On the way to modeling large nanosystems at the atomic level

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 without solving of the Kohn-Sham equation (so called orbital-free approach). On examples of dimers Na$_2$, Al$_2$, Si$_2$, P$_2$, K$_2$, Ga$_2$, Ge$_2$ and As$_2$ the equilibrium interatomic distances and binding energies were calculated in good comparison with published data. Results for Si-Al, Si-P, and Al-P dimers are close to results of Kohn-Sham calculations