Optimisation of carbon cluster geometry using a genetic algorithm

Abstract

A genetic algorithm (GA) based global optimisation procedure has been developed and used to find the most stable configurations of small carbon clusters. The GA attempts to locate the set of atomic nuclei coordinates associated with the global minimum of the potential-energy function using an analogy to Darwinian natural selection. This algorithm uses a novel encoding scheme to evolve a population of cluster geometries towards a low-energy final state. Two semi-empirical many-body potential-energy functions have been encoded for carbon interactions. The binding energies and structural forms of carbon clusters between C₃ and C₆₀ are reported. It has been shown that the algorithm can determine structures with a lower energy than those previously published using more classical local optimisation procedures. The GA can also be used to predict the global minimal energy configuration of pairwise interaction potentials.