Stochastic Global Search on Molecular Potential-Energy Surfaces: A Narrative Survey and a Reported Numerical Illustration

Abstract

Stochastic global search connects geometric exploration of potential-energy surfaces with the cost of evaluating electronic-structure models. This narrative survey relates population methods, basin hopping, minima hopping and surrogate-assisted search across clusters, molecular conformers, surface adsorbates and crystal structures. It distinguishes changes in the search policy from changes in the energy model and from evidence of computational savings. A surrogate-assisted hybrid search (SAHS) is discussed as an integration sketch, followed by the numerical illustration reported in the source manuscript for Lennard-Jones clusters and thirty synthetic potential functions. The retained summaries are not an independently reproduced electronic-structure experiment. The component table reports 3,600 evaluations for SAHS and 14,200 with its GP disabled, a count ratio of 3.94, while the corresponding accuracy entries differ. The reported timing of 295 seconds cannot be reconciled with a uniform 22-second parent calculation on sixteen cores without additional accounting. Negative differences from the stated energy reference, nonmonotone best-so-far traces and a reported p-value below the minimum for an exact two-sided thirty-pair test also require the original records. Recalculation gives a conventional Nemenyi critical difference of approximately 1.377 for six algorithms and thirty blocks, rather than the embedded annotation 1.318; the reported BH comparison does not reject. The survey therefore provides a methodological synthesis and a qualified interpretation of preserved numerical summaries, without establishing DFT acceleration, a globally certified molecular geometry or universal algorithm superiority.