Multiplicity
Definition and meaning of Multiplicity in chemistry.
Multiplicity tells you how many spin states are available to the electrons in an atom or molecule. Chemists calculate it using the formula 2S + 1, where S stands for the total spin quantum number.
In more detail
Every electron carries a built-in property called spin, and two electrons in the same orbital must have opposite, or paired, spins. When electrons are unpaired instead, they add up to a nonzero total spin, S. A singlet has multiplicity 1, meaning every electron is paired and S equals 0.
A doublet has multiplicity 2, with one unpaired electron and S equal to one half. A triplet has multiplicity 3, with two unpaired electrons spinning the same direction and S equal to 1. Scientists can directly observe multiplicity using electron paramagnetic resonance (EPR) spectroscopy.
Multiplicity also controls which electronic transitions are allowed. A transition is allowed only if the spin does not change, following the rule that delta S must equal zero. This rule strongly affects how fast certain reactions happen and shapes a molecule's magnetic behavior.
A common misconception is that all molecules with paired electrons behave identically. Even singlet molecules, with multiplicity 1, can differ enormously in reactivity depending on their electronic structure. Multiplicity becomes especially important in photochemistry.
A molecule excited by light can end up in either a singlet or triplet excited state, and each type follows very different reaction pathways afterward.
Key facts
| Formula | 2S + 1 |
|---|---|
| Field | Physical Chemistry |
| Observable By | Electron paramagnetic resonance (EPR) spectroscopy |
| Spin Selection Rule | Allowed transitions have ΔS = 0 |
| Common States | Singlet (1), doublet (2), triplet (3) |
Molecular oxygen (O2) has two unpaired electrons spinning in the same direction in its normal, lowest-energy state, giving it S equal to 1. Its multiplicity is 2(1) + 1 = 3, making it a triplet. This triplet nature is why O2 reacts slowly with many organic molecules, since the reaction would require a spin change that is not easily allowed.
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, called a quartet.
Why does multiplicity matter for chemical reactions?
Multiplicity determines which electronic states can interact and which transitions are allowed, controlling reaction rates and mechanisms. Oxygen's triplet ground state, for example, makes it slow to react with singlet molecules.
What is the difference between multiplicity and spin quantum number?
The spin quantum number, S, is the total spin of all unpaired electrons combined. Multiplicity is calculated from S using the formula 2S + 1, and it tells you how many distinct spin states that total spin can take.