Molecular dynamics integration and molecular vibrational theory. I. New symplectic integrators.

New symplectic integrators have been developed by combining molecular dynamics integration with the standard theory of molecular vibrations to solve the Hamiltonian equations of motion. The presented integrators analytically resolve the internal high-frequency molecular vibrations by introducing a translating and rotating internal coordinate system of a molecule and calculating normal modes of an isolated molecule only. The translation and rotation of a molecule are treated as vibrational motions with the vibrational frequency zero. All types of motion are thus described in terms of the normal coordinates. The method's time reversibility requirement was used to determine the equations of motion for internal coordinate system of a molecule. The calculation of long-range forces is performed numerically within the generalized second-order leap-frog scheme, in the same way as in standard second-order symplectic methods. The new methods for integrating classical equations of motion using normal mode analysis allow us to use a long integration step and are applicable to any system of molecules with one equilibrium configuration.