IMPLICIT INTEGRATION IN MOLECULAR DYNAMICS SIMULATION

摘要

Molecular Dynamics (MD) simulation is a versatile methodology that has found many applications in materials science, chemistry and biology. In biology, the models employed range from mixed quantum mechanical and fully atomistic to united atom and continuum mechanical. These systems are evolved in discrete time by solving Newton 's equations of motion at each time step. The numerical methods currently in use limit the step size of a typical all atom simulation to 1 femtosecond. This step size limitation means that many steps need to be taken in order to reach biologically relevant time scales. At each time step, an evaluation of the forces on each atom must be performed resulting in heavy computational loads. This work investigates the use of implicit integration methods in MD. Implicit integration methods have been proven superior to their explicit counterparts in classical mechanical simulation, with which MD has many similarities. Longer time steps reduce the number of force evaluations that must be performed and the corresponding computational load. Herein we present results that compare implicit integration techniques with the current standard for molecular dynamics, the explicit velocity Verlet integration scheme. Total energy conservation is used as a metric for evaluating the dependability of simulations in the microcanonical ensemble. In order to understand the nature of the problem, several long simulations were run and analyzed by performing a Fourier analysis on the position, velocity and acceleration signals. Lastly, several methods for improving the viability of implicit integration methods are consid- ered including replacing the Jacobian used in the Quasi-Newton method with a constant, diagonal mass matrix, evaluating the Jacobian infrequently and finding a better prediction of the system configuration to improve the convergence of the Quasi-Newton method.