## equivalent nuclei in cw ESR spectra

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### equivalent nuclei in cw ESR spectra

Dear colleagues,

I have a strange result with very simple task of modelling cw ESR spectra. I have a system with two equivalent Sc nuclei and large hyperfine coupling constant. And I get different results if I treat them as two equivalent nuclei or if I treat them independently. The former model gives reasonable results (at least they agree with experimental spectrum), whereas the latter is not correct. Have I done something wrong? The problem is at the next step I would like to simulate fast motion regime, and here I cannot use two equivalent nuclei....

two equivalent nuclei
Exp=struct('mwFreq',9.85,'nPoints',64000);
Sc2=struct('g',1.9980,'Nucs','45Sc','n',2,'lw',0.2);
Sc2.A=532;
garlic(Sc2,Exp);

two different nuclei with the same coupling constant:
Exp=struct('mwFreq',9.85,'nPoints',64000);
Sc2=struct('g',1.9980,'Nucs','45Sc,45Sc','lw',0.2);
Sc2.A=[532;532];
garlic(Sc2,Exp);
alxyppv
Newbie

Posts: 2
Joined: Mon Dec 15, 2014 5:26 pm

### Re: equivalent nuclei in cw ESR spectra

So I played around with it a little bit, I'm not entirely clear where the problem lies(in garlic), but its partially related to the magnitude of the hyperfine interaction.
As a workaround for now I'd suggest you use pepper when modeling multiple nuclei.
Matt Krzyaniak
EasySpin Guru

Posts: 96
Joined: Tue Jul 22, 2014 11:01 am
Location: Northwestern University

### Re: equivalent nuclei in cw ESR spectra

The Breit-Rabi method implemented in garlic() is exact for a single nucleus and for multiple equivalent nuclei, but not for multiple non-equivalent nuclei, In the latter case, it neglects any cross-nuclear terms. These become significant if the hyperfine coupling of one of the nuclei is large. Physically, the nucleus with the large hyperfine coupling is affecting the electron spin state, which affects the nuclear spin states of the other nucleus.

garlic() treats the case of equivalent nuclei a little differently, which results in accurate spectra: Since the nuclei are equivalent, they can be exactly transformed to a coupled representation where the spin Hamiltonian separates into independent blocks: two 45Sc (I1 = I2 = 7/2) give several exactly independent nuclear spins with F = 0, 1, 2, ..., 7 (the "spin ladder" from |I1-I2| up to I1+I2). garlic() then simulates the spectra for each of these F spins separately and then adds them up.

Matt is right: In case of doubt always use pepper() as a reference.

BTW, pretty rare to see 2x 45Sc hyperfine simulations! I guess this relates to endohedral Sc fullerenes.
Stefan Stoll
EasySpin Creator

Posts: 528
Joined: Mon Jul 21, 2014 10:11 pm
Location: University of Washington

### Re: equivalent nuclei in cw ESR spectra

Good guess, it is endohedral fullerene:) BTW, we had even four Sc atoms in one radical recently (Sc4O2@C80, http://dx.doi.org/10.1021/ja306728p).
Thank you for your answers. When I compare to experimental data, I have no doubt that treating the two nuclei as equivalent gives correct result in line positions. But I also see a distribution of line widths in the spectrum. And here comes the next question - is there any chance to model then fast motion regime for such a system? I mean, according to user-guide, in fast motion regime I have to treat equivalent nuclei independently...
alxyppv
Newbie

Posts: 2
Joined: Mon Dec 15, 2014 5:26 pm

### Re: equivalent nuclei in cw ESR spectra

Unfortunately, fast motion regime for equivalent nuclei is currently not possible, but I see why you might need it. If you can point me to a reference, I can look into implementing it.
Stefan Stoll
EasySpin Creator

Posts: 528
Joined: Mon Jul 21, 2014 10:11 pm
Location: University of Washington

### Re: equivalent nuclei in cw ESR spectra

By the way, endohedral fullerene, or Endofullerene is pretty amazing material. I know one company, that is focusing on tailoring these nano-materials. Maybe you can try to get to touch with them if you are working in similar area.
char33
Newbie

Posts: 1
Joined: Mon Dec 04, 2017 3:48 am