Hund's rules

In atomic spectroscopy, Hund's rules predict which atomic energy level with quantum numbers L, S and J is lowest. The rules are called after Friedrich Hund who formulated them in 1925.^[1] A group of atomic energy levels, obtained by Russell-Saunders coupling, is concisely indicated by a term symbol. A term (also known as multiplet) is a set of simultaneous eigenfunctions of L² (total orbital angular momentum squared) and S² (total spin angular momentum squared) with given quantum numbers L and S, respectively. If there is no spin-orbit coupling, the functions of one term are degenerate (have the same energy).

Hund's rules are:

Of the Russell-Saunders states arising from a given electronic configuration those with the largest spin quantum number S lie lowest, those with the next largest next, and so on; in other words, the states with largest spin multiplicity are the most stable.
Of the group of terms with a given value of S, that with the largest value of L lies lowest.
Of the states with given values of S and L in an electronic configuration consisting of less than half the electrons in a closed subshell, the state with the smallest value of J is usually the most stable, and for a configuration consisting of more than half the electrons in a closed subshell the state with largest J is the most stable.

The levels of the second sort, largest J most stable, can be seen as arising from holes in the closed subshell.

Examples:

The ground state carbon atom, (1s)²(2s)²(2p)², gives by Russell-Saunders coupling a set of energy levels labeled by term symbols. Hund's rules predict the following order of the energies

^{3}P_{0}<^{3}P_{1}<^{3}P_{2}<^{1}D_{2}<^{1}P_{2}

The ground state oxygen atom, (1s)²(2s)²(2p)⁴, (a two-hole state) gives by Russell-Saunders coupling a set of energy levels labeled by term symbols. Hund's rules predict the following order of the energies

^{3}P_{2}<^{3}P_{1}<^{3}P_{0}<^{1}D_{2}<^{1}P_{2}

References

↑ F. Hund, Zur Deutung verwickelter Spektren, insbesondere der Elemente Scandium bis Nickel. [On the interpretation of complicated spectra, in particular the elements scandium through nickel]. Zeitschrift für Physik, vol. 33, pp. 345-371 (1925).

L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, 3rd edition (1960)

[1] F. Hund, Zur Deutung verwickelter Spektren, insbesondere der Elemente Scandium bis Nickel. [On the interpretation of complicated spectra, in particular the elements scandium through nickel]. Zeitschrift für Physik, vol. 33, pp. 345-371 (1925).

[1]

Hund's rules

References

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