Application of Direct Search Methods in Molecular Conformation Problems

Deterministic optimization algorithms, that are combination of direct search methods and local search algorithms, are proposed for molecular conformation problems. We apply these methods to solve the Lennard-Jones atomic cluster problem. The deterministic optimization algorithms are embedded in a build-up scheme. At each stage, an atom is added to an optimized structure of a small cluster, and then the resulting structure is minimized again. Our direct search method is either the Nelder-Mead Simplex (NMS) or the Derivative Free Optimization (DFO) method. For local search, a Quasi Newton method with BFGS update is used. This way the global optimum for Lennard-Jones atomic clusters containing up to 30 atoms are located.