Simulation of slow-motional cw EPR spectra

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

See also the user guide 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.

chili takes up to three input arguments

• Sys: static and dynamic parameters of the spin system
• Exp: experimental 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, 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. The used static parameters are g, gpa, Nucs, A, Apa. See the documentation on spin system structures for details. The nuclear quadrupole interaction (specified in Q and Qpa) is neclected by chili.

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.

Sys should contain dynamic parameters relevant to the motional simulation. One of the field tcorr, logtcorr, Diff or logDiff should be given. If more than one of these is given, the first in the list logtcorr, tcorr, logDiff, Diff takes precedence over the other(s).

Sys.tcorr = 1e-9;         % isotropic diffusion, 1ns correlation time
Sys.tcorr = [5 1]*1e-9;   % axial anisotropic diffusion, 5ns around x and y axes, 1ns around z
Sys.tcorr = [5 4 1]*1e-9; % rhombic anisotropic diffusion

Exp contains the following experimental parameters.

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

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 D^L_K,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, which is appropriate for most organic radicals. It is inaccurate for transition metal complexes, e.g. Cu²⁺ or VO²⁺. 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 then used to convolve the SLE-simulated spectrum of the first nucleus.

For full details of the algorithm see

• K. A. Earle, D. E. Budil, in: S. Schlick, Advanced ESR Methods in Polymer Research, Wiley, 2006, chapter 3.
• D. J. Schneider, J. H. Freed, Biol. Magn. Reson. 8, 1-76 (1989).

esfit, fastmotion, garlic