Motional narrowing

Formulas

The line widths have the from

with

(Atherton 1993, p. 331). Δg and ΔA are the anisotropic parts of the g and A matrix. X:Y indicates the sum over all elements of the element-by-element product of the matrices X and Y. ΔA in the above expressions is in angular frequency units.

If more than one nuclear spin are present in the paramagnetic molecule, the more general expression is

(Atherton 1993, p.332).

The nuclear quadrupole with the quadrupolar coupling matrix Q contributes

(Atherton 1993, p. 348).

The m_I-dependent values of 1/T₂ are converted to Lorentzian line widths (FWHM) in magnetic field units by

References

J. H. Freed, G. K. Fraenkel, J. Chem. Phys. 39, 326-348 (1963).
N. M. Atherton, Principles of Electron Spin Resonance, Prentice Hall, 1993.