EasySpin forum

In a previous post of 18 December 2020 I pointed out that esfit resulted in values of E>D/3 which corresponds to a principal axis error of the D-tensor. Stefan Stoll told me that this was a current limitation of the program and that I could recalculate the principal values of the tensor which I did.
I have the same problem again to simulate a rhombic S=3/2 spectrum with a large value of D=9.9 cm-1 (magnetic measurements). I can only determine in this case the E/D ratio and the best fit gives E/D=0.3478. When I recalculate the D values I find D=-10.11 cm-1.If I run esfit again with this new value of D I find a ratio E/D=0.3503.
In short I am going round in circles and I would like to have a solution because I cannot publish a simulation with a value of E>D/3. If I block the E/D ratio at 0.33333 and only determine the g values, the simulation is less good

best regards

Yves

I suggest to take the D and E values from the best fit and then convert them to the conventional frame using zfsframes. Let's say the fit results in D=1.2 (in some units) and E/D = 0.4. Then the principal values of the D tensor are

D = 1.2;
EoD = 0.4;
Dpv = [-1/3+EoD, -1/3-EoD, 2/3]*D

Using zfsframes you can now look at the D and E values for all possible permutations of the principal axes:

zfsframes(Dpv)

This gives

==================================================================
D tensor in various axis system conventions
==================================================================
Principal values (PVs) of D tensor in input order:
  D1 = +0.08     D2 = -0.88     D3 = +0.8
This D tensor is traceless (sum of PVs is zero).
This D tensor is neither exactly axial nor exactly orthorhombic.
Principal axis system conventions:
  Poole 1974:    |Dz|>=|Dx|>=|Dy|    (used for organic triplets)
  Blumberg 1967: |Dz|>=|Dy|>=|Dx|    (used for transition metals)
  (for references see documentation)
Computation of D and E:
  D = 3/2*Dz      E = (Dx-Dy)/2
  Dx = -D/3+E     Dy = -D/3-E        Dz = 2/3*D
D and E in all possible principal axis systems:
  123->xyz:  D = +1.200    E = +0.480    E/D = +0.40    
  132->xyz:  D = -1.320    E = -0.360    E/D = +0.27    Blumberg 
  213->xyz:  D = +1.200    E = -0.480    E/D = -0.40    
  231->xyz:  D = +0.120    E = -0.840    E/D = -7.00    
  312->xyz:  D = -1.320    E = +0.360    E/D = -0.27    Poole 
  321->xyz:  D = +0.120    E = +0.840    E/D = +7.00    
The Blumberg convention is the recommended one.

This shows that you can get the Blumberg convention (0=<E/D=<1/3) if you swap the second and the third axis (132->xyz). You can verify this by calculating D and E from the principal values:

Dpv_ = Dpv([1 3 2]);   % swap axes
D_ = 3/2*Dpv_(3)
E_ = (Dpv_(1)-Dpv_(2))/2
E_/D_

which gives

D_ =
   -1.3200
E_ =
   -0.3600
ans =
    0.2727

All the above tensors are equivalent, and using any of them in a simulation will give the same spectrum. Be aware though that you might need to add DFrame if you swap axes and if there are other tensors in the system.

Hello
Thank you for these long explanations, I did not know the zfsframe function. However if the Blumberg convention gives me effectively the same spectrum with a ratio E/D <1/3 these new values of D and E do not give me a good simulation of the magnetic data. As the best fit from esfit gives a value of E/D very close to 1/3 I locked the E/D ratio at 1/3 and only optimised the values of the g tensor.
I am really grateful to you for spending so much time answering questions in the forum when you have your own research to do at the University

Please post a self-contained minimal script that demonstrates the problem you are encountering, so we can look into this.