References and Equations

Molecular Dynamics

This module implements the molecular dynamics integrator with micro-canonical ensemble (NVE), first and second order langevin, and velocity rescale methods.

The velocity Verlet method is used. See Eq. 3.10.31, 3.10.32 in P111-P112 of Statistical Mechanics: Theory and Molecular Simulation by Mark E. Tuckerman.

$x(\Delta t) = x(0) + \Delta t v(0) + {{\Delta t^2}\over{2m}} F(x(0))$

$v(\Delta t) = v(0) + {{\Delta t}\over{2m}} [F(x(0))+F(x(\Delta t))]$

The first and second order langevin integrator see

1. Chapter 15 of Statistical Mechanics: Theory and Molecular Simulation by Mark E. Tuckerman

Eq. 23 in E. V.-Eijnden, and G. Ciccotti, Chem. Phys. Lett. 429, 310 (2006)

TO DO: implement dt/rescale method