Lattice Free Energies of Molecular Crystals Using Normalizing Flow

Accurate free energy calculations are essential for predicting thermodynamic stability across complex molecular materials. Classical approaches such as the Einstein crystal method (ECM) provide benchmark accuracy but are computationally prohibitive for flexible, high-dimensional systems. Here we develop a scalable framework that couples targeted free energy perturbation with normalizing flow neural networks trained to learn bijective mappings between Boltzmann ensembles and analytical reference states. This enables robust lattice free energy estimates directly from molecular dynamics trajectories, eliminating the need for intermediate alchemical sampling. The method handles supercells with up to 3 x 10^3 degrees of freedom and supports multi-polymorph training within 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 free energy prediction toward automation and high-throughput applications in molecular and materials design.