Binding free energy from umbrella sampling at ML-enhanced Born-Oppenheimer MD simulations

Molecular dynamics (MD) simulations of systems with many atoms are often constrained by computational limitations, requiring either short simulation times or the use of force-field methods. Recently, we demonstrated that machine-learning (ML) potentials can be trained on small molecular systems, such as molecular clusters, that are computationally explorable via accurate quantum chemistry methods. These ML potentials can subsequently be used to model larger molecular systems while maintaining the same energy-per-atom and force-per-atom accuracy. This allows us to perform Born-Oppenheimer MD (BOMD) simulations using Hamiltonians derived from ML-modeled quantum chemistry calculations.

 

In this work, we calculate the binding free energies of molecular clusters using umbrella sampling (US) combined with the aforementioned ML-enhanced BOMD simulations. We validated this approach on small molecular dimers, such as water and sulfuric acid dimers, where the use of a low level of theory (e.g., GFN1-xTB) allowed us to perform and compare quantum chemistry calculations, BOMD, and ML-enhanced BOMD simulations. Furthermore, we extended the methodology to compute the binding free energies of larger molecular clusters.

 

Our approach highlights the advantage of US in accounting for free energy contributions arising from multiple energy minima (i.e., conformers) and vibrational anharmonicity. These entropic effects, often neglected in traditional statistical thermodynamics applied to quantum chemistry calculations, are crucial for an accurate understanding of binding free energies in complex molecular systems.