Brownian Dynamics

In the limit of high friction, stochastic dynamics reduces to Brownian dynamics, also called position Langevin dynamics. This applies to over-damped systems, i.e. systems in which the inertia effects are negligible. The equation is

(117)dridt=1γiFi(r)+ri

where γi is the friction coefficient [amu/ps] and ri(t) is a noise process with ri(t)rj(t+s)=2δ(s)δijkBT/γi. In GROMACS the equations are integrated with a simple, explicit scheme

(118)ri(t+Δt)=ri(t)+ΔtγiFi(r(t))+2kBTΔtγirGi,

where rGi is Gaussian distributed noise with μ=0, σ=1. The friction coefficients γi can be chosen the same for all particles or as γi=miγi, where the friction constants γi can be different for different groups of atoms. Because the system is assumed to be over-damped, large timesteps can be used. LINCS should be used for the constraints since SHAKE will not converge for large atomic displacements. BD is an option of the mdrun program.