Spin multiplicity

Spin multiplicity

In quantum mechanics, spin multiplicity denotes the number of possible quantum states of a system with given principal spin quantum number S. The different states are distinguished by the spin projection quantum number Sz, which can take the values -S, -S+1, ..., S-1, S. Therefore, the multiplicity is 2S+1.

A system with S=0 has exactly one possible state; it is therefore in a singlet state. A system with S=1/2 is a doublet; S=1 is a triplet, and so on.

The most important application is to electrons. A single electron (as in a free radical) has S=1/2; it is therefore always in a doublet state. Two electrons (as in a diradical) can pair up in a singlet or in a triplet state. Normally the triplet is the ground state.


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