Introduction

One of the challenging problems in computational chemistry is the determination of lowest energy structures of atomic and molecular clusters. This can be attributed to the presence of a large number of minima such clusters can possess. A cluster of only 13 atoms has more than 10³ local minima [1]. Some studies [2,3] estimate that the number of local minima increase as rapidly as exp(n²), where n is the number of atoms in a cluster. Wille and Vennik [4] have proved that the determination of lowest energy cluster, interacting under two-body central force, is an NP-hard problem. Therefore an exhaustive search of all possible structures in not feasible, thus necessitating usage of global optimization techniques.

One of the promising global optimization techniques are Genetic algorithms (GAs) [5]. GAs are search methods inspired by nature and are based on Darwin's principle of survival of the fittest. GAs employ a population of candidate solutions and utilize genetic operators like reproduction, recombination, and mutation to create new candidates with higher fitness. Recently a class of GAs called competent GAs have been proposed [6] which are far superior to the conventional GAs. Competent GAs are defined as GAs that can solve hard problems quickly, reliably and accurately. In essence, competent GAs take problems that were intractable with earlier GAs and renders them tractable.

The objective of the current study is to employ extended compact genetic algorithm (ECGA) [7], one of the competent GAs for the task of cluster optimization and to evaluate its effectiveness in predicting globally optimal structures. Silicon clusters are taken as a test case. We have successfully predicted optimal structures for small clusters (n = 4-11) and efforts are currently under way to predict structures of bigger clusters. This paper is structured as follows: First we present a brief literature review followed by a note on the atomic potential used in the present study. Section 4 describes the parameter encoding procedure and a brief description of ECGA is presented in section 5. The cluster optimization algorithms is described in section 6 and the results obtained are discussed in section 7 followed by conclusions.