A short introduction - Unpaired electrons in molecules

The free electron case

The classical example is that of an unpaired electron, with quantum number S=1/2.

For this system there is a magnetic moment μ associated with the spin S which is oriented by the magnetic field because of the Zeeman interaction. For this quantum system the projection of the magnetic moment along the field is quantized; the quantization is given by the quantum number ms so that:

where β is the Bohr magneton and ge is the g-factor of the electron.

The two states ms =±1/2 interact with the field and the strength of the interaction is given by the Zeeman term:





A transition between the two levels can be induced by a radiation that fulfil the requirement:


this is the resonance condition.

A continuous wave (cw) EPR spectrum is normally acquired by measuring the absorption of microwaves while sweeping the magnetic field. Most EPR spectrometers use lock-in detection, and the spectra are in derivative form. 

Additional information