# Predictive Free Energy Simulations Through Hierarchical Distillation of Quantum Hamiltonians

arXiv: https://arxiv.org/abs/2509.10967 · HTML: https://mlsanity.com/paper/2509.10967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 68 references that are in the map.
- First posted on arXiv 13 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [NNP/MM: Accelerating molecular dynamics simulations with machine learning potentials and molecular mechanic](https://mlsanity.com/paper/2201.08110/) (2022)
- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)

## Abstract (arXiv)

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.