Development of a Structural Comparison Method to Promote Exploration of the Potential Energy Surface in the Global Optimization of Nanoclusters

A structural comparison method (SCM) was created to quantify the structural diversity of nanoclusters and was implemented into a global optimization algorithm to evaluate structural diversity between generated clusters on the fly and promote exploration of the potential energy surface. The SCM evaluated topological differences between clusters using the common neighbor analysis and provided a numerical measure of similarity between the two clusters. The SCM was implemented into a genetic algorithm by integrating it into a new structure + energy fitness operator such that structural diversity of clusters in the population and their energies were used to assign fitness values to clusters. The efficiency of the genetic algorithm with this new fitness operator was benchmarked against several Lennard-Jones clusters (LJ(38), LJ(75), and LJ(98)) known to be difficult cases for global optimization algorithms. For LJ(38) and LJ(75), this new structure + energy fitness operator performed equally well or better than the energy fitness operator. However, the efficiency of locating the global minimum of LJ(98) decreased using this new structure + energy fitness operator. Further analysis of the genetic algorithm with this fitness operator showed that the algorithm did indeed promote exploration of the PES of LJ(98), as desired but hindered refinement of clusters, preventing it from locating the global minimum even if the energy funnel of the global minimum had been located.

Automated summary

A structural comparison method (SCM) was developed to quantify the structural diversity of nanoclusters and implemented into a global optimization algorithm to evaluate and promote exploration of the potential energy surface. The efficiency of the algorithm was benchmarked against known difficult cases for global optimization algorithms, showing success in some cases but hindrance in refining clusters to locate the global minimum.