Molecular dynamics by the Backward-Euler method

This paper introduces a new computational method for molecular dynamics. The method combines the Backward-Euler scheme for the solution of stiff differential equations with a Langevin-equation approach to the establishment of thermal equilibrium. The method allows the user to choose a cutoff frequency ω_c. Vibrational modes with frequencies below ω_c will be fully excited (receive a mean energy of kT per mode), while modes with frequencies greater than ω_c will be effectively frozen by the method. By setting ω_c = kT/h, one can obtain reasonable agreement with the quantum-mechanical energy distribution among the various modes, despite the classical character of the computation.