Quantifying Packing Efficiency in Molecular Crystals: A Close Packing Index Based on Hirshfeld Surfaces

Abstract

The degree of close packing in molecular crystals can dictate their mechanical, chemical, and photophysical properties. Here, we present a simple descriptor of close packing in molecular crystals, based on Spackman’s intermolecular boundary surfaces, known as Hirshfeld surfaces. In comparison to Kitaigorodskii’s packing index (KPI), the values of this close packing index (CP_i) offer a more accurate description of packing efficiency and demonstrate stronger correlations with properties such as melting point and lattice cohesive energy examined in two different series of crystal structures in this study. The usefulness of this CP_i is demonstrated here for comparing multi-component cocrystals, high Z′ structures, and isostructural molecular crystals of chemical analogs, for which the direct comparison of crystal density would be less meaningful. Correlations of the CP_i values with the lattice cohesive energies, melting points, and mechanical properties such as Young’s moduli have been examined. These results imply that CP_i may serve as a simple yet useful structural tool in crystal engineering studies.