Multiplicity
Definition and meaning of Multiplicity in chemistry.
Multiplicity is the number of possible spin states available to electrons in an atom or molecule, calculated as 2S + 1, where S is the total spin quantum number.
In more detail
Each electron has intrinsic spin angular momentum that can be paired (opposite spins) or unpaired. A singlet has multiplicity 1 (all electrons paired, S = 0); a doublet has multiplicity 2 (one unpaired electron, S = 1/2); a triplet has multiplicity 3 (two unpaired electrons with parallel spins, S = 1). Multiplicity is directly observable in electron paramagnetic resonance (EPR) spectroscopy and determines which electronic transitions are quantum mechanically allowed through the spin selection rule: transitions with ΔS = 0 are permitted, while those with ΔS ≠ 0 are forbidden or weakly allowed. This profoundly affects molecular magnetic properties and reaction pathways.
Key facts
| Formula | 2S + 1 |
|---|---|
| Field | Physical Chemistry |
| Observable by | Electron paramagnetic resonance (EPR) spectroscopy |
| Spin selection rule | Allowed transitions have ΔS = 0 |
Molecular oxygen (O2) in its ground state has two unpaired electrons with parallel spins (S = 1), giving a multiplicity of 2(1) + 1 = 3, making it a triplet. This triplet character explains why O2 reacts slowly with many singlet organic molecules, as a spin-forbidden transition would be required.
Frequently asked questions
What is the multiplicity of a molecule with three unpaired electrons?
With three unpaired electrons, S = 3/2, so multiplicity = 2(3/2) + 1 = 4 (a quartet).
Why does multiplicity matter for chemical reactions?
Multiplicity determines which electronic states can interact and which transitions are quantum mechanically allowed, controlling reaction rates and mechanisms. For example, oxygen's triplet ground state makes it unreactive with singlet molecules unless a spin-forbidden transition occurs.