Hund's rule of maximum multiplicity

Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that for a given electron configuration, the lowest energy term is the one with the greatest value of spin multiplicity. This implies that if two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs. The rule, discovered by Friedrich Hund in 1925, is of important use in atomic chemistry, spectroscopy, and quantum chemistry, and is often abbreviated to Hund's rule, ignoring Hund's other two rules.

The multiplicity of a state is defined as 2S + 1, where S is the total electronic spin. A high multiplicity state is therefore the same as a high-spin state. The lowest-energy state with maximum multiplicity usually has unpaired electrons all with parallel spin. Since the spin of each electron is 1/2, the total spin is one-half the number of unpaired electrons, and the multiplicity is the number of unpaired electrons + 1. For example, the nitrogen atom ground state has three unpaired electrons of parallel spin, so that the total spin is 3/2 and the multiplicity is 4.

The lower energy and increased stability of the atom arise because the high-spin state has unpaired electrons of parallel spin, which must reside in different spatial orbitals according to the Pauli exclusion principle. An early but incorrect explanation of the lower energy of high multiplicity states was that the different occupied spatial orbitals create a larger average distance between electrons, reducing electron-electron repulsion energy. However, quantum-mechanical calculations with accurate wave functions since the 1970s have shown that the actual physical reason for the increased stability is a decrease in the screening of electron-nuclear attractions, so that the unpaired electrons can approach the nucleus more closely and the electron-nuclear attraction is increased.

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