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

Stochastic Constrained Extended System Dynamics for Solving Charge Equilibration Models

“…Langevin Thermostat and Integration Algorithm. We utilize the Langevin thermostat approach we have developed previously for thermostating polarizable models, 20 which requires us to define both dissipation Γ = diag{γ q I n , γ µ } and temperature T = diag{T q I n , T µ } parameters corresponding to the latent variables. Once defined, the "BAOAB" scheme is used to achieve efficient thermostatting 27 by propagating the equations of the extended system as follows:…”

“…15,19 In this work we further extend the iEL/SCF method for CEM by eliminating SCF cycles altogether, as we have done previously for non-reactive force field models using iEL/0-SCF. 18,20 For polarizable models, the auxiliary induced dipoles evolve under a harmonic potential that keeps their values close to the converged real dipole solution, as approximated by a one-time step estimation derived from a local-kernel mixing of the real and auxiliary variables using an optimal mixing parameter γ. This SCF-free approximation works well if the real dipole dynamics evolve on a longer timescale, well-separated from the discretized time step, so that a local-kernel mixing remains a good approximation to the true SCF solution.…”

“…errors in the time-integration of the harmonic forces that leak to the auxiliary kinetic energy and create numerical instabilities, but which can be controlled through a separate thermostat for the auxiliary variables as we have shown previously. 18,20 Recently, An and co-workers have developed a new formulation of an iteration-free scheme, Stochastic-XLMD, where a thermostat coupling parameter ε replaces the mixing parameter γ, and the effect of a Langevin thermostat applied to the latent induced dipole variables for classical polarization was shown to be robust, although not strictly tiem-reversible. 20 However, the generalization of the resulting iEL/0-SCF method from induced dipoles to fluctuating charges is not straightforward for three reasons: (1) the characteristic decorrela-tion time for charges is more than one order of magnitude faster than for induced dipoles, (2) the charges are derived under a constraint that the net charge of the entire system is conserved, and (3) the resonance problem may be more severe under a harmonic potential now applied to two sets of coupled linear equations.…”

“…18,20 Recently, An and co-workers have developed a new formulation of an iteration-free scheme, Stochastic-XLMD, where a thermostat coupling parameter ε replaces the mixing parameter γ, and the effect of a Langevin thermostat applied to the latent induced dipole variables for classical polarization was shown to be robust, although not strictly tiem-reversible. 20 However, the generalization of the resulting iEL/0-SCF method from induced dipoles to fluctuating charges is not straightforward for three reasons: (1) the characteristic decorrela-tion time for charges is more than one order of magnitude faster than for induced dipoles, (2) the charges are derived under a constraint that the net charge of the entire system is conserved, and (3) the resonance problem may be more severe under a harmonic potential now applied to two sets of coupled linear equations. To illustrate, an iteration-free XLMD scheme for CEM, 21,22 was found to be unstable after time propagation of no more than several picoseconds, 19 which is generally not sufficient for converging thermodynamic quantities.…”

“…In this work, we have addressed these issues through careful formulation of an XLMD procedure that utilizes two latent variables -the charge and chemical potential -and enforces the conservation of charge through a holonomic constraint scheme that is conforming for both energy and forces. 23 We have combined this new SCF-less solution for CEM with the Stochastic-XLMD (SXLMD) method for thermostatting, 20 and implemented it within the ReaxFF force field in the Large-scale Atomic and Molecular Massive Parallel Simulation (LAMMPS) library. 24 We show that the stochastic and constrained extended Lagrangian scheme with no iteration, SC-XLMD, is capable of producing stable trajectories over a timescale of nanoseconds, while retaining energy conservation and equivalent thermodynamics properties of the typical CG-SCF solution.…”