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The authors fulfilled calculations of the total energy and electronic states of CdnSen nanoparticle:“wurzite”, “sphalerite” and “rock-salt” types of the structure. It was shown that at n ≤ 72 the “rock-salt” type is the most favorable energetically. However the extrapolation of the behavior of the energy per Cd-Se atomic pair shows that for n > 130 (corresponding to a size of about 2 nm), particles with a “wurtzite” structure can be more advantageous. Particles of the “wurtzite” and “rock-salt” types have an electronic structure with an energy gap. For particles with the “wurtzite”structure, the gap width decreases with increasing particle size: from 3.3 eV to 2.2 eV as the particle increases from 0.5 nm to 1.5 nm. For particles of the “rock-salt” type, the gap width grows slightly, remaining about 3 eV.“Sphalerite”-type particles have a metal-like electronic structure.

We studied a principal opportunity to develop a full-potential orbital-free method for modeling of multi-atomic systems using results of Kohn-Sham calculations for single atoms. We have obtained equilibrium bond lengths and binding energies for homoatomic dimers Li 2 , Be as well as for heteroatomic dimers CSi, CB, CN, CO, SiO, NO, AlO, AlC, and NaCl. We analyzed our results and concluded that they are coordinated with experimental data not worse, than the results received by means of full-electrons calculations by the Kohn-Sham method.

It is shown that the variation principle can be used as a practical way to find the electron density and the total energy in the frame of the density functional theory (DFT) without solving of the Kohn-Sham equation. On examples of diatomic systems Si 2 , Al 2 , and N 2 , the equilibrium interatomic distances and binding energies have been calculated in good comparison with published data. The method can be improved to simulate nanoparticles containing thousands and millions atoms.