Molecular Dynamics (MD) simulation is a versatile methodology that has
found many applications in material 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. We are currently investigating the utility of
implicit integration methods for use in MD. Implicit integration
methods have been proven superior to their explicit counterparts in
classical mechanical simulation, with which MD has many
similarities. If longer time steps can be taken then this reduces 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
Fourier transforms of the position, velocity and acceleration
signals. Lastly, several methods for improving the viability of
implicit integration methods are considered 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.
Keywords: explicit integration, implicit integration, molecular
dynamics
