Stability of Symplectic Integrators in Molecular Dynamics Simulations

Abstract

In this research, the experiments have been performed based on diffusion coefficients of Green-Kuboand Einstein expressions and conservation energy to investigate the accuracy and stability of the secondorder explicit symplectic integrators of position Verlet and velocity Verlet algorithms compared to nonsymplecticintegrators (fourth order Runge Kutta and fourth order Gear predictor-corrector). The simulationswere performed by invoking the Green-Kubo and Einstein relations including global errors in energycalculations. Computer simulations were performed using double precision of calculations. Also they wereperformed on a system of 256 Lennard-Jones particles interacting with a potential that was truncated at3.0 . The essence of the study was to run series of simulations, starting from the same initial configuration,with each simulation being run the same reduced time. They differ in the size of the time step used and hencethe total number of steps actually made during the simulation. The simulation runs were divided into 10independent batches such that these 10 batches formed an approximate Gaussian distribution for which themean and its uncertainty can be calculated. This technique gives reliable error estimates from computersimulations.Results showed that the position and velocity Verlet algorithms were very competitive compare to theRunge Kutta and Gear predictor-corrector methods. Both Verlet methods use approximately the same CPUtime due to less force evaluations per time step compare to non-symplectic integrators. The appropriate timestepsize for velocity Verlet algorithm should be lower than 0.01 as well as the time-step size that used formolecular dynamic simulation must depend on temperature and density of system.