Physical Prior Mean Function-Driven Gaussian Processes Search for Minimum-Energy Reaction Paths with a Climbing-Image Nudged Elastic Band: A General Method for Gas-Phase, Interfacial, and Bulk-Phase Reactions.

The climbing-image nudged elastic band (CI-NEB) method serves as an indispensable tool for computational chemists, offering insight into minimum-energy reaction paths (MEPs) by delineating both transition states (TSs) and intermediate nonstationary structures along reaction coordinates. However, executing CI-NEB calculations for reactions with extensive reaction coordinate spans necessitates a large number of images to ensure a reliable convergence of the MEPs and TS structures, presenting a computationally demanding optimization challenge, even with mildly costly electronic-structure methods. In this study, we advocate for the utilization of physically inspired prior mean function-based Gaussian processes (GPs) to expedite MEP exploration and TS optimization via the CI-NEB method. By incorporating reliable prior physical approximations into potential energy surface (PES) modeling, we demonstrate enhanced efficiency in multidimensional CI-NEB optimization with surrogate-based optimizers. Our physically informed GP approach not only outperforms traditional nonsurrogate-based optimizers in optimization efficiency but also on-the-fly learns the reaction path valley during optimization, culminating in significant advancements. The surrogate PES derived from our optimization exhibits high accuracy compared to true PES references, aligning with our emphasis on leveraging reliable physical priors for robust and efficient posterior mean learning in GPs. Through a systematic benchmark study encompassing various reaction pathways, including gas-phase, bulk-phase, and interfacial/surface reactions, our physical GPs consistently demonstrate superior efficiency and reliability. For instance, they outperform the popular fast inertial relaxation engine optimizer by approximately a factor of 10, showcasing their versatility and efficacy in exploring reaction mechanisms and surface reaction PESs.