow. A symplectic implicit Runge-Kutta (RK) integration schemes, the s-stage Gauss-Legendre (GL) methods of order 2s, in particular, the two-stage fourth-order GLRK method, the implicit midpoint rule, and the diagonally implicit three-stage method are described. Also described are the new explicit, the second and the fourth-order, split integration symplectic method (SISM) for MD integration. The technique is based on the splitting of the total Hamiltonian of the system into two pieces, each of which can either be solved exactly or more conveniently than bg using standard methods. The proposed symplectic methods for MD integration permit a wide range of time steps, are highly accurate and stable, and thus suitable for the MD integration. particularly SISM, which possess long term stability and ability to take large time steps. It is by an order of magnitude faster than the standard leap-frog Verlet (LFV) method which is known to be symplectic and of second order.