Proof of Two Conjectures of Mulliken Concerning the Electronic Energy of Diatomic Molecules for Small R

This paper deals with the coefficient $E_2$ in the $R$ expansion of the electronic energy of diatomic molecules for the manifold of molecular states (characterized by the quantum number $\Lambda$ or $\Omega$ ) originating from a given state of the united atom. Explicit expressions for $E_2\mathrm{(\Lambda )}$ and $E_2\mathrm{(\Omega )}$ are derived, which generalize two conjectures of Mulliken concerning the $\Lambda$ (or $\Omega$ ) dependence of $E_2$ . As an example, the six lowest states of the BH molecule, which originate from the three lowest states of the carbon atom, are treated numerically.