GLOBAL GEOMETRY OPTIMIZATION OF ATOMIC CLUSTERS USING A MODIFIED GENETIC ALGORITHM IN SPACE-FIXED COORDINATES

In a recent paper, Gregurick, Alexander, and Hartke [S. K. Gregurick, M. H. Alexander, and B. Hartke, J. Chem. Phys. 104, 2684 (1996)] propo sed a global geometry optimization technique using a modified Genetic Algorithm approach for clusters. They refer to their technique as a de terministic/stochastic genetic algorithm (DS-GA). In this technique, t he stochastic part is a traditional GA, with the manipulations being c arried out on binary-coded internal coordinates (atom-atom distances). The deterministic aspect of their method is the inclusion of a coarse gradient descent calculation on each geometry. This step avoids spend ing a large amount of computer time searching parts of the configurati on space which correspond to high-energy geometries. Their tests of th e technique show it is vastly more efficient than searches without thi s local minimization. They report geometries for clusters of up to n = 29 Ar atoms, and find that their computer time scales as O(n(4.5)). I n this work, we have recast the genetic algorithm optimization in spac e-fixed Cartesian coordinates, which scale much more favorably than in ternal coordinates for large clusters. We introduce genetic operators suited for real (base-10) variables. We find convergence for clusters up to n = 55. Furthermore, our algorithm scales as O(n(3.3)). It is co ncluded that genetic algorithm optimization in nonseparable real varia bles is not only viable, but numerically superior to that in internal candidates for atomic cluster calculations. Furthermore, no special ch oice of variable need be made for different cluster types; real Cartes ian variables are readily portable, and can be used for atomic and mol ecular clusters with no extra effort. (C) 1996 American Institute of P hysics.