Application Research of the Gear's Predictor-Corrector Algorithms in A Molecular Dynamics Simulation to the EXP-6 Potential Function of Liquid Helium

摘要

Molecular dynamics (MD) is a method for computationally evaluating the thermodynamic and transport properties of materials by solving the classical equations of motion at the molecular level. There are many algorithms that can be used to integrate the Newton"s equation of motion in the simulation process. Each has its own advantages and disadvantages. GPC method keeps track of several time derivatives of the particle positions. Moreover, the GPC method requires only one evaluation of the forces per time step. This is of chief importance because we will find that the evaluation of forces is the most computationally expensive part of the molecular dynamics simulation. Therefore, the intermolecular interaction resulted from the potentials is very important for the molecular reaction dynamics and Molecular Dynamics. For helium, the repulsive part of the potential expressed in minus twelve power of r is not fit for it and exponential function form is used instead. EXP-6 potential is one of the potential functions with exponential repulsive interaction could explain the multi-body interaction between the liquid helium atoms and the attractive part is the main part of the Van der Waals attractive interaction. The behavior of GPC algorithm is observed during a canonical MD simulation of liquid helium. The relationship between the stability and accuracy of the GPC algorithm and the size of the time step will be explained in detail.