Multiplicity in quantum chemistry is used to distinguish between several degenerate wavefunctions that differ only in the orientation of their angular spin momenta. It is defined as 2S+1, where S is the angular spin momentum.
Multiplicity is the quantification of the amount of unpaired electron spin. Multiplicity is a result of Hund's rule which favors the single filling of degenerate (same energy) orbitals. The result is the filling of multiple orbitals with electrons or multiplicity. Multiplicity is calculated using the expression 2 S + 1, where S = Σms or, more simply put, S = ½(No. of unpaired electrons). When all electrons are paired S = 0, and the multiplicity = 2(0) + 1 = 1. This case is called a singlet. If a molecule has 1 unpaired electron S = +½ and 2S + 1 = 2, which is called a doublet. Two unpaired electrons would result in a triplet, etc.
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