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

Extended Lagrangian molecular dynamics (XLMD) is a general method for performing simulations using quantum and classical many-body potentials. Recently several new XLMD schemes have been proposed tested on classes of polarization models such as induced dipoles or Drude charges, by creating an auxiliary set these same degrees freedom that are reversibly integrated through time. This gives rise to singularly perturbed Hamiltonian system provides good approximation the time evolution real mutual field. To further improve upon accuracy in context polarizable force field simulation, potentially extend it other potentials, we introduce stochastic modification which leads Langevin equations with degenerate noise. We prove resulting Stochastic-XLMD converges accurate dynamics, convergence rate both sharp independent initial carefully study scaling damping factor numerical noise efficient simulation Stochastic-XLMD, demonstrate effectiveness water molecules described