Opposite signs of ZFS parameters for 2 triplets

[sg_epr]

I am trying to fit two exchange coupled triplets. I am getting opposite signs of D & E parameters for them (D > 0, E < 0 and D < 0, E > 0) with similar magnitudes. Which of two inference should I make -
1. I have chosen different frames of reference for them while giving preliminary D&E values
2. First of them has oblate spin distribution and second one prolate
Thanks

[Stefan Stoll]

Are you sure the sign of D is significant in your analysis? Typically, EPR spectra are not sensitive to the sign of D, unless you are at low temperatures. If you have a simulation, try inverting the sign of D and E and check whether the spectrum changes.

The sign of E is a matter of ZFS axis labeling (x vs y), so this does not hold any physical information by itself for a single ZFS tensor - only in relation to another tensor.

Here is a quick demonstration.

Code: Select all

clear

Exp.mwFreq = 9.5;
Exp.Range = [280 400];
Exp.Temperature = 20;

Sys.S = 1;
Sys.lwpp = 2;

D = 1000;
E = 150;
Sys.D = [ D  E]; [B,spc_pp] = pepper(Sys,Exp);
Sys.D = [ D -E]; [B,spc_pn] = pepper(Sys,Exp);
Sys.D = [-D  E]; [B,spc_np] = pepper(Sys,Exp);
Sys.D = [-D -E]; [B,spc_nn] = pepper(Sys,Exp);

plot(B,spc_pp,B,spc_pn,B,spc_np,B,spc_nn);
legend('D > 0, E > 0','D > 0, E < 0','D < 0, E > 0','D < 0, E < 0');

[sg_epr]

Thanks Stefan, for the suggestion. I tried reversing the sign for one D&E set, and simulated spectrum is quite different. In fact the data I am trying to fit is collected at 5K...so it makes sense, as you said sign of D only relevant at low T. Does this mean that the opposite signs of D are related to prolate/oblate spin distribution ? It is quite unexpected, as my two S = 1 centers are same, other than variable crystal field due to crystallographically nonidentical positions. Thanks

[Stefan Stoll]

Please post a short script that does the simulation.

[sg_epr]

Here is the script, attached is the experimental data.

Code: Select all

Sys1.S = [1 1];
Sys1.g = [3.4 3.2 5.15; 3.67 3.92 2.82];
Sys1.HStrain = [13540 9.73E-12 926];
Sys1.DStrain = [1.7E-08 86; 1.14E-09 7.4E-06];
Sys1.D = [7714 -852; -2230 427];
Sys1.J = 1700;
Exp.mwFreq = 9.538;
Exp.Range = [0 250];
Exp.Harmonic = 1;
Exp.Mode = 'perpendicular';
Exp.Temperature = 4.2;
Exp.CrystalSymmetry = 161;
Opt.Method = 'hybrid';
options.Output = 'summed';
Verbosity = 1;
pepper({Sys1}, Exp);
[Field,Spec] = pepper({Sys1}, Exp);

[Stefan Stoll]

These are a lot of fitting parameters for a spectrum that doesn't have a lot of features. There are 11 parameters, plus 9 linewidth parameters. Without additional data (e.g. higher-frequency EPR) it is going to be difficult to be certain that you found the correct minimum. Therefore, I would not dare to interpret these values at this point.

An additional concern is that you are assuming all the g and D tensors to be collinear, which might not be realistic for your system.

Regarding the many linewidth parameters, it's odd to have HStrain with 1e-12 along one direction and >13000 along another, and a similar unbalance in DStrain. Looks pretty unphysical to me. Try omitting HStrain altoghether.

[sg_epr]

Thanks Stefan for number of suggestions. To be honest, I was more interested in g, D, E & J values and did not give much importance to D&H strains. What you pointed out about D&H strain values makes sense, now, attached picture is the best I achieved so far without HStrain, though DStrain values remain bit odd [2.98E-8 1.75; 1.33E-9 4.84E-6].
When you suggest having non-collinear Reference frames for D & g, does it mean making them independent from molecular frame of reference using code something like this ? Thanks

Code: Select all

Sys.gFrame = [30 30 30; 30 30 30]*Pi/180;
Vary.gFrame =  [29 29 29; 29 29 29]*Pi/180;
Sys.DFrame = [30 30 30; 30 30 30]*Pi/180;
Vary.DFrame =  [29 29 29; 29 29 29]*Pi/180; 

[Stefan Stoll]

Yes. You can use one of the tensor frames as the molecular frame, so that need one fewer sets of Euler angles.

This is going to increase your parameter space substantially. You need to look at the (expected) molecular structure of your system and come up with a reasonable assumption for the relative orientations between the various tensors. Quantum chemical calculations might help here. Even better, try to get EPR spectra at higher/lower field to get more data.