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The combinatorial-topological analysis and simulation of self-assembly of the Na96Hg36-hR132 (space group R-3c, a = b = 9.228 A, c = 52.6380 A, V = 3881.91 A3) and Na12Hg8-tP20 (space group P42/mnm, a = b = 8.520, c = 7.800 A, V = 566.2 A3) crystal structures are conducted by computer-based methods (ToposPro program package). Polyhedral cluster precursors K11 = 0@11(Na8Hg3) and K9 = Hg@Na8 are first determined for the intermetallic compound Na96Hg36-hR132, while polyhedral cluster precursors K5 = 0@Na3Hg2 are determined for the intermetallic compound Na12Hg8-tP20. The symmetry and topology code of the self-assembly processes of the 3D structure Na96Hg36-hR132 from the nanocluster precursors K11 and K9, and of the 3D structure Na12Hg8-tP20 from the K5 clusters are reconstructed as the primary chain $$S_{{\text{3}}}^{1}$$ → layer $$S_{{\text{3}}}^{2}$$ → frame $$S_{{\text{3}}}^{3}.$$ The structural analysis of all known intermetallic compounds is conducted, and numerous examples of the assembly of their structures from the K5, K9, and K11 clusters are found.

We present a novel approach to the generation of new crystalline phases, which is based on a combination of the topological description of crystal structures as a periodic net and the extended Zintl-Klemm concept, which establishes the structural relations between chemically and structurally simpler and more complex inorganic compounds. With this approach, we have explored the structural similarities between all known binary sulfides, selenides, and the corresponding simple sulfates and selenates and have theoretically revealed seven new high-pressure phases in the last two groups of compounds. Using density functional theory methods, we have studied the thermodynamic and mechanical stability of the new phases, have adjusted the transition pathways in the sulfate and selenate systems, and have revealed new structural correlations of the baric polymorphism in these systems. The advantages of the topological approach compared to conventional methods of modeling crystal structures are discussed and illustrated.