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

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.