Spin–Spin Interaction and the Energy Splitting of the Rovibronic Levels of a Linear Triatomic Molecule

Spin–spin interaction and spin–orbit interaction are both considered in studying the fine structure energy splitting of a rovibronic level. The molecule under study is linear triatomic and in the ${}^3\Pi$ state. The first‐order spin–orbit interaction is found to be zero except for the vibronic level with ${\mathrm{K\hspace{0.17em}=\hspace{0.17em}\upsilon }}_2\text{\hspace{0.17em}+\hspace{0.17em}1}$ , and the first‐order fine structure splitting is therefore due to spin–spin interaction only. By nature of the second‐rank tensor, the spin–spin interaction is also shown to split the over‐all inversion symmetry pairs, namely the + and − of certain $J$ levels. Hund's case $a$ , case $b$ and intermediate cases are considered. The energy of a fine structure level is expressed explicitly in terms of all the quantum numbers and coupling constants such that direct experimental comparison can easily be made. Examples of ${\upsilon }_2\text{\hspace{0.17em}=\hspace{0.17em}1}$ and ${\upsilon }_2\text{\hspace{0.17em}=\hspace{0.17em}2}$ are worked out in detail.