Optimizing Atomic Structures Through Geno-Mathematical Programming (Communications in Computational Physics, 2018)
In this paper, we describe our initiative to utilize a modern well-tested numericalplatform 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 supercellthrough optimization. We are using the semi-empirical Tersoff potential. We focus ona 2x2x1 supercell of cubic silicon unit cells; of the 32 atoms present, we have fixed 12atoms at their correct positions, leaving 20 atoms for optimization. We have been ableto find the known global minimum of the system in different 19-, 43- and 60-parametercases. We compare the results obtained with our algorithm to traditional methods ofsteepest descent, simulated annealing and basin hopping. The difficulties of the optimizationtask arise from the local minimum dense energy landscape of materials anda large amount of parameters. We need to navigate our way efficiently through theseminima without being stuck in some unfavorable area of the parameter space. Weemploy different techniques and optimization algorithms to do this.
Keywords: Optimization; geno-mathematical programming; bulk silicon; semi-empirical potential.