Diatomic-molecule model for a mixed-valence system

A model for a homopolar diatomic molecule is presented. It contains the following: (a) one $s$-like and one $f$-like orbital per atom, (b) an interatomic transfer term between the $s$ states, (c) an interatomic hybridization term between $s$ and $f$ states, (d) a very strong intra-atomic Coulomb repulsion between two $f$ electrons, and (e) an intra-atomic Coulomb repulsion between $s$ and $f$ electrons. The ground-state energy for the two-electron system is analyzed in detail for a variety of cases. The phenomenon of mixed valence is examined. It is found that the Coulomb interaction between $s$ and $f$ electrons tends to suppress the average occupation of $f$ states between values of one-third and one; depending on the other parameters, the occupation tends to take either values between zero and one-third or one, the full occupation.