Issue with Exchange-Interaction Strength J

[lidonglin12]

I see some articles that use MFH-TB to calculate Exchange-Interaction Strength J.
But I didn't find how to calculate Exchange-Interaction Strength J in examples. Can you teach me how to obtain the J values? Thank you in advance.

[sofiasanz]

Hi @lidonglin12, thank you for your interest. The way we calculate the approximate exchange value is by computing the difference between the total energy for the ferromagnetic case and the antiferromagnetic case. This is, by simulating the approximate triplet by fixing the number of up electrons (NUP) to NUP = NDN+2 (being NDN the number of down electrons). While the antiferromagnetic case (approximate singlet), similarly, is found by fixing NUP=NDN. This is of course assuming the system has an even number of electrons. The charge of each spin channel can be accessed through the attribute q which is a tuple where the first index correspond to NUP and the second one to NDN.

If you want to see an example, you can take a look at this script (examples/molecules/kondo-paper/fig_S15.py), which generates the figure S15 of the supplemental information of Ref. Nature Communications volume 10, Article number: 200 (2019). There we calculate the J value with respect to the Coulomb repulsion parameter U.

Please note that this script has been changed (I have changed it right now) due to a minor update that needed to be done. So please download the last version!

If you have any further questions please let me know.

[lidonglin12]

Thank you for your kind reply. I have another question. If I remove a hydrogen atom from a molecule, it will produce a radical. Then, if I use this script (examples/molecules/anthracenes/compute.py) to calculate the spin polarization of this molecule with radical, I could get the spin polarization of the molecule with the hydrogen removed, right?

[sofiasanz]

Beware of that kind of calculations since removing an hydrogen atom would mean that you also loose the sp2 configuration. Then the molecule would have a sigma dangling bond that would require further treatment to simulate it accurately.

Actually, although we do not include the hydrogen atoms in the Hamiltonian, we are assuming that the atoms at the edges are in fact saturated by hydrogen atoms. Otherwise the assumption of considering the carbon atoms at the edges equal (or almost equal) to those in the middle of the molecule would be completely wrong.

In fact, some tight-binding models make a differentiation between the carbon atoms at the edges and those in the middle of the molecule by, eg, considering different hopping elements or onsite energies. See for instance Phys. Rev. B 81, 245402.

The radicals can and do appear for a molecule that is saturated by hydrogen atoms. Anytime you get a spin-polarized molecule (open-shell configuration), means that the preferred configuration is to have radicals (unpaired electrons) over a closed-shell configuration (energetically speaking) for that particular Coulomb repulsion parameter. There is a nice discussion about the presence of the radicals in a carbon structure in Ref. Nature Communications volume 10, Article number: 200 (2019). In the supplemental information you can also find a nice explanation of the appearance of the radicals in more "chemical terms".

[sofiasanz]

Dear @lidonglin12 is there anything else you would like to discuss about this topic or can we close this issue?

[lidonglin12]

Thank you very much. We can close this issue.