Spin-Orbit and Spin-Spin Interactions in Diatomic Molecules. I. Fine Structure ofH2

The fine structure separations of para and ortho ${\mathrm{H}}_2$ are calculated by assuming that besides the spin-orbit, spin-other orbit, and spin-spin interactions, no other perturbation contributes significantly to the splitting. The interactions are expressed as contractions of irreducible tensors, and the resulting energy separations are obtained by applying the theory of angular momentum to a representation in strict case $b$ coupling. It is shown that for II states the ${Y_2}^2$ component of the quadrupole-type spin-spin interaction gives nonvanishing matrix elements which arise from the coupling of the electronic states ${\Psi }_e(\Lambda =+1)$ and ${\Psi }_e(\Lambda =-1)$. The additional term in the spin-spin interaction yields anomalous alternations of the fine structure separation from one rotational level to the next, and produces a splitting of the $J$ levels into a "regular" and an "irregular" component. This splitting is quite different from the usual $\Lambda$-type doubling which arises from the interaction of the orbital angular momentum with the rotation of the nuclei. In low rotational states of ${\mathrm{H}}_2$ the contribution of the ${Y_2}^2$ component of the spin-spin interaction is considerably larger than the $\Lambda$-type doubling. The theoretical predictions for the fine structure of the $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state compare favorably with experimental values.