chili
Introduced in 2.5
Synopsis

Simulation of slow-motional cw EPR spectra

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

See also the tutorial on how to use chili.

Description

chili computes cw EPR spectra of systems with one unpaired electron and one or more nuclei in the slow-motional regime.

Up to four input arguments are accepted:

If no input argument is given, a short help summary is shown (same as when typing help chili).

Up to two output arguments are returned:

If no output argument is given, chili plots the spectrum.

Sys is a structure containing the parameters of the spin system. Only S=1/2 systems are supported. Used parameters are g, gpa, Nucs, A, Apa. See the documentation on spin system structures for details. The nuclear quadrupole interaction is not included in the computation.

Dyn is a structure collecting values for dynamic parameters of the spin system. The following parameters are possible:

tcorr Scalar
Rotational correlation time for isotropic rotational diffusion, in seconds. If tcorr is set, Diff is ignored.

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

Diff Scalar or 2-element vector
Rotational diffusion rates (principal values of the rotational diffusion tensor), in second^-1. Scalar: isotopic diffusion, 2-element vector: axial diffusion tensor with [Dxy Dzz].
Diff is ignored if tcorr is given.
Diffpa 3-element vector
Euler angles describing the orientation of the rotational diffusion tensor in the molecular frame.
lw Scalar
Residual line width (Lorentzian FWHM), in Hz.
Exchange Scalar
Heisenberg spin exchange frequency, in Hz.

Exp contains the following experimental parameters.

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.

Opt, the options structure, collects all settings relating to the algorithm used and the behaviour of the function. The following fields are available:

LLKM 4-element vector [evenLmax oddLmax Kmax Mmax]
Specifies the basis size by giving the maximum values for, in that order, even L, odd L, M and K. M and K must be less than or equal to the maximum value of L.
If this field, is not specified, chili sets the basis size automatically. This is adequate for most, but not all, cases.
Verbosity 0 (default), 1
Determines how much information chili prints to the screen. If Opt.Verbosity=0, is is completely silent. 1 prints details about the progress of the computation.
Example

The cw EPR spectrum of a slow tumbling nitroxide radical can be simulated with the following lines.

Sys = struct('g',[2.008 2.0061 2.0027],'Nucs','14N','A',[16 16 86]);
Exp = struct('mwFreq',9.5);
Dynamics = struct('lw',0.01,'tcorr',32e-9);
chili(Sys,Dynamics,Exp);
Algorithm

chili solves the Stochastic Liouville equation in an eigenbasis of the diffusion operator. The eigenfunctions are normalized Wigner rotation functions DLK,M(Ω) with -L≤K,M≤L. The number of basis functions is determined by maximum values of even L, odd L, K and M. The larger these values, the larger the basis and the more accurate the spectrum.

chili computes EPR line positions to first order. For the diffusion, both secular and nonsecular terms are included.

If the spin system contains more than one nucleus, only the first nucleus is included in the full SLE simulation. The effect of all the others is added by post-convolution: The isotropic stick spectrum due to all other nuclei is simulated and the used to convole the SLE-simulated spectrum of the first nucleus.

For full details of the method see

See also

fastmotion, garlic