Locating critical points on multi-dimensional surfaces by genetic algorithm: test cases including normal and perturbed argon clusters

Abstract

It is demonstrated that Genetic Algorithm in a floating point realisation can be a viable tool for locating critical points on a multi-dimensional potential energy surface (PES). For small clusters, the standard algorithm works well. For bigger ones, the search for global minimum becomes more efficient when used in conjunction with coordinate stretching, and partitioning of the strings into a core part and an outer part which are alternately optimized The method works with equal facility for locating minima, local as well as global, and saddle points (SP) of arbitrary orders. The search for minima requires computation of the gradient vector, but not the Hessian, while that for SP's requires the information of the gradient vector and the Hessian, the latter only at some specific points on the path. The method proposed is tested on (i) a model 2-d PES (ii) argon clusters (Ar₄-Ar₃₀) in which argon atoms interact via Lennard-Jones potential, (iii) Ar_mX, m=12 clusters where X may be a neutral atom or a cation. We also explore if the method could also be used to construct what may be called a stochastic representation of the reaction path on a given PES with reference to conformational changes in Ar_n clusters.