Integrating firefly algorithm with density functional theory for global optimization of Al42- clusters

The crux of quantum chemistry lies in the minimization of energy functional to obtain the optimized geometry of a molecule. This involves formulating the energy minimization task as a global optimization (GO) problem and using an appropriate algorithm for determining the best solution out of a number of feasible solutions. Several new and unconventional algorithms are proposed that augment the efforts toward GO of clusters of atoms using rigorous quantum chemical methods. Among these, swarm intelligence-based nature-inspired metaheuristic algorithms have particularly drawn considerable attention. However, it still has certain drawbacks. In this work, we propose the use of firefly algorithm (FA) in conjunction with density functional theory (DFT)-based calculations for solving the GO problem and establish its superioriority in performance over particle swarm optimization (PSO) through extensive computational studies. Specifically, we show how such a FA + DFT approach can be used for GO of Al-4(2-) clusters. Each possible structure in the three-dimensional search space is treated as a firefly particle. Starting with an initial pool of particles, newer sets of particles are generated using an evolutionary mechanism, thereby moving toward solutions with particles having better structures. This novel approach also enables the possibility of incorporating molecule specific domain knowledge. For example, knowing that Al-4(2) clusters are planar, we can restrict the search space so that only planar structures are explored, thereby achieving faster convergence of the algorithm. As an extension of the current technique, an important correlation between energy stabilization and aromaticity is established.