In rotational-vibrational and electronic spectroscopy of diatomic molecules, Hund's coupling cases are idealized descriptions of rotational states in which specific terms in the molecular Hamiltonian and involving couplings between angular momenta are assumed to dominate over all other terms. There are five cases, proposed by Friedrich Hund in 1926-27 and traditionally denoted by the letters (a) through (e). Most diatomic molecules are somewhere between the idealized cases (a) and (b).
Angular momenta To describe the Hund's coupling cases, we use the following angular momenta (where boldface letters indicate vector quantities):
L {\displaystyle \mathbf {L} } , the electronic orbital angular momentum
S {\displaystyle \mathbf {S} } , the electronic spin angular momentum
J a = L + S {\displaystyle \mathbf {J} _{a}=\mathbf {L} +\mathbf {S} } , the total electronic angular momentum
R {\displaystyle \mathbf {R} } , the rotational angular momentum of the nuclei
J = R + J a {\displaystyle \mathbf {J} =\mathbf {R} +\mathbf {J} _{a}} , the total angular momentum of the system (exclusive of nuclear spin)
N = R + L = J − S {\displaystyle \mathbf {N} =\mathbf {R} +\mathbf {L} =\mathbf {J} -\mathbf {S} } , the total angular momentum exclusive of electron (and nuclear) spin These vector quantities depend on corresponding quantum numbers whose values are shown in molecular term symbols used to identify the states. For example, the term symbol 2Π3/2 denotes a state with S = 1/2, Λ = 1 and J = 3/2.
Choosing the applicable Hund's case Hund's coupling cases are idealizations. The appropriate case for a given situation can be found by comparing three strengths: the electrostatic coupling of L {\displaystyle \mathbf {L} } to the internuclear axis, the spin-orbit coupling, and the rotational coupling of L {\displaystyle \mathbf {L} } and S {\displaystyle \mathbf {S} } to the total angular momentum J {\displaystyle \mathbf {J} } . For 1Σ states the orbital and spin angular momenta are zero and the total angular momentum is just the nuclear rotational angular momentum. For other states, Hund proposed five possible idealized modes of coupling.
The last two rows are degenerate because they have the same good quantum numbers. In practice there are also many molecular states which are intermediate between the above limiting cases.
… excerpt ends here. Continue reading the full article.
