Revisiting and Accelerating the Basin Hopping Algorithm for Lennard-Jones Clusters: Adaptive and Parallel Implementation in Python

TL;DR

Global optimization of Lennard-Jones clusters is challenged by rugged potential-energy surfaces. The authors implement an adaptive Basin Hopping framework with parallel evaluation of multiple trial structures and a Metropolis acceptance criterion at $T = 1.0$, with step-size adaptation toward a target of $0.5$ acceptance. The approach provides an accessible Python tool that achieves near-linear speedup up to eight concurrent minimizations and demonstrates robust identification of low-energy minima such as LJ_38. This framework is readily extensible to ab initio calculations and machine-learned potentials on HPC resources, enabling efficient near-DFT-level exploration of cluster landscapes.

Abstract

We present an adaptive and parallel implementation of the Basin Hopping (BH) algorithm for the global optimization of atomic clusters interacting via the Lennard-Jones (LJ) potential. The method integrates local energy minimization with adaptive step-size Monte Carlo moves and simultaneous evaluation of multiple trial structures, enabling efficient exploration of complex potential energy landscapes while maintaining a balance between exploration and refinement. Parallel evaluation of candidate structures significantly reduces wall-clock time, achieving nearly linear speedup for up to eight concurrent local minimizations. This framework provides a practical and scalable strategy to accelerate Basin Hopping searches, directly extendable to ab initio calculations such as density functional theory (DFT) on high-performance computing architectures.

Figures (6)

• Figure 1: Schematic representation of the accelerated Basin Hopping workflow. Multiple trial structures are generated and locally optimized in parallel, enabling faster identification of low-energy configurations.
• Figure 2: Basin Hopping energy landscape for a Lennard-Jones cluster. Trial energies (blue), accepted configurations (red), and the running lowest energy (green) are shown as a function of the BH step.
• Figure 3: Energy of the best accepted structure at each BH step. Adaptive control enables efficient descent.
• Figure 4: Cumulative wall-clock time as a function of Basin Hopping step for different numbers of trial structures evaluated concurrently. Parallel evaluation substantially reduces runtime.
• Figure 5: Speedup and parallel efficiency of the Basin Hopping algorithm as a function of the number of trial structures evaluated concurrently. Efficiency approaches saturation beyond eight candidates per step due to communication and synchronization overhead.