Organic Biradical and finding the distance between spins

[zdubs]

Hello and sorry for the dumb question. I have a powder spectrum of an organic triplet biradical collected at room temp. I can roughly simulate as an S =1 system and lwpp seems to give better fits than DStrain (although that might be my own lack of experience with powder spectra!). I get out D = 26 MHz and E = 1.1 MHz which converting to cm^-1 gives D = 0.001, E = 6.3e-5. At the very least, the D value is consistent with other biradicals of this type.
The problems start when I try to use the attached equation to find the distance between unpaired electrons. The screencap is from the textbook "Electron Spin Resonance Spectroscopy of Organic Radicals" by Gerson and Huber (Wiley, 2003) page 28. When I try to calculate D' using the equation in the text \D'\ = D/(ge*ub), I get crazy numbers, D' = 5e19 T which then gives an electron distance using equation 2.7 as 0.003 pm! Following reference 366 doesnt help (J . Am. Chem. Soc. 1975, 97, 696), they use an entirely different equation.

Ive been staring at this stuff for a week and I dont know how to proceed. Ive triple checked all my conversions and equations. Any ideas? Happy to post simulation scripts and include my powder spectrum if needed/curious

[Matt Krzyaniak]

There are two slightly different forms, which depend on whether the two spin are like or unlike. And what I mean by like or unlike really comes down to there being appreciable exchange coupling or spin correlation, you can find some discussion of this in Slichter (3rd ed. pg 79-80), and it deals with the terms from Abragam's dipolar alphabet of interactions.

But the short of it is that you get:

Code: Select all

clear
% like electrons
%D =@(r) 2.785/r^3; % mT nm^3
%D =@(r) 78.049/r^3; % MHz nm^3

% unlike electrons
%D =@(r) 1.8526/r^3;% mT nm^3
%D =@(r) 51.92/r^3;% MHz nm^3
r = @(D) nthroot(51.92./D,3); % nm

nuperp = (mu0/4/pi)*bmagn^2*gfree^2/(1e-9)^3/planck/1e6; % MHz nm^3
%D = nuperp*(3*cos(theta).^2-1); % MHz nm^3

A couple notes:

• The first, like, value is common in the photosynthetic literature; while the second, unlike, value is what you will find in the DEER literature

• There is an extra 3/2 factor when the spins are like.

• This assumes the free electron g. You could divide it out and add in your own g-values(if there are significant differences)

[thanasis]

Many thanks to both of you, since this is a question that has been on my mind for quite some time.

I have come to the conclusion that the most versatile way to deal with it is to treat it exactly.

I express the local g-tensors in the molecular frame after first having defined their gFrames. Once this is done, it's as straightforward as:

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D12_M = transpose(g1M)*g2M - 3 * (transpose(g1M)*R12) * (transpose(R12)*g2M); % This is the unitless interaction matrix.
dip12_M = 12993 * r12^-3 * D12_M; % This is the interaction matrix In MHz.

R12 is the unit vector between 1 and 2. r12 is in Angstrom, the 12993 constant is in MHz Angstrom³. Instead of the 12993 MHz Angstrom³, one can use the 0.433 cm-1 Angstrom³ value given by Bencini & Gatteschi, but its simpler to just plug in the MHz values in to Easyspin interaction matrix.

Matt, I'm curious, how do your values compare to these for the calculation of the dipolar-induced zfs? Don't we need to also take into account the projection coefficients defined by Bencini & Gatteschi (p. 55, Table 3.3)?

While we can simply diagonalize the final dip12_M and calculate D and E from the xx, yy and zz elements, is there an analytical correlation between the dipolar matrix and the dipolar-induced zfs?