A Jacobian-corrected minimum-mode following bias potential for hyperdynamics

Abstract

Rare-event molecular dynamics simulations are limited by the separation between atomic and activated timescales. Hyperdynamics accelerates these processes via bias potentials while preserving correct transition kinetics. The minimum-mode following (MMF) formulation provides a ridge-based bias construction but typically employs an identity approximation for the Jacobian together with local force evaluation, which introduces inconsistency in high-dimensional systems. Here, we develop a Jacobian-corrected MMF (J-MMF) method that improves both accuracy and consistency. The method introduces a path-informed semi-analytical Jacobian based on the sequential evolution of minimum-mode vectors and an orthogonal projection that removes spurious force components along the reaction coordinate, without additional force evaluations. Benchmark simulations of adatom diffusion on the Cu(100) surface (1–201 mobile atoms) demonstrate improved accuracy and robust, largely size-independent acceleration compared with standard MMF and bond-boost methods. J-MMF provides a scalable and consistent framework for rare-event simulations in complex atomistic systems.