Predicting the Atomic Configuration of 1- and 2-Dimensional Nanostructures via Global Optimization Methods

Abstract

In the cluster structure community, global optimization methods are common tools for arriving at the atomic structure of molecular and atomic clusters. The large number of local minima of the potential energy surface of these clusters, and the fact that these local minima proliferate exponentially with the number of atoms in the cluster simply demands the use of fast stochastic methods to find the optimum atomic configuration. Therefore, much of the development work has come from (and mostly stayed within) the cluster structure community. Partly due to wide availability and landmark successes of high resolution microscopy techniques, finding the structure of periodically reconstructed semiconductor surfaces was not posed as a problem of stochastic optimization until recently, when we have shown that high-index semiconductor surfaces can posses a rather large number of local minima with such low surface energies that the identification of the global minimum becomes problematic. We have therefore set out to develop global optimization methods for systems other than clusters, focusing on periodic systems in one- and two- dimensions as such systems currently occupy a central place in the field of nanoscience. In this article, we review some of our recent work on global optimization methods (the parallel-tempering Monte Carlo method and the genetic algorithm) and show examples/results from two main problem categories: (1) the two-dimensional problem of determining the atomic configuration of clean semiconductor surfaces, and (2) finding the structure of freestanding nanowires. While focused mainly on optimization the atomic structure for a system with set periodic boundary conditions, our account also reviews a recent example of using genetic algorithms for growth of nanostructures into their global energy minima compatible with given confinement conditions