I like to ask eigenvalues of that matrix. It's relevant to QM and sadly it's a very high bar that is very useful to filter and try to get a good conversation.
My research area is similar, but we use smaller molecules, so I can't understand all the details here.
I took a look an it makes sense. I can't be sure if it's 100% correct, but it's not obviously wrong (and I've seen a lot of obviously wrong post in the /newest page, so I start assuming everything is nonsense until I take a look).
It took a while to understand that [2Fe-2S] is actually Fe2S6C4H12. I guess it's obvious for people working with more biology background. My handwaving is not good enough if the unpaired electron in the Fe couple to S=0 or S=1, but after fooling around in google it looks like S=0 is the correct answer.
Assuming your calculations are correct, they get <S^2>=4.7 that is really a lot and shows it has contamination from S=2 or higher. I can't imagine how to get S=1 with the spin in both Fe in the same direction, but a higher spin confuses me, it may be related to some additional freedom using the d orbitals that is beyond my handwaving.
They claim:
> We study the ground-state properties of these molecular systems in the _ = 0 and ^2 = 0 subspace
So as you say they are trying to get a S^2=0 state, not only an energy bound. Some contamination is expected, but 4.7 is too much in my opinion.
You say:
> A caveat that our own third finding compels: at residual 3.5 × 10−4
in a manifold this dense, energy stability does not certify the eigenvector, so we did not stop at 1.287: the certification run below closes the point.
How many orbitals are near that energy? Do you have a graphic?
> Table 1: [2Fe-2S] followed sector-root energies and spin content vs subspace size D
It's super interesting. It looks like the better energy is caused by the spin contamination. This is not unusual or unexpected, but that's too much contamination in my opinion.
It's hard to suggest what to do with this. But perhaps a super short version (2 or 3 pages?) that get's directly to the results in table 1 may help.
> 2) +1 and -1.
I like to ask eigenvalues of that matrix. It's relevant to QM and sadly it's a very high bar that is very useful to filter and try to get a good conversation.
My research area is similar, but we use smaller molecules, so I can't understand all the details here.
I took a look an it makes sense. I can't be sure if it's 100% correct, but it's not obviously wrong (and I've seen a lot of obviously wrong post in the /newest page, so I start assuming everything is nonsense until I take a look).
It took a while to understand that [2Fe-2S] is actually Fe2S6C4H12. I guess it's obvious for people working with more biology background. My handwaving is not good enough if the unpaired electron in the Fe couple to S=0 or S=1, but after fooling around in google it looks like S=0 is the correct answer.
Assuming your calculations are correct, they get <S^2>=4.7 that is really a lot and shows it has contamination from S=2 or higher. I can't imagine how to get S=1 with the spin in both Fe in the same direction, but a higher spin confuses me, it may be related to some additional freedom using the d orbitals that is beyond my handwaving.
They claim:
> We study the ground-state properties of these molecular systems in the _ = 0 and ^2 = 0 subspace
So as you say they are trying to get a S^2=0 state, not only an energy bound. Some contamination is expected, but 4.7 is too much in my opinion.
You say:
> A caveat that our own third finding compels: at residual 3.5 × 10−4 in a manifold this dense, energy stability does not certify the eigenvector, so we did not stop at 1.287: the certification run below closes the point.
How many orbitals are near that energy? Do you have a graphic?
> Table 1: [2Fe-2S] followed sector-root energies and spin content vs subspace size D
It's super interesting. It looks like the better energy is caused by the spin contamination. This is not unusual or unexpected, but that's too much contamination in my opinion.
It's hard to suggest what to do with this. But perhaps a super short version (2 or 3 pages?) that get's directly to the results in table 1 may help.