Model analysis of ground-state dissociation energies and equilibrium separations in alkali-metal diatomic compounds

Ground-state dissociation energies $D_e$ and equilibrium distances $R_e$ for the series of homonuclear alkali-metal diatomic molecules ${\mathrm{Li}}_2$,${\mathrm{Na}}_2$,..., as well as those for six heteronuclear alkali-metal diatomic compounds, are evaluated on the basis of a simple valence-bond model. Each alkali-metal atom in a diatomic molecule is characterized by two quantities: a Gaussian parameter ${\beta }_e$ of the valence-electron function and a valence-to-core ‘‘relative-size’’ parameter γ≡(${\beta }_c$/${\beta }_e$ ${)}^2$, with ${\beta }_c$ the Gaussian parameter for the core-electron charge distribution. For the homonuclear diatomic molecules, accurate results are obtained with a 2s Gaussian valence function ($r^2$-$a^2$)G orthogonalized to the core. For each homonuclear diatomic molecule there exists an optimal (${\beta }_e$,γ) set yielding values of $D_e$ and $R_e$ in practically quantitative agreement with experiment. The quantities ${\beta }_e$ and γ exhibit the expected physical behavior over the series in that ${\beta }_e$ decreases from ${\mathrm{Li}}_2$ to ${\mathrm{Cs}}_2$, and γ is highest for the lightest diatomic molecule ${\mathrm{Li}}_2$. The compounds ${\mathrm{K}}_2$, ${\mathrm{Rb}}_2$, and ${\mathrm{Cs}}_2$ are found to be ‘‘Heitler-London’’ molecules to within 5% of their binding energies. An approximate, similar, analysis of six heteronuclear diatomic compounds yields close agreement with experiment for LiNa and RbCs, whereas with the other four compounds (LiK, NaK, NaRb, and NaCs) the agreement with experimental $D_e$ and $R_e$ is to within at most 5%. Also RbCs is a ‘‘Heitler-London’’ molecule to a very good approximation.