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Concept
Multiplicity (chemistry)
Summary
In spectroscopy and quantum chemistry, the multiplicity of an energy level is defined as 2S+1, where S is the
total spin angular momentum. States with multiplicity 1, 2, 3, 4, 5 are respectively called singlets, doublets, triplets, quartets and quintets.
In the ground state of an atom or molecule, the unpaired electrons usually all have parallel spin. In this case the multiplicity is also equal to the number of unpaired electrons plus one.
The multiplicity is often equal to the number of possible orientations of the total spin relative to the total orbital angular momentum L, and therefore to the number of near–degenerate levels that differ only in their spin–orbit interaction energy.
For example, the ground state of a carbon atom is 3P ([]). The superscript three (read as triplet) indicates that the multiplicity 2S+1 = 3, so that the total spin S = 1. This spin is due to two unpaired electrons, as a result of Hund's rule which favors the single filling of degenerate orbitals. The triplet consists of three states with spin components +1, 0 and –1 along the direction of the total orbital angular momentum, which is also 1 as indicated by the letter P. The total angular momentum quantum number J can vary from L+S = 2 to L–S = 0 in integer steps, so that J = 2, 1 or 0.
However the multiplicity equals the number of spin orientations only if S ≤ L. When S > L there are only 2L+1 orientations of total angular momentum possible, ranging from S+L to S-L. The ground state of the nitrogen atom is a 4S state, for which 2S + 1 = 4 in a quartet state, S = 3/2 due to three unpaired electrons. For an S state, L = 0 so that J can only be 3/2 and there is only one level even though the multiplicity is 4.
Most stable organic molecules have complete electron shells with no unpaired electrons and therefore have singlet ground states. This is true also for inorganic molecules containing only main-group elements. Important exceptions are dioxygen (O2) as well as methylene (CH2) and other carbenes.
Official source
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