Motional narrowing

Formulas

The linewidths have the from

[eqn]
[eqn]
[eqn]

with

[eqn]

(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

[eqn]

(Atherton 1993, p.332).

The nuclear quadrupole with the quadrupolar coupling matrix Q contributes

[eqn]

(Atherton 1993, p. 348).

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

[eqn]
References