Predictive Free Energy Simulations Through Hierarchical Distillation of Quantum Hamiltonians

Obtaining the free energies of condensed phase chemical reactions remains computationally prohibitive for high-level quantum mechanical methods. We introduce a hierarchical machine learning framework that bridges this gap by distilling knowledge from a small number of high-fidelity quantum calculations into increasingly coarse-grained, machine-learned quantum Hamiltonians. By retaining explicit electronic degrees of freedom, our approach further enables a faithful embedding of quantum and classical degrees of freedom that captures long-range electrostatics and the quantum response to a classical environment to infinite order. As validation, we compute the proton dissociation constants of weak acids and the kinetic rate of an enzymatic reaction entirely from first principles, reproducing experimental measurements within chemical accuracy or their uncertainties. Our work demonstrates a path to condensed phase simulations of reaction free energies at the highest levels of accuracy with converged statistics.