F-centr in KCl. How to describe the second and other shells?

[Smirnova38]

Hello, experts!
In the book "Electron paramagnetic resonace: a practioner's toolkit" chapter 13, p.494-497 I've found out the iteresting example. There is in figure 13.8 simulation of the EPR spectrum of the F center in KCl considering the first and second coordination spheres only. I've written a code using Euler angles for the first coordination sphere, it was simple, but I can't understand how to describe the second sphere. I mean, I've determined Euler angles for the second one, but the length of the vector will change: the square root of 2 instead 1. How can I describe this things? Thank you for your time.

Code: Select all

clear
S=1/2;
g=2.0;
Sys.Nucs = '35Cl,39K,39K,39K,39K,39K,39K';
A_35Cl = 4664; 
A_39K = 231;
Sys.A = [A_35Cl;A_39K;A_39K;A_39K;A_39K;A_39K;A_39K];
Sys.Apa = [0 0 0; 0 0 0;0 2 0;0 1 0; 0 1 1; 0 1 2; 0 1 3]*pi/2;
Sys.lwpp = [0 0.65];

Exp.mwFreq = 9.05;
Exp.Range = [300 350];

Opt.Method = 'perturb';
Opt.nKnots = [61 0];

pepper(Sys,Exp,Opt);

[Stefan Stoll]

The Euler angles are only relevant if you are using anisotropic interactions. Since you are using isotropic values for both g and all the A, the Euler angles have no effect. You can safely drop them.

Also, as you are simulating an isotropic system, you can use garlic instead of pepper. It will be better able to handle the degeneracies due to the many equivalent nuclei, and it will be a lot faster.

Finally, check the magnitude of your hyperfine couplings. ES expects them to be in MHz. Your values look a little large.

[Smirnova38]

The Euler angles are only relevant if you are using anisotropic interactions. Since you are using isotropic values for both g and all the A, the Euler angles have no effect. You can safely drop them.

Also, as you are simulating an isotropic system, you can use garlic instead of pepper. It will be better able to handle the degeneracies due to the many equivalent nuclei, and it will be a lot faster.

Finally, check the magnitude of your hyperfine couplings. ES expects them to be in MHz. Your values look a little large.

Stefan, hello. Thank you for the answer. Using your advice, I managed to imrove my graph, it doesn't have any unnecessary lines.

Code: Select all

clear
S=1/2;
g=2.0;
Sys.Nucs = '39K,39K,39K,39K,39K,39K';
%Sys.Nucs = '35Cl,39K,39K,39K,39K,39K,39K';
%A_35Cl = 4664; 
A_39K = 231;
Sys.A = [A_39K;A_39K;A_39K;A_39K;A_39K;A_39K];
%Sys.Apa = [0 0 0; 0 0 0;0 2 0;0 1 0; 0 1 1; 0 1 2; 0 1 3]*pi/2;
Sys.lwpp = [0 0.65];

Exp.mwFreq = 9.5;
Exp.Range = [250 450];

%Opt.Method = 'perturb';
%Opt.nKnots = [61 0];

garlic(Sys,Exp);

But I have questions again. The first, I took hyperfine coupling from the book "Electron Spin Resonance. Elementary Theory and Practical Applications" authors Wertz and Bolton. Here they are - table c. What's wrong with them? The second question is if I want to change the orientation of magnetic field <110> instead <100>, should I use Euler angles or any another tools of EasySpin?

[Matt Krzyaniak]

I might be mistaken on this but I thought the hyperfine values from that table in Wertz and Bolton correspond to isolated the neutral atoms. Where in your example you have an unpaired electron trapped in the crystal, in which case that unpaired spin density is distributed across multiple atoms so you actually have to scale the interactions down appropriately.

As for the orientation of the magnetic field there are sort of two ways to get at that, First off you'll have to go back to using pepper. Now you can use either Exp.Orientations.
From the pepper documentation:

3xN array of real
Specifies single-crystal orientations for which the EPR spectrum should be computed. Each column of Orientation contains the three Euler rotation angles [phi;theta;chi] of the magnetic field in a molecule fixed frame. If Orientation is empty or not specified, the full powder spectrum is computed.

Exp.Orientations = [0;0;0]; % crystal with z axis aligned with B0
Exp.Orientations = [0;pi/2;0]; % crystal with z axis perpendicular to B0
Exp.Orientations = [0 0 0;0 pi/2 0].'; % two orientations
Exp.Orientations = []; % powder

Or alternatively you could fix the orientation as above and in your spin system vary the euler angle of the hyperfine through Sys.Apa. That provides you a handle with which you can vary and fit using esfit.
Though for either of these to actually result in spectral changes you'd need to include hyperfine anisotropy for each of the nuclei.

[Smirnova38]

Hello, experts. The problem I faced: the second coordination shell has 12 equivalent nuclei of Cl, I tried to use the tip to describe them with 6 equivalent nuclei of K the first coordination shell together:

Sys.n gives the number of equivalent nuclei. So

Sys.Nucs = '1H';
Sys.n = 1;
Sys.A = 5.3;
indicates a single proton, whereas

Sys.Nucs = '1H';
Sys.n = 2;
Sys.A = 5.3;
specifies two equivalent protons, i.e. protons with identical hyperfine coupling constants. The statements

Sys.Nucs = '1H,1H';
Sys.n = [4 4];
Sys.A = [-14 -5];
specify two groups of protons with 4 equivalent nuclei in each (as in a naphthalene radical anion or cation).

Code: Select all

clear
S=1/2;
g=2.0;
Sys.Nucs = '39K,35Cl';
Sys.n = [6 12];
Sys.A = [40 410];
Sys.lwpp = [0 0.65];
Exp.mwFreq = 9.5;
Exp.Range = [0 500];
garlic(Sys,Exp);

but my graph is not good. What's wrong with my code?

[Matt Krzyaniak]

Well that's interesting.
Anyway, the problem you're seeing is related to you specifying Exp.Range and likely not increasing Exp.nPoints. If you remove Exp.Range, or increase it to about [0 700] that fixes things a little bit. Some artifacts still appear unless you increase Exp.nPoints.

I pulled the hyperfine couplings from that section in Electron paramagnetic resonance: a practitioner's toolkit you referenced in the first post.

Code: Select all

clear
S=1/2;
g=2.0;
Sys.Nucs = '39K,35Cl';
Sys.n = [6 12];
Sys.A = [20.7 6.9];
Sys.lwpp =  0.06;
Exp.mwFreq = 9.5;
Exp.nPoints = 2^13;
garlic(Sys,Exp);

This replicates the figures in that section reasonably well. Changing lwpp from 0.06 to 0.6 replicates the change in spectrum illustrated in figure 13.8.

[Smirnova38]

Hello, experts! I try to simulate the spectrum of F-centr in KCl using coordinates of the vertices of a crystall. In this example unpaired electron is trapped into an anion vacancy surrounded by 6 K(+) cations that form the first coordination shell around vacancy at a distance r. But my code doesn't feel Exp.Orientations again. The spectrum looks like <100>-direction, but the angle [0 45 0]*pi/180 corresponds to <110>. Do you have any idea???

And second question. I need to describe the second shell (12 Cl-ions). Can I use the same angles (theta and psi) for that?

Code: Select all

clear
Sys.S = 1/2;
Sys.g = 2;
theta = [0 180 0 0 90 -90]*pi/180 ;
psi = [0 0 90 -90 0 0]*pi/180;
for i=1:6
    A = 20*[1 1 1];
    Sys = nucspinadd(Sys,'39K',A,[psi(i) theta(i) 0]);
end
Sys.lwpp = 0.06;
Exp.mwFreq = 9.5;
Exp.Orientations = [0 45 0]*pi/180;
Exp.nPoints = 2^13;
Opt.Method = 'perturb1';
pepper (Sys,Exp,Opt);

[Stefan Stoll]

Your hyperfine tensor is isotropic, therefore you don't see any orientation dependence.

As for adding the second shell, you need to figure out the polar coordinates of the ligands relative to your center. Assuming you have the coordinates of the chlorides and the vacancy, you can use something like

Code: Select all

% rVacancy: xyz coordinates of vacancy
% rCl: 3x12 array of xyz coordinates of Cl anions, one column per anion
for iCl = 1:12
  r(:,iCl) = rCl(:,iCl) - rVacancy;  % calculate vector vacancy->Cl anion
end
[phi2,theta2] = vec2ang(r);
% phi2 and theta2 are now the polar coordinates of the 12 chloride ions relative to the vacancy