Time-Reversible Velocity Predictors for Verlet Integration with Velocity-Dependent Right-Hand Side

Time-reversible velocity predictors (TRVPs) with increasing orders of the time-reversibility error are developed to be used with the Verlet integrator for equations of motion with the right-hand side depending on velocities. The method performs outside a possible SHAKE algorithm to constrain bond lengths and does not require repeated SHAKE iterations nor RATTLE. We have tested the TRVPs with the Nosé-Hoover thermostat on four model systems (coupled harmonic and anharmonic oscillators, liquid argon, SPC/E water, and a small peptide), comparing them to the Gear integrator with the Lagrangian formulation of constraint dynamics, the Martyna, Tuckerman, Tobias, and Klein (MTTK) method, and the velocity iteration method. The TRVP method performs similarly to the iteration method. In addition, we discuss three methodology improvements: (i) We tested several formulas for the kinetic energy compatible with the Verlet/SHAKE algorithm and found that the leapfrog velocities are usually the best; (ii) we proposed two modifications of the MTTK method; and (iii) we suggest that thermostats directly controlling the translational kinetic temperature may give more accurate values of some thermodynamic quantities.