Optimizing atomic structures through geno-mathematical programming

Abstract

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