Stochastic phase space dynamics with constraints for molecular systems

Constraining fast degrees of freedom and using a Langevin-like description of the dynamics are standard tools to simulate complex systems that allow for comparatively large time steps in the numerical integration of the equations of motion. Here we start with the Hamiltonian description of classical mechanics for the incorporation of stochastic and frictional forces. Constraints are incorporated into Hamiltonian dynamics following a procedure put forward by Dirac. Combining these two approaches, in general, requires a different treatment of the constraints from that which is usually done in deterministic dynamics. The numerical algorithm we chose for the integration of these equations is a second-order Runge-Kutta scheme modified by a Euler treatment for the constraints. The resulting algorithm is stable up to large time steps and generates averages in the canonical ensemble. The applicability of the method to the simulation of large molecular systems is shown for a melt of n-C₁₃ alkane chains by a comparison to results from a Nos\'e-Hoover molecular dynamics simulation.