Spheroid models to elaborate the broken symmetry and equivalent volume of molecules in crystalline phase

Dense packing of particles has provided powerful models to elaborate the important structural features of matter in various systems such as liquid, glassy, and crystalline phases. The simplest sphere packing models can represent and capture salient properties of the building blocks for covalent, metallic, and ionic crystals; it, however, becomes insufficient to reflect the broken symmetry of the commonly anisotropic molecules in molecular crystals. Here, we develop spheroid models with a minimal degree of anisotropy, which serve as a simple geometrical representation for a rich spectrum of molecules-including both isotropic and anisotropic, convex and concave ones-in crystalline phases. Our models are determined via an inverse packing approach: Given a molecular crystal, an optimal spheroid model is constructed using a contact diagram, which depicts the packing relationship between neighboring molecules within the crystal. The spheroid models are capable of accurately capturing the broken symmetry and characterizing the equivalent volume of molecules in the crystalline phases. Moreover, our model retrieves such molecular information from low-quality x-ray diffraction data with poorly resolved structures, and by using soft spheroids, it can also describe the packing behavior in cocrystals.