Molecular dynamics algorithms and hydrodynamic screening

In this paper molecular dynamics simulations of a system of Brownian particles in an explicit bath of solvent particles are considered. Generalized algorithms (Langevin simulations), in which both the Brownian particles and the solvent particles are artificially coupled to a heat bath, are analyzed for their dynamical properties on long length scales. Although such a dynamic is clearly unphysical, its analysis is useful for two reasons: The Langevin algorithm is frequently applied in an ad hoc fashion, and the deviation of its dynamical properties from the physical Hamiltonian case can be made arbitrarily small by choosing a sufficiently weak coupling to the heat bath. By a direct application of the Mori–Zwanzig projection operator formalism it is shown that the violation of global momentum conservation results in an artificial screening of the hydrodynamic interactions, with a screening length proportional to the inverse square root of the friction constant of the algorithm. The result is formally similar to expressions given in phenomenological theories of hydrodynamic screening in semidilute polymer solutions.