OGRe: Optimal grid refinement protocol for accurate free energy surfaces and its application to proton hopping in zeolites and 2D COF stacking

While free energy surfaces are the crux of our understanding in many chemical and biological processes, their accuracy is generally unknown. Moreover, many developments to improve their accuracy are often complicated, impeding their general use. Luckily, several tools and guidelines are already in place to identify these shortcomings, but they are typically lacking in flexibility or fail to systematically determine how to improve the accuracy of the free energy calculation. To overcome these limitations, this work introduces OGRe--a python package for optimal grid refinement in an arbitrary number of dimensions. OGRe is based on three metrics which gauge the confinement, consistency, and overlap of each simulation in a series of umbrella sampling (US) simulations, an enhanced sampling technique ubiquitously adopted to construct free energy surfaces for hindered processes. As these three metrics are fundamentally linked to the accuracy of the weighted histogram analysis method, adopted to generate free energy surfaces from US simulations, they facilitate a systematic construction of accurate free energy profiles, where each metric is driven by a specific umbrella parameter. This allows for the derivation of a consistent and optimal collection of umbrellas for each simulation, largely independent of the initial values, thereby dramatically increasing the ease-of-use towards accurate free energy surfaces. As such, OGRe is particularly suited to determined complex free energy surfaces, with large activation barriers and shallow minima, which underpin many physical and chemical transformations, and hence to further our fundamental understanding of these processes.