Accurate Lattice Free Energies of Packing Polymorphs from Probabilistic Generative Models

Finite-temperature lattice free energy differences between polymorphs of molecular crystals are fundamental to understanding and predicting the relative stability relationships underpinning polymorphism, yet are computationally expensive to obtain. Here, we implement and critically assess machine-learning-enabled targeted free energy calculations derived from flow-based generative models to compute the free energy difference between two ice crystal polymorphs (Ice XI and Ic), modeled with a fully flexible empirical classical force field. We demonstrate that even when remapping from an analytical reference distribution, such methods enable a cost-effective and accurate calculation of free energy differences between disconnected metastable ensembles when trained on locally ergodic data sampled exclusively from the ensembles of interest. Unlike classical free energy perturbation methods, such as the Einstein crystal method, the targeted approach analyzed in this work requires no additional sampling of intermediate perturbed Hamiltonians, offering significant computational savings. To systematically assess the accuracy of the method, we monitored the convergence of free energy estimates during training by implementing an overfitting-aware weighted averaging strategy. By comparing our results with ground-truth free energy differences computed with the Einstein crystal method, we assess the accuracy and efficiency of two different model architectures, employing two different representations of the supercell degrees of freedom (Cartesian vs quaternion-based). We conduct our assessment by comparing free energy differences between crystal supercells of different sizes and temperatures and assessing the accuracy in extrapolating lattice free energies to the thermodynamic limit. While at low temperatures and in small system sizes, the models perform with similar accuracy. We note that for larger systems and high temperatures, the choice of representation is key to obtaining generalizable results of quality comparable to that obtained from the Einstein crystal method. We believe this work to be a stepping stone toward efficient free energy calculations in larger, more complex molecular crystals.