Curvature-assisted Minima Hopping on Lennard–Jones Energy Landscapes: Reusing Quasi-Newton Information for Escape Directions

Global structure optimization in computational chemistry is often limited not by leaving the current local minimum, which can be achieved by sufficiently large random moves, but by proposing productive moves that exploit local funnel structure without losing diversity. Minima hopping addresses this problem through short molecular-dynamics escape trajectories, local relaxation, and history-dependent feedback, but its efficiency depends strongly on the initial escape direction. We benchmark a curvature-assisted variant in which inverse-Hessian information accumulated by Broyden–Fletcher–Goldfarb–Shanno (BFGS) and limited-memory BFGS (L-BFGS) relaxation is recycled as an escape model. This requires no explicit second derivatives and no additional force evaluations before proposing low-curvature directions. Lennard–Jones (LJ) clusters with 60–74 particles provide controlled landscapes for comparing random and softened random directions, single Hessian modes, multi-mode Hessian combinations, and mixed Hessian-random directions. Dense BFGS curvature information identifies physically meaningful escape subspaces and can reduce repeated local exploration. Single deterministic modes, however, oversample local funnels, and L-BFGS curvature information is not reliable enough for direct mode selection. Combining several BFGS modes improves robustness, but softened random directions with L-BFGS remain the lowest-cost baseline. Curvature reuse is therefore most useful when it provides an inexpensive soft-mode subspace while preserving stochastic diversity, especially when conventional softening or trial-move optimization is expensive.