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Extended Lagrangian molecular dynamics (XLMD) is a general method forperforming molecular dynamics simulations using quantum and classical many-bodypotentials. Recently several new XLMD schemes have been proposed and tested onseveral classes of many-body polarization models such as induced dipoles orDrude charges, by creating an auxiliary set of these same degrees of freedomthat are reversibly integrated through time. This gives rise to a singularlyperturbed Hamiltonian system that provides a good approximation to the timeevolution of the real mutual polarization field. To further improve upon theaccuracy of the XLMD dynamics, and to potentially extend it to other many-bodypotentials, we introduce a stochastic modification which leads to a set ofsingularly perturbed Langevin equations with degenerate noise. We prove thatthe resulting Stochastic-XLMD converges to the accurate dynamics, and theconvergence rate is both optimal and is independent of the accuracy of theinitial polarization field. We carefully study the scaling of the dampingfactor and numerical noise for efficient numerical simulation forStochastic-XLMD, and we demonstrate the effectiveness of the method for modelpolarizable force field systems.

Convergence of Stochastic-extended Lagrangian molecular dynamics method for polarizable force field simulation