Simulation of slow-motional cw EPR spectra
chili(Sys,Exp) spec = chili(...) [B,spec] = chili(...) ... = chili(Sys,Exp,Opt)
See also the tutorial on how to use chili.
chili computes cw EPR spectra of systems with
one unpaired electron and one or more nuclei in the slow-motional
regime.
Up to three input arguments are accepted:
Sys: static and dynamic parameters of the spin system
Exp: eperimental parameters
Opt: options and settings
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:
B: magnetic field axis vector, in mT
spc: spectrum
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.
In addition, Sys collects values for dynamic parameters
of the spin system. The following parameters are possible:
tcorr |
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).
For anisotropic rotational diffusion, use Diff or logDiff.
|
logtcorr |
Base-10 logarithm of the correlation time, offering an alternative way to input the correlation time.
If given, tcorr is ignored.Use this instead of tcorr for least-squares fitting
with esfit.
|
Diff |
Rotational diffusion rates (principal values of the rotational diffusion tensor),
in second-1.
Diff is ignored if tcorr is given.
|
logDiff |
Base-10 logarithm of Diff. If given, Diff is ignored.
Use this instead of Diff for least-squares fitting
with esfit.
|
Diffpa |
3-element vector Euler angles describing the orientation of the rotational diffusion tensor in the molecular frame. |
lw |
1- or 2-element array of FWHM linewidths (all in mT).
|
lambda |
An array of coefficients for the orienting potential, with up to five elements
corresponding to the five
coefficients λ2,0, λ2,2, λ4,0,
λ4,2, and λ4,4 (sometimes, the symbols c or ε
are used instead in the literature).
|
Exchange |
Heisenberg spin exchange frequency, in Hz. |
Exp contains the following experimental parameters.
mwFreq | Spectrometer frequency in GHz |
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. |
MOMD |
1 or 0, depending on whether the MOMD model should be used.
If
If |
psi |
angle between magnetic field and director axis, in radians.
If given, it specifies the angle between the external magnetic field and the director axis (ie the principal axis of the orienting potential). This angle is often called the "director tilt". If not given, zero is assumed.
If the MOMD model is used, |
Opt, the options structure, collects all settings relating to
the algorithm used and the behaviour of the function. The following fields
are available:
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.
|
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.
|
nKnots |
Number of orientations used in a MOMD simulation (see Exp.MOMD).
Default is 5. Increase this value if the orienting potential coefficients
Sys.lambda are large.
|
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]);
Sys.tcorr = 1e-9; % 1 ns
Exp = struct('mwFreq',9.5);
chili(Sys,Exp);
chili solves the Stochastic Liouville equation (SLE) in the eigenframe
of the diffusion tensor and 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 algorithm see