Melting Transitions in Small Aluminum Clusters Simulated with Energies Approaching DFT Accuracy

We describe a computational framework for modeling melting-like transitions in atomic clusters that combines first-principles energy calculations, global optimization, and machine-learned interatomic potentials. A diverse set of configurations is generated by global optimization, and Density Functional Theory calculates the associated energies. These energies are then fitted to an accuracy of 10 meV/atom or better with an Allegro E(3)-equivariant neural network potential. The resulting model allows for efficient parallel tempering Monte Carlo simulations with near-DFT-level accuracy. This methodology is validated by simulating Na₂₀ and comparing it to earlier experimental and computational results. Using this approach, we study melting-like transitions in Al_n⁺ clusters (n = 9 to 16), Al_n and Al_n^- (n = 12, 13, 14). The simulated heat capacity of these clusters, in particular Al₁₆⁺, is in qualitative agreement with experiments. We also observe that the melting point of Al_n⁺ clusters with n = 11-16 are well above the bulk melting point (934 K), with the closed-shell Al₁₃^- species possessing an exceptionally high melting point close to 2100 K.