The most common case is case (a) in which  is electrostatically coupled to the internuclear axis, and  is coupled to  by spin-orbit coupling.  Then both  and  have well-defined axial components,  and  respectively. As they are written with the same Greek symbol, the spin component  should not be confused with  states, which are states with orbital angular component  equal to zero.  defines a vector of magnitude  pointing along the internuclear axis.  Combined with the rotational angular momentum of the nuclei , we have .  In this case, the precession of  and  around the nuclear axis is assumed to be much faster than the nutation of  and  around .
The good quantum numbers in case (a) are , , ,  and . However  is not a good quantum number because the vector  is strongly coupled to the electrostatic field and therefore precesses rapidly around the internuclear axis with an undefined magnitude. We express the rotational energy operator as , where  is a rotational constant.  There are, ideally,  fine-structure states, each with rotational levels having relative energies  starting with . For example, a Π state has a Π term (or fine structure state) with rotational levels  = 1/2, 3/2, 5/2, 7/2, ... and a Π term with levels  = 3/2, 5/2, 7/2, 9/2.... Case (a) requires  > 0 and so does not apply to any Σ states, and also  > 0 so that it does not apply to any singlet states.
The selection rules for allowed spectroscopic transitions depend on which quantum numbers are good. For Hund's case (a), the allowed transitions must have  and  and  and  and . In addition, symmetrical diatomic molecules have even (g) or odd (u) parity and obey the Laporte rule that only transitions between states of opposite parity are allowed.