Drag Assisted Simulated Annealing Method for Geometry Optimization of Molecules

Abstract

One of the methods to find the global minimum of a potential energy surface of a molecular system is simulated annealing. The main idea of simulated annealing is to start you system at a high temperature and then slowly cool it down so that there is a chance for the atoms in the system to explore the different degrees of freedom and ultimately find the global minimum. Simulated annealing is traditionally used in classical Monte Carlo or in classical molecular dynamics. In molecular dynamics, one of the traditional methods was first implemented by Woodcock in 1971. In this method the velocities are scaled down after a given number of molecular dynamics steps, let the system explore the potential energy surface and scale down the velocities again until a minimum is found. In this work we propose to use a viscous friction term, similar to the one used in Langevin dynamics, to slowly bring down the temperature of the system in a natural way. We use drag terms that depend linearly or quadraticaly on the velocity of the particles. These drag terms will naturally bring the temperature the system down and when the system reaches equilibrium they will vanish. Thus, imposing a natural criterion to stop the simulation. We tested the method in Lenard-Jones clusters of up to 20 atoms. We started the system in different initial conditions and used different values for the temperature and the drag coefficients and found the global minima of every one of the clusters. This method demonstrated to be conceptually very simple, but very robust, in finding the global minima.