Development of an orbital-free approach for simulation of multi-atomic nanosystems with covalent bonds

On the example of the three-atomic clusters $\mathrm{Al}_3$, $\mathrm{Si}_3$, and $\mathrm{C}_3$, it is shown that an orbital-free version of the density functional theory may be used for finding equilibrium configurations of multi-atomic systems with both metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found to be in good agreement with known data.