A pseudo-atom method in potential energy minimization for crystals

Three energy minimization algorithms analogous to molecular dynamics, when each atom is displaced independently in the direction of the unbalanced force, are presented and compared. The displacements are governed by the local potential field, defined by the atom's neighbours, and it is assumed that its collective effect corresponds to that of a single pseudo-atom. In one of the algorithms the atom at each iteration step is moved directly into the position of the local minimum, and in the other two it moves toward this position according to either a linear law or an exponential one. The examples for 2D hexagonal Lennard-Jones lattices with different numbers of atoms are used in this study. It is shown that the computational efficiency is of the order O(N2) for all three approaches but the rate of convergence for the algorithm with an exponential law of displacements gives the best results for the examples considered.