Quantum-mechanical modeling without wave functions

It has been shown that the variational principle can be used as the practical way to find the electron density and the total energy in terms of the density functional theory without solving the Kohn-Sham equations (the so-called orbital-free approach). The equilibrium interatomic distances and binding energies found using examples of diatomic systems Si-2, Al-2, and P-2 are in good agreement with the published data. The results obtained for Si-Al, Si-P, and Al-P dimers are also close to the results obtained by the Kohn-Sham method.