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Hyperdiamonds are covalently bonded carbon phases, more or less related to the diamond network, having a significant amount of sp3 carbon atoms and similar physical properties. Many of them have yet a hypothetical existence but a well-theorized description. Among these, the diamond D5 was studied in detail, as topology, at TOPO GROUP CLUJ, Romania. The theoretical instrument used was the Omega polynomial, also developed in Cluj. It was computed in several 3D network domains and analytical formulas have been derived, not only for D5 but also for the well-known diamond D6 and other known networks.

Shape is a very important molecular feature for describing ligand molecules interacting with receptor, and other various complex chemical and biological processes. During the last years, there is a strong interest in developing several molecular shape descriptors. In this chapter we present our attempts for deriving van der Waals (vdW) shape molecular descriptors from two size molecular descriptors – the molecular vdW volume (VW) and the molecular vdW surface (SW). The ovality Θ iD , i = 1,2,3 descriptors measure the deviation of the shape of a molecule from a spherical form in one-, two-, and three dimensions, respectively, whilst the {δ,G} molecular shape parameters take into consideration the cylindrical shape of a molecule or substituent. The application of these molecular descriptors in the study of the toxicity of a series of aliphatic amines on the protozoan ciliate Tetrahymena pyriformis (Θ iD ) and for the correlation of rate constants of bimolecular nucleophilic substitution, acid-catalyzed hydrolysis of esters and esterification reactions (δ) is also reported in this chapter. The MTD (minimal topologic difference) method allows a receptor site mapping in the frame of a series of bioactive compounds. The MVD (minimal volume difference) method is an improved variant of the MTD method, which takes into account the 3D extension of a molecule. These methods are described here in some detail. The results obtained in the study of anti-carcinogenic activity of some retinoids and in the inhibition of carbonic-anhydrase (CA) by a series of sulfonamides are also presented in this chapter.