Determination of stable structure of a cluster using convolutional neural network and particle swarm optimization

Minimization of the energy of a molecule is an important research problem in quantum chemistry. The use of appropriate global optimization algorithms for determining the most stable configuration is a matter of active interest, and various efforts have been made toward achieving the same. Instead of using single method-based techniques, a recent method has been developed for constructing new models where particle swarm optimization can be made use of. In the present study, we propose a convolutional neural network (CNN) model for learning and predicting the energy of a system by training geometries of cluster units containing both metal and non-metal atoms, viz. C 5 , N 4 2− , N 6 4− , Au n ( n = 2 − 8) and Au n Ag m (2 ≤ n + m ≤ 8) clusters as prototype examples. Initially, several random clusters are generated within a given range in the three-dimensional space and their energies determined using the atom-centered density matrix propagation molecular dynamics simulation (ADMP). A CNN model is constructed from this initial set of clusters, which is later used for generating a huge number of systems required while searching for the stable structure, instead of using time-consuming quantum mechanical calculations in an iterative process. While several global optimization algorithms could have been used, we choose to employ particle swarm optimization (PSO) due to its ease of implementation and efficient rate of convergence.