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Mathematics for Physics

121 Hund’s Rule

A guideline that is used to occupy degenerate orbitals singly with parallel spins before pairing, where degenerate orbitals are orbitals that share the same energy.

Maximum multiplicity. Electrons in a subshell occupy different orbitals with parallel spins until each orbital has one electron. This principle is used to maximize the total spin \(S\) of the ground term.

Maximum \(L\). For a given \(S\), the term with the largest orbital angular momentum \(L\) lies lowest. This principle is used to choose the ground term among terms of the same spin.

The \(J\) ordering of Hund’s third rule. For a subshell that is more than half full, the term with larger \(J\) lies lower; for a less than half-full subshell, the smaller \(J\) lies lower. This principle is used to assign the ground \(J\) value.

121.1 References

  1. Atkins, P., de Paula, J., & Keeler, J. Atkins’ Physical Chemistry. — Hund’s rules.
  2. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — Hund’s rule for degenerate orbitals.