Exchange-correlation interaction and AO-hybridization of alkali-metal atomic clusters

The structure of alkali-metal atomic clusters is optimized with B3P86 hybrid functional for the highest spin state as well as with B3LYP hybrid functional for the lowest spin state. A dramatic change from plane to solid occurs in the highest spin state when the number of constituent atoms is four. The binding, exchange, and correlation energies are evaluated for both the highest and lowest spin states. Next, we explore the dependence of the exchange and correlation energies on the binding energy. The exchange energy contributes to the formation of the highest spin clusters, whereas the correlation energy contributes to the formation of the lowest spin clusters. The highest spin clusters are most stable when the exchange energy is a minimum. Then, to see why the ferromagnetic bond among spin-aligned identical atoms arises against Pauli exclusion principle, we estimate the mixing ratio of p orbitals in molecular orbitals. The s-p hybridization increases the binding energy in absolute value due to the extensive overlap of molecular orbitals and leads to generation of the highest spin clusters.