GMUPC: a new package for global-minimum search of large uranyl peroxide clusters with machine learning potentials and DFT calculations

Abstract

Context

This study presents the development of the GMUPC package, which integrates machine learning potentials (MLPs) to efficiently and accurately identify the possible structures of fullerene-like uranyl peroxide U_n clusters spanning a broad size range from U₂₀ to U₁₀₂₆₀. The computational workflow incorporates symmetric structure generation from Wyckoff positions, isomer perturbation, duplicate structure removal, and four distinct global optimization algorithms, including the particle swarm optimization (PSO), genetic algorithm (GA), standard basin-hopping (BH), and improved basin-hopping (IBH), to systematically explore the potential energy surfaces of large uranyl peroxide systems. We note that the symmetry-seeded structural generation within GMUPC prioritizes high-symmetry cage topologies for computational efficiency; highly distorted, low-symmetry metastable isomers with significant steric strain are less frequently sampled compared to carbon fullerene search algorithms, representing a defined limitation of the present computational framework. Structural explorations uncover non-classical fullerene-like U₂₂ clusters with unique topological structure and a series of giant icosahedral fullerene-like U_60n² (n = 1~12) clusters adhering to the isolated pentagon rule (IPR), with consistent retention of 12 pentagonal faces across all cluster sizes. Geometry analyses establish scalable evolutionary trends in cluster radius, surface area, and volume as functions of uranium atomic count, while energy analyses reveal a monotonic decrease in total energy per uranium atom with increasing cluster size. The GMUPC package enables unprecedented exploration of uranyl peroxide cluster chemistry across size scales previously inaccessible via conventional computational methods, providing atomic-level insights into structure-energy relationships and possible self-assembly principles that bridge fundamental cluster science and nuclear materials chemistry.

Methods

In the present study, the geometrical structures of fullerene-like uranyl peroxide U_n (n = 20~10,260) clusters were systematically explored to identify their possible thermodynamically stable geometries. Global-minimum structural searches of U_n (n = 20~60) clusters with even number of uranium atoms were independently performed using two advanced computational approaches: the recently developed GMUPC code interfaced with the multi-atomic cluster expansion (MACE) machine learning potential. For high-accuracy structural refinement, all low-energy isomers derived from preliminary searches were further re-optimized using density functional theory (DFT). The searched low-lying isomers of U₂₂ clusters were re-optimized at the DFT Perdew-Burke-Ernzerhof (PBE) functional by using the CP2K (v2024.3) package.