Approaches for high-spin systems with complicated HFIs?

[tscmacdonald]

Hi all,

I'm interested in high-spin organic excited states (triplets and quintets) that form from singlet fission. Recently, I've been running a few calculations with Orca to obtain ZFS D-tensors and hyperfine couplings. Here's the system imported into Easyspin as the result of a calculation on a TIPS-pentacene triplet, calculating HFC couplings for each of the 12 hydrogens on the central pentacene group:

Code: Select all

Sys = 
  struct with fields:

      S: 1
    xyz: [100×3 double]
  Atoms: [1×100 double]
 Charge: 0
      g: [2.0023 2.0028 2.0029]
 gFrame: [-0.0576 1.6056 -3.1402]
      D: [-5.3387e+03 -4.0682e+03 -3.7507e+03]
 DFrame: [3.1400 1.5622 3.1411]
   Nucs: 'H,H,H,H,H,H,H,H,H,H,H,H'
NucsIdx: [11 12 13 14 23 24 25 26 31 32 33 34]
      A: [12×3 double]
 AFrame: [12×3 double]
      Q: [12×3 double]
 QFrame: [12×3 double]

As you could probably guess from the pseudo-d2h symmetry, there are 4 sets of 3x roughly equivalent protons with roughly equivalent HFCs:

Code: Select all

 Sys.A
ans =
   -2.8087   -8.4654  -10.3759
   -2.7906   -8.4641  -10.3703
   -2.8093   -8.4640  -10.3795
   -2.7899   -8.4627  -10.3678
   -0.4247   -1.9482   -2.5083
   -0.4241   -1.9608   -2.5112
   -0.4256   -1.9520   -2.5104
   -0.4237   -1.9592   -2.5105
   -0.1656   -2.3620   -3.0961
   -0.1668   -2.3648   -3.1016
   -0.1645   -2.3599   -3.0926
   -0.1668   -2.3648   -3.1014
 

My problem is that I'm not sure how to use this information with Easyspin. The first 4 nuclei have much higher coupling constants and so for simulating EPR spectra it feels reasonable to call pepper(nucspinkeep(Sys,1:4),Exp) and drop the rest: that runs in a reasonable time and gets me a spectrum.

My problem is that I'd also like to be able to simulate ENDOR data, and specifically orientation-selected MIMS ENDOR data taken at the canonical field positions, as in this paper:

I can run saffron on up to 6 or so nuclei without great difficulty, but considering all 12 seems entirely intractable. Running the calculation with perturbation theory rather than matrix diagonalisation might be helpful, but Easyspin doesn't support perturbation theory on high-spin systems so I can't do that here. My one thought is that maybe it would be possible to use symmetry to simplify the spin system (since we only have three unique hyperfine couplings, repeated four times) but I have no idea if this is possible from a user's perspective, or how to go about doing so if it is.

If anyone has a clever suggestion here for something that I could be doing differently, I'd love to hear it!

[Matt Krzyaniak]

Well speaking from experience on organic triplets, very rarely will you observe the hyperfine interaction in your Continuous Wave or Echo Detected spectra. The HFIs tend to get washed out in the inhomogeneous broadening, strain, or disorder.

With respect to ENDOR, you were on the right path trying to utilize the symmetry and group the Hydrogen into equivalent or nearly equivalent nuclei in order to approximate your system. This partially depends on the orientation of the zerofield splitting but it is likely such that you can group nuclei [11 12 13 14], [23 24 25 26], and [31 32 33 34]. The last 4 might be a little tricky depending on how rhombic your ZFS so may not be completely equivalent. This should collapse your simulation down to just 3 nuclei and as a first approximation should be pretty good. With the number of Hydrogen, it occurring on a photo-generated triplet(where sometimes S/N can be a problem) and that your triplets may also be moving in the material on the timescale of the ENDOR experiment(especially if you want long RF pulses to increase resolution), I would doubt that you need to get much better than this approximation.

btw in the development version ES has the capability to simulate the (TT) pair from singlet fission, I just haven't yet updated the documentation. If you're interested I could share an example.

[tscmacdonald]

Hi Matt,

Thanks for the reply, and I'd love to see that documentation. We've been simulating spins polarised in the high-field basis by just setting Opt.Output = 'separate' and then getting the polarised Z+/Z- spectra with [B,spc] = pepper(Sys,Exp,Opt); Spc = Spc{1}-Spc{2}; or similar, but if you've got some new and better options I'd love to read about them.

Otherwise: 100% agree that this is all irrelevant from the EPR side, but the ENDOR side remains a bit tricky (we're hoping to eventually combine MIMS ENDOR with simulations to get information about the spin localisation of our SF triplets). How would I actually go about putting in multiple equivalent nuclei? salt doesn't seem to accept Sys.n parameters for equivalent nuclei, so I'm not sure how to collapse the system down to 3 nuclei (i.e. Sys.n = [4 4 4]) and run that simulation. We're yet to actually run any ENDOR measurements, but we're looking a intramolecular singlet fission materials such as pentacene dimers diluted into glassy matrices so I don't anticipate seeing much exciton hopping/transport over the measurement timescale.

I also don't really follow why the ZFS rhombicity would be more important for the outer nuclei (31 - 34) than for the others, but here's my ZFS matrix for good luck:

Code: Select all

disp(Sys.D)
   1.0e+03 *
   -5.3387   -4.0682   -3.7507

(D ~ 1430 MHz, E/D = 0.11)

[Matt Krzyaniak]

Here is a fairly commented example script, it should work with the development version.
Keep in mind that this would represent your initial (TT) state following singlet fission. And how we generate the spectrum we are throwing out the coherences that might be present as has historically been done when simulating spin correlated radical pairs.

Code: Select all

clear Sys Exp Opt

Sys.S = [1 1];
Sys.g = [2.002 2.002];
Sys.lwpp =1;

% ZFS close to pentacene
Sys.D = [1100 20;1100 20]; % MHz

Sys.J = 20000; % MHz

% D = 78049/r^3 MHz*A^3
Sys.dip =  0;

% The new feature is in how you define the population basis. 
% The default is 'molecular' which populates the eigenstates
% based on the zerofield or field independent eigenstates.
% 
% However for singlet fission or spin correlated radical pairs, 
% the population is based on the spin character of the high field eigenstates.
% we can switch to this by changing the population basis to 'Spin'
Sys.PopBasis = 'Spin'; 

% Then we need to define a state vector which corresponds to the spin 
% character of the spectrum
nElStates = prod(2*Sys.S+1);
r = zeros(1,nElStates); 
% in the coupled basis the state vector would be:
% [q2 q1 q0 q-1 q-2 t1 t0 t-1 s] 
% and for SF it should start as a singlet:
r(end) = 1;
% However, Easyspin defines the spin system in the uncoupled basis  

% so we just need to rotate our state vector 
U2C = cgmatrix(Sys.S(1), Sys.S(2));
r = r*U2C;
% then pass that statevector into Pop. 
Sys.Pop = r;
% population of the sublevels are calculated as the overlap between the 
% eigenvectors and the provided state vector as:
%
% PopulationU = abs(Sys.Pop.'*U).^2; % lower level
% PopulationV = abs(Sys.Pop.'*V).^2; % upper level
% Polarization = PopulationU - PopulationV;
% where U and V are the eigenvectors for a given transition

Exp.Harmonic = 0;
Exp.mwFreq = 9.5;% GHz
Exp.Range = [290 390];
Exp.nPoints = 1024;

Opt = [];
% The sorting of the resonances into transition manifolds can get 
% a little confused(I think) resulting in seperate output that looks a bit weird  

Opt.Output = 'separate';

[field,sim,trans] = pepper(Sys,Exp,Opt);

figure(1)
plot(field,sim,field,sum(sim),'k')

leg = [num2str(trans(:,1)) repmat(' -> ',size(trans,1),1) num2str(trans(:,2))];
legend(leg)
set(gca,'yticklabel',' ')
xlabel('Magnetic Field (mT)')
xlim([290 390])


figure(2)
ori = 'xyz';

B = 0:390;
E = zeros(length(B),9);
for i = 1:3
  subplot(1,3,i)
  levelsplot(Sys,ori(i),B,9.5)
  %E(:,(1:3)+(i-1)*3) = levels(Sys,ori(i),0:450);

  title(['B||',ori(i)])
  %hold all
end
hold off

[Matt Krzyaniak]

How would I actually go about putting in multiple equivalent nuclei? salt doesn't seem to accept Sys.n parameters for equivalent nuclei, so I'm not sure how to collapse the system down to 3 nuclei (i.e. Sys.n = [4 4 4]) and run that simulation.

For ENDOR, if you have equivalent nuclei you can effectively ignore all of the other equivalent ones and just simulate a single nuclei. So you don't need Sys.n.

I also don't really follow why the ZFS rhombicity would be more important for the outer nuclei (31 - 34) than for the others, but here's my ZFS matrix for good luck:

Code: Select all

disp(Sys.D)
   1.0e+03 *
   -5.3387   -4.0682   -3.7507

(D ~ 1430 MHz, E/D = 0.11)

I was just thinking that if your ZFS tensor is rotated relative to the symmetry of the molecule, that those outer nuclei are no longer exactly equivalent, that said it would never be an observable effect unless you have a single crystal.