A geometry-matched structure generator outperforms basin hopping for silicon cluster global optimisation at fixed relaxation budget

In cluster global optimisation the cost is dominated by local relaxations, so the number of relaxations—not wall-clock time—is the natural budget whenever each relaxation is a first-principles or machine-learned potential evaluation. We ask how much of that budget can be saved by the initial structure generator alone. We study a motif-agnostic generator that places each new atom by trilateration at a fixed bond distance from at least three alreadyplaced atoms, subject to a steric admissibility test, and we benchmark it as a drop-in initialiser for Stillinger–Weber silicon clusters with n = 24–60 atoms against three baselines: random structure search, a specialised basin-hopping implementation with single-atom, collective and surface moves and an adaptive step, and a growth-pattern beam search in the spirit of GOALS and GrowPAL. At equal relaxation budget the generator reaches lower minima than specialised basin hopping at every size from n = 32 upward, winning 8/8 paired replicates at n = 48 and n = 60 with complete distributional separation at n = 48, and it beats growth-pattern search in 7/8 paired replicates at both sizes. It also exhibits markedly lower run-to-run variance, and it was the only method to locate the deepest structure found at n = 32, n = 40 and n = 60. The advantage is absent at n = 16, marginal at n = 24, and clean from n = 32; a structural analysis of the resulting minima shows that they are more highly coordinated than the baselines’ but not more tetrahedral in bond angle, so we report the size onset as an unexplained empirical observation rather than attribute it to angular matching. We report the opposite accounting as well: because growth-pattern relaxations start from an already-optimised sub-cluster they are roughly an order of magnitude cheaper in wall-clock, and on equal CPU time the two methods are comparable, while the advantage over basin hopping persists on both accountings.