fastmotion

Line widths in the fast-motional regime.

Syntax

lw = fastmotion(Sys,B0,tcorr)
lw = fastmotion(Sys,B0,tcorr,domain)
[lw,mI] = fastmotion(...)

Description

Given the g, A and Q tensors in Sys, the magnetic field (mT) in B0 and a rotation correlation time (seconds) in tcorr, fastmotion computes the EPR line widths resulting from rotational motion of the paramagnetic molecules. The widths depends on the anisotropies of g, A and Q. The widths are returned in lw (in units of mT or MHz, depending on domain), and the associated lines are identified by sets of m_I numbers in mI. One row corresponds to one EPR resonance line.

The four input parameters are

Sys

Spin system structure containing the list of nuclei Nucs, the g, A and Q tensors g, A, Q, and, optionally, the tensor orientations in gFrame and AFrame. The field QFrame is not used.
For a description of all fields, see garlic.

B0

External magnetic field, in mT.
To compute line widths for a field-swept EPR spectrum, take the center field, as long as the spectrum is not too wide.

tcorr

Rotational correlation time for isotropic Brownian rotational diffusion, in seconds.
The correlation time tcorr and the diffusion rate D are related by tcorr = 1/(6*D).

domain

Indicates the domain for the line widths, either 'field' for field sweeps (units of mT) or 'freq' for frequency sweeps (units MHz). Default is 'field'.

The two output parameters are

lw

All line widths (FWHM for Lorentzians), in mT or MHz.

mI

The m_I values for the lines, one line per row.

Algorithm

fastmotion uses the Kivelson formula to compute line widths. Outside the fast-motion regime (Redfield limit, motional narrowing), the formulas are not valid.

The formulas used in fastmotion are from Neil Atherton, Principles of Electron Spin Resonance, 1993. The relevant expressions are on pages 331 (9.2.48-51) and 348 (9.5.2).

The original theory can be found in J.H. Freed and G.K. Fraenkel, J. Chem. Phys. 39 (1963), 326-348.

Example

The X-band spectrum of a nitroxide radical in the fast motional regime features three lines with different widths. The widths and the mI values for the associated lines are

Nitroxide = struct('g',[2.0088 2.0064 2.0027],'Nucs','14N');
Nitroxide.A = unitconvert([7.59 5.95 31.76]/10,'mT->MHz');

Field = 350;
tcorr = 1e-10;
[lw,mI] = fastmotion(Nitroxide,Field,tcorr,'field')