garlic
Introduced in 2.1
Synopsis

Computes isotropic and fast-motional cw EPR spectra of radicals in solution.

garlic(Sys,Exp)
spec = garlic(Sys,Exp)
[B,spec] = garlic(Sys,Exp)

See also the tutorial on how to use garlic.

Description

garlic computes isotropic and fast-motional cw EPR spectra of douplet radicals in solution, i.e., of spin systems with an electron spin S=1/2 coupled to an arbitrary number of nuclear spins I>=1/2 with small hyperfine couplings.

The composition of the spin system is specified in Sys, and the experimental settings are given in Exp.

garlic then returns the spectrum in spec and, if requested, a field range vector in B (in units of mT). If neither B nor spec are requested, garlic plots the simulated spectrum.

The following table lists all possible fields in the spin system structure Sys. Note that Sys here contains only a few fields of the general spin system structure as used by functions like pepper and salt. All fields except n are mandatory.

gScalar or 3-element vector
Either isotropic g factor, e.g. Sys.g = 2.0029, or g tensor principal values, e.g. Sys.g = [2.001 2.0015 2.003]
NucsString with comma-separated list of isotopes, e.g. Sys.Nucs = '1H,13C'.
nVector of number of equivalent nuclei, e.g. Sys.n = [2,3], if the spin system contains two 1H and three 13C nuclei. Can be omitted if all nuclei in Sys.Nucs occur only once.
A 1xN or Nx3 array
Vector of isotropic hyperfine couplings in MHz, e.g. Sys.A = [10 52].
Alternatively, array containing the principal values for all hyperfine tensors, one row per nucleus. E.g., Sys.A = [15 15 40;-4 -3 7] for two nuclei.
lw1- or 2-element vector of linewidths (all in mT).
  • 1 element: Lorentzian FWHM.
  • 2 elements: [LorentzianFWHM GaussianFWHM].

For simulations in the fast motional regime, the principal values of the g and all A tensors have to be given. One more parameter in Sys specifies the speed of the rotational motion:

tcorr Scalar
Rotational correlation time for isotropic rotational diffusion, in seconds. See also the function fastmotion. If tcorr is omitted or set to zero, the isotropic limit spectrum is computed.

For isotropic rotational motion, the correlation time tcorr and the diffusion rate D are related by tcorr = 1/(6*D).

If tcorr is given, the fast-motional spectrum is computed. The resulting spectrum is broadened by Lorentzian and Gaussian broadenings specified in Sys.lw using convolution, just as in the isotropic case.

If the inverse of the correlation time becomes similar in magnitude to the spectral anisotropy, the fast-motional model used by garlic (via fastmotion) is not valid anymore.

The following table lists all possible fields in the experiment structure Exp. Of these fields, only mwFreq is mandatory.

mwFreqSpectrometer frequency in GHz
nPointsNumber of points along field axis (default 1024)
CenterSweep2-element vector [center sweep] with center field center and full field sweep range sweep, both in mT. If both CenterSweep and Range are not specified, the magnetic field range is automatically determined to cover the full spectral range.
Range2-element vector [minField maxField] with lower and upper limit of field scan range in mT. Range is only used if CenterSweep is not given. If both CenterSweep and Range are not specified, the magnetic field range is automatically determined to cover the full spectral range.
HarmonicDetection harmonic (0, 1 or 2), default is 1.
Algorithm

To compute resonance fields, garlic uses a fixed-point iteration based on the exact Breit-Rabi solutions for a S=1/2 with an arbitrary nuclear spin. This is superior to using high-order perturbation expressions, since it gives resonance field values accurate to within numerical error.

Only allowed transitions are computed. If the hyperfine couplings are too large, garlic will refuse to run. All transition intensities are assumed to be equal.

Sets of equivalent nuclei are transformed into a coupled representation (see equivcouple). Non-equivalent groups of equivalent nuclei are treated sequentially, i.e. cross terms are neglected.

For the computation of fast-motional line widths, the function fastmotion is used.

Examples

Spectra from systems with many nuclei are easily simulated.

Sys = struct('g',2,'Nucs','1H,14N','A',[30,40],'n',[5 4]);
Sys.lw = [0.1 0]; % only Lorentzian broadening
Exp = struct('mwFreq',9.7);
garlic(Sys,Exp);
To simulate a radical spectrum with its 13C satellite lines, two separately computed spectra have to be added up. Note that the magnetic field range is given explicitly.
Exp = struct('mwFreq',9.7,'Range',[345.2 347.8]);

% Spectrum with 12C (no nuclear spin)
Sys = struct('g',2,'Nucs','1H,1H','n',[2 3],'A',[10 11],'lw',0.02);
[x,y1] = garlic(Sys,Exp);

% Spectrum with 13C (spin 1/2)
Sys = struct('g',2,'Nucs','1H,1H,13C','n',[2 3 1],'A',[10 11 3],'lw',0.02);
[x,y2] = garlic(Sys,Exp);

% Combine 12C and 13C spectra, weighted by natural abundances
y = 0.99*y1 + 0.01*y2;
plot(x,y);
xlabel('magnetic field [mT]'); axis tight

Zoom in to see the 13C satellite lines.

A simple example of a spectral simulation in the fast motional regime using the rotational correlation time:

A = mt2mhz([5.8 5.8 30.8]/10);
Sys = struct('g',[2.0088 2.0061 2.0027],'Nucs','14N','A',A);
Sys.tcorr = 5e-9;
Exp = struct('mwFreq',9.5);
garlic(Sys,Exp);
See also

fastmotion, pepper, salt, resfields