g-Factor
Definition and meaning of g-Factor in chemistry.
The g-factor (g-value) is a dimensionless number that relates a particle's magnetic moment to its angular momentum, and in electron paramagnetic resonance (EPR) spectroscopy it sets the magnetic field at which a paramagnetic species absorbs microwave radiation of a given frequency.
In more detail
A free electron has g = 2.0023, but in molecules and metal complexes spin-orbit coupling mixes orbital angular momentum into the electron's magnetic moment, shifting g away from this value. Because the shift depends on the symmetry and orbital makeup of the unpaired electron's environment, the measured g-factor reveals structural and electronic information about radicals, transition-metal centers, and defect sites. Many species show an anisotropic g-tensor (gx, gy, gz) rather than one number, reflecting how the molecule is oriented relative to the applied field. The resonance condition linking these quantities is hν = gμBB, where h is Planck's constant, ν is the microwave frequency, μB is the Bohr magneton, and B is the magnetic field strength.
Key facts
| Field | Physical Chemistry |
|---|---|
| Free-electron value | ge = 2.0023 |
| Resonance condition | hν = gμBB |
| Also called | Landé g-factor, spectroscopic splitting factor |
DPPH (2,2-diphenyl-1-picrylhydrazyl), a stable free radical used as an EPR calibration standard, has g = 2.0036, close to the free-electron value because its unpaired electron is delocalized over a largely non-bonding pi system with little orbital contribution.
Frequently asked questions
Why does the g-factor differ from the free-electron value in molecules?
Spin-orbit coupling mixes orbital angular momentum into the electron's spin magnetic moment, shifting g up or down depending on the symmetry of the metal and ligand orbitals involved.
Is the g-factor always a single number?
No. Many paramagnetic species have an anisotropic g-tensor with distinct gx, gy, and gz values that depend on the molecule's orientation relative to the magnetic field.