Global Optimization of Dinitrogen Clusters Bound to Monolayer and Bilayer Graphene: A Swarm Intelligence Approach

Locating the global minimum of a potential energy surface is an arduous task. The complexity of the potential energy surface increases as the number of degrees of freedom of the system increases. The highly rugged nature of the potential energy surface makes the minimization of the total energy of the molecular clusters a difficult optimization problem. A solution to this conundrum is the use of metaheuristic techniques that efficiently track down the global minima through a trade-off between exploration and exploitation. Herein, we use the swarm intelligence technique, particle swarm optimization to locate the global minima geometries of N₂ clusters of size 2-10, in free and adsorbed states. We have investigated the structures and energetics of bare N₂ clusters, followed by N₂ clusters adsorbed on graphene and intercalated between the layers in bilayer graphene. The noncovalent interactions between dinitrogen molecules are modeled using the Buckingham potential as well as the electrostatic point charge model, while those of the N₂ molecules with the carbon atoms of graphene are modeled using the improved Lennard-Jones potential. The interactions of the carbon atoms belonging to different layers in a bilayer are modeled using the Lennard-Jones potential. The bare cluster geometries and intermolecular interaction energies obtained using particle swarm optimization are found to be the same as reported in the literature, validating the use of particle swarm optimization for studying molecular clusters. The N₂ molecules are found to adsorb as a monolayer on top of the graphene sheet and intercalate themselves right in the middle of the two sheets of bilayer graphene. Our study establishes that particle swarm optimization is a feasible global optimization technique for performing the optimization of high-dimensional molecular clusters, both in pristine and in confined forms.