Minimization of small silicon clusters using the space-fixed modified genetic algorithm method

Abstract

A space-fixed modified genetic algorithm (SFMGA) approach was used to obtain global minima for the silicon clusters (Si) n using a semiempirical potential. One modification to the usual GA is the use of gradient-driven minimization of each geometry. A novel feature of the method is the use of space-fixed atomic coordinates. The advantages of these coordinates are discussed. The method found all minima previously reported for n = 3−10, and improved on those for n = 5−8. That the commonly-used method of seeding a cluster can actually detract from minimization efficiency, is also shown.