A Unified Hyperdynamics Framework for Rare-Event Simulations Across Complex Energy Landscapes

The collective variable-driven hyperdynamics (CVHD) method has been proven effective in extending the accessible time scales of molecular simulations at experimentally relevant temperatures. However, this incremental biasing can lead to reduced efficiency, particularly for transitions involving high-energy barriers. In the present work, we integrate on-the-fly probability-enhanced sampling (OPES) with CVHD, resulting in a hybrid approach denoted as OPESCVHD, specifically designed for the efficient acceleration of rare events and the extraction of physically meaningful kinetic rates in complex and poorly characterized systems. To address the presence of widely separated energy barriers common in complex systems, the barrier parameter of the OPES implementation is periodically updated, which is akin to progressively filling a tank with water. This strategy effectively combines the adaptive nature of dynamical biasing in complex systems with the efficiency of static biasing methods in well-characterized systems, wherein the simulation can converge to a predefined bias very quickly. The performance and applicability of OPESCVHD are demonstrated by using several representative systems. These results highlight OPESCVHD as a powerful and general tool for rare-event simulations in chemical and materials systems.