Lattice free energies of molecular crystals using normalizing flow

Abstract

Abstract Accurate free-energy calculations are essential for predicting thermodynamic stability in complex molecular materials, such as the polymorphic crystal landscapes of pharmaceutical molecules. Classical methods such as the Einstein crystal method (ECM) provide benchmark accuracy but are computationally prohibitive in larger crystal landscapes generated by Crystal Structure Prediction. Here, we develop a scalable framework for the anharmonic free-energy ranking of molecular crystals, based on targeted free-energy perturbation. In particular, we utilise the targeted Bennett acceptance ratio (tBAR) method, where the targeting step employs a bijective map learned via a normalising flow. The maps are trained to analytically transform supercell configurations between the crystal Boltzmann ensembles of interest and an analytical reference state. Exact likelihoods, in turn, enable reliable lattice free-energy estimates directly from physical molecular dynamics data, without alchemical sampling. The method handles supercells with up to 3 × 10 3 degrees of freedom and permits multi-state training with a single model. Validation across succinic acid, Veliparib, and Mivebresib demonstrates excellent agreement with ECM at significantly lower cost. By combining statistical mechanics and machine-learning expressivity, this approach advances anharmonic free energies towards automation and high-throughput applications in molecular and materials design.

The authors' abstract, as published at the source. npj Computational Materials, 2026 · DOI ↗