Global geometry optimization of atomic clusters using a modified genetic algorithm in space-fixed coordinates

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Abstract
In a recent paper, Gregurick, Alexander, and Hartke [S. K. Gregurick, M. H. Alexander, and B. Hartke, J. Chem. Phys. 104, 2684 (1996)] proposed a global geometry optimization technique using a modified Genetic Algorithm approach for clusters. They refer to their technique as a deterministic/stochastic genetic algorithm (DS‐GA). In this technique, the stochastic part is a traditional GA, with the manipulations being carried 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 spending a large amount of computer time searching parts of the configuration space which correspond to high‐energy geometries. Their tests of the technique show it is vastly more efficient than searches without this local minimization. They report geometries for clusters of up to n=29 Ar atoms, and find that their computer time scales as O(n4.5). In this work, we have recast the genetic algorithm optimization in space‐fixed Cartesian coordinates, which scale much more favorably than internal 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(n3.3). It is concluded that genetic algorithm optimization in nonseparable real variables is not only viable, but numerically superior to that in internal candidates for atomic cluster calculations. Furthermore, no special choice of variable need be made for different cluster types; real Cartesian variables are readily portable, and can be used for atomic and molecular clusters with no extra effort.