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Supercomputer simulation by first-principles DFT (GGA PBE, scalar-relativistic theory, large relativistic full-electron basis sets) was used as the efficient initial stage in the design of arificial highly selective receptor for tetrahedral oxo-anions and for actinides and lanthanides separation. The methods are developed for the convergent syntesis of the most promising selected structures by anion and cationc template reactions under thermodynamic control. The phenomenon of "anionic selection in dynamic combinatorial libraries" was discovered in the study of anionic template effect. Large series of macrocyclic receptors on tetrahedral oxo-anions has been synthesized, including structural analogs of phosphate and sulfate binding sites in natural phosphate and sulfate-binding proteins, and selective receptors on perrenat- and pertechnetate-anions. New receptors and their complexes with target ions were studied in detail by NMR, UV-vis, IR and X-ray diffraction techniques. It has been shown that these receptors may be effectively used for the extraction of pertehnetate anion from highly radioactive wastes arising from the reprocessing of spent nuclear fuel and for environmental monitoring. Based on the theoretical simulation results new polydentate N-donor heterocyclic ligands (pyridine-2,6-dicarboxamides, 1,10-phenantroline-2,9-dicarboxamides and related compounds) were predicted to be promising ligands with unusual and unprecedentally high selectivity for lanthanides and actinides separation in the reprocessing of spent nuclear fuel. The synthesis of large series of these ligands has been performed, and the results of theoretical predictions were confirmed experimentally in extraction experiments. Selectivity factors were obtained as high as SFAm/Eu> 150 and SFAm/Cm> 7. 1. Ustynyuk Yu. A. et al., Chem. Com., 2015, 51: 7466-7469. 2. Ustynyuk Yu. A. et al., Solv. Extr. Ion Exch., 2014, 32: 508–528. 3. Katayev E.A., Ustynyuk Yu.A., Sessler J.L., Coord. Chem. Rev., 2006, 250: 3004-3037. 4. Borisova N.E., Reshetova M.D., Ustynyuk Yu.A., Chem. Rev., 2007, 107: 46-79. 5. Katayev E.A., Pantos G.D., Reshetova M.D., Khrustalev V.N., Lynch V.M., Ustynyuk Yu.A., Sessler J.L., Angew. Chem.Int.Ed., 2005, 44: 7386-7390. 6. Sessler J.L., Katayev E., Pantos G.D., Scherbakov P., Reshetova M.D., Khrustalev V.N., Lynch V.M., Ustynyuk Yu.A., J. Am.Chem. Soc., 2005, 127: 11442-11446. 7. Е.А. Катаев, Д. Сесслер, Ю. А. Устынюк, Изв.РАН. сер. хим., 2009, № 9: 1729 -1742. 8. Katayev E.A., Sessler J.L., Khrustalev V.N., Ustynyuk Yu.A., J. Org.Chem., 2007, 72: 7244-7252.