Λ-Type Doubling and Electron Configurations in Diatomic Molecules

Abstract

Van Vleck's equations for $\ensuremath{\Lambda}$-type and spin doubling in $^{1}\ensuremath{\Pi}$, $^{2}\ensuremath{\Sigma}$, and $^{2}\ensuremath{\Pi}$ states are restated in convenient form for application to empirical data, explicit equations being given for each component separately in a $\ensuremath{\Lambda}$-type or spin doublet. The equations have been applied to a wide variety of data on many molecules, including data on $^{2}\ensuremath{\Pi}$ states corresponding to numerous intermediate coupling cases between $a$ and $b$, and have been found to fit excellently (cf. Figs. 1-4). Incidentally this has made possible a revision of the hitherto doubtful assignment of $J$ values for the ${Q}_{2}$ lines in the $^{2}\ensuremath{\Pi}$, $^{2}\ensuremath{\Sigma}$ bands of CaH, and has permitted identification of the $^{S}R$ branch. Empirical values of the coefficients in Van Vleck's equations have been obtained for many molecules, and are given in Tables I and II.From the observed values of these constants further confirmation of Van Vleck's theoretical results is obtained. In most of the molecules examined a $\ensuremath{\Pi}$ and a $\ensuremath{\Sigma}$ state are found which stand to each other in the relation called "pure precession" by Van Vleck, or something similar; that is, the $\ensuremath{\Pi}$ and the $\ensuremath{\Sigma}$ state act as if they had electron configurations essentially alike in all respects except that one electron has $\ensuremath{\lambda}=0$ in the $\ensuremath{\Sigma}$ state but $\ensuremath{\lambda}=1$ in the $\ensuremath{\Pi}$ state, or vice versa. The existence of such relations strongly indicates that the $n$ and $l$ values previously assigned to outer electrons in hydrides have almost the same well-defined significance as they would in an atom formed by uniting the H nucleus with the heavier nucleus. For example, in the normal ($^{2}\ensuremath{\Sigma}$) and first excited ($^{2}\ensuremath{\Pi}$) state of CdH, with configurations... $5s{\ensuremath{\sigma}}^{2}5p\ensuremath{\sigma}$ and... $5s{\ensuremath{\sigma}}^{2}5p\ensuremath{\pi}$, the present evidence shows that the last electron really behaves like a $5p$ atomic electron, even though the normal ($^{2}\ensuremath{\Sigma}$) state is formed with a small energy of formation from a normal Cd atom (... $5{s}^{2},^{1}S$) and a normal H atom ($1s,^{2}S$). Another type of case, in which a close similarity of the electron orbits to two separate atoms is evident, is one which is found in ${\mathrm{He}}_{2}$, ${\mathrm{Li}}_{2}$, and ${\mathrm{Na}}_{2}$. In ${\mathrm{He}}_{2}$ the $1s{\ensuremath{\sigma}}^{2}2p\ensuremath{\sigma}3p\ensuremath{\sigma}$, $^{3}{\ensuremath{\Sigma}}_{g}^{+}$ and the $1s{\ensuremath{\sigma}}^{2}2p\ensuremath{\sigma}2p\ensuremath{\pi}$, $^{3}\ensuremath{\Pi}_{g}$ states act as if the relation of pure precession were fulfilled. This is presumably because the $3p\ensuremath{\sigma}$ election acts essentially like $2p\ensuremath{\sigma}$, the $3p\ensuremath{\sigma}$ and $2p\ensuremath{\pi}$ both becoming $2p$ on dissociation of the molecule.---In the CaH molecule an interesting complicated case, earlier discussed by Watson, occurs in which strong $l$-uncoupling and spin uncoupling occur simultaneously in a $^{2}\ensuremath{\Pi}$ state. The theory accounts well for the observed relations in this case (Figs. 2, 3, 4).