Λ-Type Doubling and Electron Configurations in Diatomic Molecules

Van Vleck's equations for Λ-type and spin doubling in ¹Π, ²Σ, and ²Π states are restated in convenient form for application to empirical data, explicit equations being given for each component separately in a Λ-type or spin doublet. The equations have been applied to a wide variety of data on many molecules, including data on ²Π 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 Q₂ lines in the ²Π, ²Σ bands of CaH, and has permitted identification of the SR 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 Π and a Σ state are found which stand to each other in the relation called "pure precession" by Van Vleck, or something similar; that is, the Π and the Σ state act as if they had electron configurations essentially alike in all respects except that one electron has λ=0 in the Σ state but λ=1 in the Π 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 (²Σ) and first excited (²Π) state of CdH, with configurations... 5sσ²5pσ and... 5sσ²5pπ, the present evidence shows that the last electron really behaves like a $5p$ atomic electron, even though the normal (²Σ) state is formed with a small energy of formation from a normal Cd atom (... 5s²,¹S) and a normal H atom (1s,²S). 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 He₂, Li₂, and Na₂. In He₂ the 1sσ²2pσ3pσ, ³Σg⁺ and the 1sσ²2pσ2pπ, ³Πg states act as if the relation of pure precession were fulfilled. This is presumably because the 3pσ election acts essentially like 2pσ, the 3pσ and 2pπ 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 ²Π state. The theory accounts well for the observed relations in this case (Figs. 2, 3, 4).