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 number of possible orientations of spin angular momenta.
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 in the shell). 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. Atoms and molecules with odd multiplicities are usually more stable than those with even multiplicities. The singlet ground state is S0, excited singlet states are Si where I = the number of states above ground state it is, for doublet states it's Di, for triplet states it's Ti, etc. As a result of spin orbital interactions energy levels may split into 2S+1 sublevels. Atoms and molecules with ground states with a multiplicity of 1 and excited states with a multiplicity of 1 and 3 tend to be stable. When S > L (the total orbital angular momentum possible) there are only 2L+1 orientations of total angular momentum possible.
In organic chemistry, carbenes are molecules which have carbon atoms with only have six valence electrons and therefore disobey the octet rule. Carbenes generally split into singlet carbenes and triplet carbenes, named for their spin multiplicities. Both have two non-bonding electrons; in singlet carbenes these exist as a lone pair and are spin-paired, while in triplet carbenes these electrons are spin-parallel.
- Atkins, Peter; de Paula, Julio (2002) [First published 1978]. Atkins' Physical Chemistry. United States: Oxford University Press. ISBN 0-19-879285-9.
- Clayden, Jonathan; Greeves, Nick; Warren, Stuart; Wothers, Peter (2001). Organic Chemistry. United States: Oxford University Press. ISBN 0-19-850346-6.
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