A short introduction - Experimental methods

 Unpaired electrons in molecules

 With respect to the free electron case, electrons in molecules are characterized by the presence of a) a  small orbital magnetic moment summing to the spin contribution, and b) the presence of coupled paramagnetic nuclei.

 

a) The g-value

 Mostly, the orbital contribution is small, and it is possible to show that it is generated by the mixing of orbitals through the spin-orbit interaction.

In this case the term can be taken into account for through a newly defined g-factor.

g in general is a tensor: the interaction depends on the direction of application of the magnetic field with respect to the molecule.

The most general Zeeman Hamiltonian for a species is then:

 

In solution the tumbling motion of the molecules averages the principal values of the tensor, and a single value is obtained.

 

b) Interactions with paramagnetic nuclei

 Paramagnetic nuclei act as perturbation on the unpaired electron(s) because of the presence of two types of interactions: a contact (isotropic) interaction, and a dipolar (anisotropic) interaction,

The Hamiltonian for the hyperfine interaction is normally written as:

 

where A is the hyperfine (hf) tensor and is the nuclear spin operator.

The simpler case is that of a fast tumbling radical (S=1/2) in a fluid solution, for which the tumbling motion of the molecule averages to zero the dipolar interaction; in this case the hf tensor reduces to a contant, aiso.

For small values of aiso the hyperfine spin Hamiltonian is simplified to:

thus the EPR line due to magnetic electron spin transition is split in two or more lines according to the nuclear angular momentum quantum number I, and this can be understood in terms of the different values of the quantum number mI (relative to the nuclear spin component along the magnetic field direction) value.

 

 


 

 



 

Splitting of the line due to an interaction of a radical (S=1/2) with a nuclear spin I=1/2.

 


 

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