EasySpin: garlic

garlic

Synopsis

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

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

See also the user guide 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.

`g`	Array with 1, 2 or 3 elements, either isotropic g factor or principal values of an axial or orthorhombic g tensor. Sys.g = 2.005; % isotropic g Sys.g = [2.001 2.004]; % axial g Sys.g = [2.001 2.002 2.004]; % orthorhombic g
`Nucs`	String with comma-separated list of isotopes, e.g. `Sys.Nucs = '1H,13C'`.
`n`	Vector 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.
`lwpp`	1- or 2-element array of peak-to-peak linewidths (all in mT). 1 element: `GaussianFWHM`. 2 elements: `[GaussianFWHM LorentzianFWHM]`.
`lw`	1- or 2-element array of FWHM linewidths (all in mT). 1 element: `GaussianFWHM`. 2 elements: `[GaussianFWHM LorentzianFWHM]`.

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)`.
`logtcorr`	Base-10 logarithm of the correlation time, offering an alternative way to input the correlation time. If given, `tcorr` is ignored.

If tcorr or logtcorr is given, the fast-motional spectrum is computed. The necessary line widths are computed via the function fastmotion (for details see there). The resulting spectrum is additionally 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.

For simulating a multi-component mixture, Sys should be a cell array of spin systems, e.g. {Sys1,Sys2} for a two-component mixture. Each of the component spin systems should have a field weight that specifies the weight of the corresponding component in the final spectrum.

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

`mwFreq`	Spectrometer frequency, in GHz. E.g. `Exp.mwFreq = 9.5;` for X band.
`nPoints`	Number of points along field axis (default 1024)
`CenterSweep`	2-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.
`Range`	2-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.
`Harmonic`	Detection harmonic (0, 1 or 2), default is 1.
`ModAmp`	Modulation amplitude (peak-to-peak), in mT.
`mwPhase`	The reference microwave phase, in radians. 0 is pure absorption (default value), and `pi/2` is pure dispersion. `mwPhase` is used only if the convolutional broadening given in `Sys.lw` or `Sys.lwpp` has a Lorentzian component. `mwPhase` allows you to include absorption/dispersion admixture in the simulation.
`Temperature`	Gives the temperature of the spin system in the EPR experiment, in Kelvin. If given, Boltzmann populations are computed and included in the EPR line intensities. E.g., `Temperature = 298` corresponds to room temperature. If not given (or set to `inf), all transitions are assumed to have equal polarizations.`

Opt contains simulation options:

Method Specifies the simulation method. 'exact' selects the exact Breit/Rabi solution (see below). Any of 'perturb1', 'perturb2', 'perturb3', 'perturb4', 'perturb5' selects perturbation theory of the corresponding order.

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 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.lwpp = [0 0.1]; % only Lorentzian broadening
Exp = struct('mwFreq',9.7);
garlic(Sys,Exp);

To simulate a radical spectrum with its ¹³C satellite lines, just specify 'C' instead of '13C' for the carbon nucleus, and EasySpin will automatically simulate the spectra of all isotope combinations, in this case 98.93% with ¹²C and 1.07% with ¹³C.

Sys.g = 2;
Sys.Nucs = '1H,1H,C';
Sys.n = [2 3 1];
Sys.A = [10 11 3];
Sys.lwpp = [0 0.01];
Exp.mwFreq = 9.7;
Exp.CenterSweep = [346.5 2.8];
garlic(Sys,Exp);

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);