Quantum Chemistry, Machine Learning and Atomistic Monte Carlo to Study Melting-Like Transitions in Small Clusters

Abstract

This thesis develops computational methods for efficiently predicting melting-like transitions in clusters. Four criteria are introduced to characterize these transitions: (i) the width of the potential energy distribution (W_U), which broadens near the melting point; (ii) a dissimilarity measure relative to the ground-state configuration, defined from the ordered interatomic distances r_ij; (iii) the effective count of r_ij values near the mean of the first two peaks of the pair distribution function; and (iv) the degree of non-uniformity in the r_ij distribution. Together with an artificial neural network classifier for estimating solid fractions, these measures identify melting transitions with two- to threefold reductions in computational effort compared to conventional heat-capacity-based (C(T)) analyses. Parallel Tempering Monte Carlo (PTMC) was combined with an E(3)-equivariant neural network potential (Allegro) trained to reproduce density functional theory (DFT) energies. The framework was validated on sodium clusters and applied to aluminum clusters containing up to 16 atoms in both neutral and charged states. Predicted melting temperatures ranged from 305 K to above 1200 K, exhibiting size- and charge-dependent nonmonotonic variations consistent with experimental and theoretical data. The methodology was further extended to global optimization, where tens of millions of candidate geometries were screened using the neural network, refined through local optimization, and classified by topological fingerprints and bond-orientational order. This reduced computational cost by three to four orders of magnitude compared to DFT-based sampling while maintaining near-DFT accuracy. The same approach was applied to heteroatomic icosahedral clusters AB_2C_10 chosen for their superatomic potential. Among them, ZrRb_2Au_10 and Sn_3Y_10 were prioritized based on atomization energies and electronic simplicity. Estimated melting temperatures 1263 K and 2061 K, respectively, exceeded the weighted average of their elemental melting points. Overall, this work provides new insights into cluster melting, revealing size-dependent trends, enhanced thermal stability in superatomic systems, and non-melting behaviour in certain aluminum clusters. By integrating multiple indicators and scalable algorithms, it advances the understanding of phase-like transitions at the nanoscale.