The modular approach is a powerful tool in current inorganic crystal chemistry. It enables not only a more detailed analysis of the known structures and the determination of structural relationships between them, but also the prediction of potentially novel structures that can be applied in modern materials science. A large number of examples of compounds with modular structures allows us to state that structural modularity is a widely spread phenomenon among natural and synthetic compounds. The use of the formalism of OD theory makes it possible to analyze the symmetry of polytypes with different crystal structures. In this review, we collected new data published in the last 15 years about OD structures and phenomena of polytypism and modularity in inorganic compounds, as well as the topological approach to the analysis of crystal structures.

For homomolecular organic crystals the critical coordination number was introduced. The possible coordination numbers were investigated.

Structural complexity measures based on Shannon information entropy are widely used for inorganic crystal structures. However, the application of these parameters for molecular crystals requires essential modification since atoms in inorganic compounds usually possess more degrees of freedom. In this work, a novel scheme for the calculation of complexity parameters (H_molNet, H_molNet,tot) for molecular crystals is proposed as a sum of the complexity of each molecule, the complexity of intermolecular contacts, and the combined complexity of both. This scheme is tested for several molecular crystal structures.

A net of intermolecular contacts in organic crystals contains a finite number of strong contacts sufficient for the net formation. These contacts constitute a subnet referred to as the critical net. Critical nets of 1754 crystalline hydrocarbons in six most common structural classes (supergiants) are studied. Coordination numbers and the critical net topology are analyzed, the predominant topological types (dia, pcu, hex, bnn, etc.) are revealed. The critical net is found to be quite economical in 95% cases and containing n + Δ (Δ = 0-2) symmetrically independent contacts, where n is their minimal possible number.

Based on Krivovichev information measures for crystal structures and the universal partitioning scheme for different sources of information described previously by Hornfeck, we proposed a general scheme of complexity calculation for heterodesmic crystals.

The molecular net complexity (H_molNet) is an extension of the combinatorial complexity (H_mol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of C_xH_yO_z characterized by the structural class P2₁/c, Z = 4 (1). The molecular nets were derived from the molecular Voronoi–Dirichlet Polyhedra (VDP_mol). The values of the molecular coordination number (CN_mol) and critical coordination number (CN_crit) are discussed in relation with the complexity of the crystal structures. A statistical distribution of the set of molecular crystals based on the values of CN_mol, CN_crit, and the complexity parameters is obtained. More than a half of the considered structures has CN_mol = 14 and CN_mol′ = 9 with the Wyckoff set of edges e⁵dcba. The average multiplicity of intermolecular contacts statistically significantly decreases from 1.58 to 1.51 upon excluding all contacts except those bearing the molecular net. The normalized value of H_molNet is of the logistic distribution type and is distributed near 0.85H_molNet with a small standard deviation. The contribution of H_mol into H_molNet ranges from 35 to 95% (mean 79%, SD 6%), and the subset of bearing intermolecular contacts accounts for 41 to 100% (mean 62%, SD 11%) of the complexity of the full set of intermolecular contacts.