Meaning of 'coupled' initState for triplet-pair

[micollins]

Hi all,

I am trying to model spectra for a coupled triplet-pair using pepper in version 6.0.0-dev.53, and have been trying out the spin-polarisation capability. As seen in the tripletpair_singletfission example, using initState = {[0,0,0,0,0,0,1,0,0],'eigen'} initialises the triplet-pair in the Q0 state, i.e S=2 and m_s=0.

According to cgmatrix(1,1), I would expect using initState = {[0,0,1,0,0,0,0,0,0],'coupled'} would also correspond to the Q0 state, but it gives a very different spectrum that seems to populate the Q2 and Q-2. It seems that the state is changing as the field is swept, but I'm not sure which state Easyspin is using at each field value. If anyone knows I would greatly appreciate the help, I've attached my code below.

Code: Select all

clear all
sys.S = [1,1];
sys.D = [1000,0;1000,0];
sys.DFrame = [0,0,0;0,0,0];
sys.J = 1e6;
sys.initState = {[0,0,1,0,0,0,0,0,0],'coupled'};
sys.lwpp = 1;

Exp.mwFreq = 9.8;
Exp.Range = [320,380];
Exp.Harmonic = 0;

pepper(sys,Exp)

[Matt Krzyaniak]

The coupled basis is meant for coupled spins. How this works in terms of singlet fission: in principle initially only the 1(TT) state is populated, so you would use sys.initState = {[0,0,0,0,0,0,0,0,1],'coupled'};. Due to the zerofield interaction of the two triplets, their dipolar coupling, and the exchange coupling, and any rotation that might be present in all of those interactions, the eigenstates are not truly pure spin states(such as Q,T, and S), but are mixed states. What this means is that in the eigenbasis, the level/state you would normally assign as Q0 is not just purely Q0 but contains some singlet character, and possibly Q+1 and Q-1. This results in some projection of that singlet population into that "Q0" state and producing EPR active transitions.

There are a number of papers out there that aim to describe why largely only Q0 is observed to be populated through EPR, so I suggest digging into that.

Now onto some practical guidelines:

• With singlet fission, often you can get away with using S=2 and sys.initState = {[0,0,1,0,0],'eigen'};

• If you have some spectral shifts that just can't be fit as above, then you need to shift to sys.S = [1 1], keep using 'eigen' and make sure sys.J is really large. This will allow you to work with the triplet-triplet orientations

• If you have an external measurement of J and/or you have a rigid dimer like system, then you may want to start thinking about trying to use 'coupled'

By working at different fields, you may be able to push from one(of the above three) regime to another.