Structure and Stability Prediction of Binary and Ternary Molecular Mixed Crystals Using Ensemble Free Energies

Abstract

Mixed crystals provide a route to tune the properties of molecular solids through continuous changes in composition. However, predicting their stability is challenging because it requires determining both substitution energies and configurational entropy across large configuration spaces. Here, we combine crystal structure prediction, force field lattice energy and lattice dynamics calculations, and Δ-machine-learning energy corrections with a scaled partition-function approach to assess structure prediction and evaluate binary and ternary mixed crystals of anthracene (ANT), acridine (ACR), and phenazine (PNZ). The composition-dependent ensemble free energy (ΔGensemble) was estimated without exhaustive enumeration of all configurations from representative ensembles of substituted supercell models of mixed crystals. Crystal structure prediction reproduces the known polymorphs as the lowest energy structures and the mixed crystal modelling approach reproduces the main experimental binary trends: ACR incorporation into ANT and the α and β polymorphs of PNZ, ANT incorporation into ACR form II, and the formation of a PNZ β-type ternary phase. Furthermore, we predict additional thermodynamically stable compositions, including PNZ incorporation into ACR form IX, and ternary crystals based on ACR forms II, VI and VII. Stable three-component regions arise from binary trends, with ACR mediating between both ANT and PNZ. These results demonstrate a practical framework for predicting the structure, thermodynamic stability and composition limits of molecular mixed crystals. The mixed crystal modelling methods are available within the mol-CSPy crystal structure prediction package.