Spectral-directed electrostatics strategy integrated within a graph neural network approach for the prediction of...

Predicting the atomic configuration of large nanoclusters from their compositions remains a formidable challenge. To overcome this, we present the spectral-directed electrostatics strategy integrated within a graph neural network (spectral-DESIGNN), a novel method for predicting stable nanocluster structures with specific sizes, symmetries, and compositions. The spectral-DESIGNN approach integrates concepts from the graph-theory (GT)-based spectral clustering method via a graph neural network (GNN) to connect the significant regions of the reference nanocluster to local minima of the molecular electrostatic potential (MESP) topography. We validate this method by constructing energetically favorable Ca_n (n = 4-150) clusters, revealing patterns of structural evolution through analysis of their total interaction energies and growth potentials (GPs). The GP is an energetic descriptor rather than a kinetic descriptor. Notably, clusters with high symmetry display particularly large GP values. To further explain the stability of larger Ca_n clusters, we propose a novel concept of partitioning clusters into core-shell based on the molecular electron density (MED)-isosurface, which highlights the complementary nature of MESP in these regions and supports the architecture proposed by Spectral-DESIGNN. The core-shell MESP complementarity further validates the Spectral-DESIGNN structure prediction method. The robustness of the building approach is further demonstrated through the successful construction of larger Ca_n clusters of sizes, n = 260, 268, 288, and 337. By integrating principles from graph theory, molecular electrostatics, and graph neural networks, Spectral-DESIGNN offers a scalable, accurate, and efficient approach for nanocluster prediction and design, advancing computational materials science.