Correlation of AtomicJValues and Molecular Quantum Numbers, with Applications to Halogen, Alkaline Earth Hydride, and Alkali Molecules

Rules are given for determining the $\Omega$ values and symmetry properties of the molecular states obtainable from the union of two atoms with specified $J$ values, assuming case $c$ coupling in the molecule. These are used to determine the correlation of molecular $\Lambda$ and $S$ values with atomic $J$ values, for cases where there is strong $L$, $S$ coupling in one or both atoms. The correlation rules are applied to I+I, Hg+H, and Cs+Cs. Difficulties which exist when a similar correlation is attempted in cases where the $L$, $S$ coupling is weak (e.g. Mg+H, or Na+Na) are discussed. Electron configurations and dissociation products are discussed in some detail in the case of the halogen molecules, and an interpretation is given, in terms of electron configurations, of the analogies and differences between the spectra of the members of homologous series of molecules such as ${\mathrm{F}}_2$, ${\mathrm{Cl}}_2$, ${\mathrm{Br}}_2$, ${\mathrm{I}}_2$, or ${\mathrm{Li}}_2$, ${\mathrm{Na}}_2$, ${\mathrm{K}}_2$,.....