On the Analysis of MolecularII3States with Application to AlH, OH+, and BH

The molecular constants $\lambda$, $B$, $D$ for the ${}_{}{}^3{}_{}{}^{}\mathrm{II}$ states of BH, AlH, and O${\mathrm{H}}^{+}$ have been calculated by the method of Gilbert, based on Van Vleck's solution of the case of intermediate coupling, but including a more accurate consideration of the rotational $D$ terms. A graphical method of obtaining $\lambda$ has also been developed based on Budó's series expansion solution of the Hill and Van Vleck energy equation for the intermediate ${}_{}{}^3{}_{}{}^{}\mathrm{II}$ state. A graph shows, for a given $K$, the variation in multiplet splitting as the coupling constant $\lambda$ is varied from -8 to +10. Graphs are plotted for $K=2,3,4,5\mathrm{}$, and application is made to the ${}_{}{}^3{}_{}{}^{}\mathrm{II}$ states of BH, AlH, O${\mathrm{H}}^{+}$ and NH. New data for AlH for lines with $K$ less than 6 are given. A comparison of corresponding electronic $\mathrm{ls}$ coupling coefficients in molecule and atom is made.