Hund's rule of maximum multiplicity

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Hund's rule of maximum multiplicity is an observational rule which states that a greater total spin state usually makes the resulting atom more stable. Accordingly, it can be taken 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. As a result this rule is often abbreviated to Hund's rule, ignoring Hund's other two rules.


The multiplicity of a state is calculated as the total number of unpaired electrons + 1, or twice the total spin + 1 written as 2S+1. A high multiplicity state is therefore the same as a high-spin state.

The increased stability of the atom, most commonly manifested in a lower energy state, arises because the high-spin state forces the unpaired electrons to reside in different spatial orbitals. An early but incorrect explanation of the increased stability 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.[1]

As a result of Hund's rule, constraints are placed on the way atomic orbitals are filled using the Aufbau principle. Before any two electrons occupy an orbital in a subshell, other orbitals in the same subshell must first each contain one electron. Also, the electrons filling a subshell will have parallel spin before the shell starts filling up with the opposite spin electrons (after the first orbital gains a second electron). As a result, when filling up atomic orbitals, the maximum number of unpaired electrons (and hence maximum total spin state) is assured.

For example a p4 subshell arranges its electrons as [↑↓] [↑] [↑] rather than [↑↓] [↑] [↓] or [↑↓] [↑↓][ ].


See also[edit]


  1. ^ Levine, I. N. (1991). Quantum Chemistry (4th ed.). Prentice-Hall. pp. 303–304. ISBN 0205127703. 
  2. ^ Slipchenko, L.; Munsch, T.; Wenthold, P.; Krylov, A. (2004). "5-Dehydro-1,3-quinodimethane: a hydrocarbon with an open-shell doublet ground state". Angewandte Chemie (International ed. in English) 43 (6): 742–745. doi:10.1002/anie.200352990. PMID 14755709.  edit

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