The prediction of a set of cage crystal-forming clusters XnYn occurrence from wich zeolite-like crystals based on compounds AIVBIV, AIIIBV and AIIBVI can be constructed, has been made by quantum mechanics methods. A set of cage crystal-forming clusters BN has been theoretically calculated and extended on alter-idem sets of isoelectronic AIVBIV, AIIIBV and AIIBVI compounds. A general approach to the design of crystal-forming fullerene-like clusters XnYn, from wich zeolite-like crystals based on IV-IV, III-V, II-VI compounds whith diamond-like sp3 bonds can be constructed and synthesized by means of copolymerization through faces has been formulated. If the number of isolated facets equals to 4, 6, 8, 12, tetrahedral, cubic and hexagonal symmetry of crystal are formed, correspondently. The properties of set of crystal-created clusters - C2n, BnNn, SinCn (n = 12, 16, 18, 24, 36, 60) and ZnnOn, GanNn. (n =12) have been researched and systematized. The clusters n = 12, 16, 18, 36 correspond to the rule of isolated squares, n = 24 - isolated octagons, and n = 60 - isolated decagons. Their optimized configuration, electronic structure, charge transfer, band gap, total energy, cohesion energy, maps of electronic density have been calculated by using spin restricted Hartree-Fock method RHF in the 6-31G basis set. IR and Raman spectra and modes of vibrations for clusters C2n, BnNn and SinCn (n = 12, 24) and ZnnOn, GanNn (n = 12) have been calculated and analysed. All the optical spectra have been calculated for the first time (except B24N24). Calculations were carried out using GAMESS and Gaussian program package. ChemCraft and Molekel program package have been used for visualization. After the optimization, the structures of all clusters deviate from a regular geometric configuration and remain stable. In all clusters (except C2n) a charge transfer and heteropolar and ionic components of the interatomic bond lead to molecular faces corrugation. Herewith, the bond lengths and bond angles deviate from those in regular geometric configurations. The Y? ions are displaced outside the cluster, while the X+ ions are displaced inside the cluster. Non-monotonic dependence of the stability of cage crystal-forming clusters (cohesive energy per atom and bond lengths) on the cluster geometry and the number of atoms have been determined. The XnYn clucters with n ? 36, 48, which do not have eight- and tenmembered rings are the most stable. The calculated cohesive energy (7,3 eV) per atom in C72 clucter is close to the experimental cohesive energy for grafite (7,4 eV). The calculated bonding energies (4,04 eV) per atom in B12N12 cluster are close to the experimental value obtaned for hexagonal boron nitide (4,0 eV). It was shown that in calculated IR absorption spectra of clusters (except C2n) the most intensive vibrations correspond to the mode with atom tangential displacement. In calculated Raman spectra the most vibrations correspond to full-symmetrical, so called "breathing motion" mode. It was shown that in calculated IR absorption spectra clusters C24, C48, the most intensive vibrations correspond to the mode with radial nonsymmetrical atom displacement. In calculated Raman spectra of clusters C24, C48 the most intensive vibrations correspond to the mode with atom tangential displacement. Frequencies of optical vibration modes are displaced in low frequency range in accordance with increasing of weight of atoms in molecule. The dimension of the effect of an increase in the number of atoms in the cage crystal-forming clusters installed - the frequency shift of the tangential stretching vibrations in the side with the higher frequencies associated with the reduction bonds. Found that the calculated IR and Raman spectra of cage crystal-forming clusters BN responsible ekperimetnalnim ІЧ and Raman spectra of the so-called "E-phase" BN. It is shown that the spectra calculated IR absorption spectra, Raman spectra and vibration mode of predicated crystal-forming clusters C2n, BnNn і SinCn (n = 12, 24) і ZnnOn, GanNn (n = 12) can be used for interpretation of experimental data and identification of these clusters in the samples if the pilot receiving.
