Molecular Crystal Structure Prediction from Conditional Flow on the Unit Cells

A molecular crystal structure is jointly described by its space group symmetry, unit cell, and the molecular alignment within the asymmetric unit. Concurrently predicting all three variables is a daunting task, as it mixes discrete symmetry choices with a high-dimensional search in the continuous space. To address this challenge, we decouple these variables using a three-step generation process. Specifically, we train a flow model to learn the conditional distribution of invariant lattice descriptors (e.g. direct- and reciprocal-lattice successive minima and Selling scalars) from a molecular graph, a Hall setting, and the number of molecules in the asymmetric unit ($Z^{\mathrm{\prime }}$). Using a two sequential quasi-random sampling processes, we first reconstruct the cell parameters that match the predicted lattice invariants and density requirements, and then conduct a molecular packing search within the give symmetry and unit cell constraint. On 84 single-component systems with $Z^{\mathrm{\prime }}\le 1$, our approach reproduces experimental matches for 83 systems; the remaining failure stems from force-field limitations in preserving the experimental structure. These results demonstrate that learned cell proposals can effectively support crystal structure prediction (CSP) for a given Hall setting and $Z^{\mathrm{\prime }}$, which may be extended to fully blind prediction with variable symmetry and $Z^{\mathrm{\prime }}$ settings in the future.