Structures and structural evolution of MN (M = Pt, Ag, Au, N=2-20) from combined revised particle swarm optimization and density function theory

Structure is the key to understanding the properties of metal nanoclusters. Finding a globally optimal structure on an extremely complex potential energy surface is a great challenge for theoretical calculations. In this article, we combine the Revised Particle Swarm Optimization algorithm (RPSO) with Density Functional Theory (DFT), called RPSO-DFT, to explore the potential energy surfaces of platinum, silver, and gold nanoclusters within 20 atoms. Four previously unreported platinum nanocluster structures and two silver nanocluster structures were found. The discovered platinum cluster structures overturn the previous definition of the magic number of platinum clusters. The gold nanocluster calculated by RPSO-DFT is the same as the previous reports, but this algorithm can find the global optimal solution of Au20 cluster with fewer iterations. The test results in this work show that the RPSO-DFT method is accurate and efficient. In addition, RPSO-DFT helped to explore the significance of the difference between the lowest energy value and the second lowest energy value, as well as the variation of the average coordination number with the cluster size based on the new lowest energy structure of small metal clusters.