Optimizing Atomic Structures through Geno-Mathematical Programming

In this paper, we describe our initiative to utilize a modern well-tested numerical platform in the field of material physics: the Genetic Hybrid Algorithm (GHA). Our aim is to develop a powerful special-purpose tool for finding ground state structures. Our task is to find the diamond bulk atomic structure of a silicon supercell through optimization. We are using the semi-empirical Tersoff potential. We focus on a 2x2x1 supercell of cubic silicon unit cells; of the 32 atoms present, we have fixed 12 atoms at their correct positions, leaving 20 atoms for optimization. We have been able to find the known global minimum of the system in different 19-, 43- and 60-parameter cases. We compare the results obtained with our algorithm to traditional methods of steepest descent, simulated annealing and basin hopping. The difficulties of the optimization task arise from the local minimum dense energy landscape of materials and a large amount of parameters. We need to navigate our way efficiently through these minima without being stuck in some unfavorable area of the parameter space. We employ different techniques and optimization algorithms to do this.