Workflow Cococcioni linear-response U

[jeffrey_zom]

From the tutorial on calculating U for NiO with response ansatz of Cococcioni et al., I understand the following procedure:

1) ionic relaxation NiO unit cell U_in=0, LDAUTYPE = 2
Use CONTCAR
Specify MAGMOM
2) SCF groundstate calculation of unit cell U_in=0, LDAUTYPE = 2
Use CHGCAR
3) for alpha in [-0.20 ... +0.20] (small pertubations):
SCF (ICHARGE=2) calculation U=J=alpha , LDAUTYPE = 3
NSCF (ICHARGE=11) calculation U=J=alpha , LDAUTYPE = 3
4) calculate U_out from derivates of occupation with respect to alpha.

This leaves me with some questions however:

1) If the MAGMOM is unknown, can the default be used?
2) For step 2, is WAVECAR also required?
2) To calculate U, does step 1 through 4 have to be repeated until U is self-consistent? The ionic structure is different when DFT+U is applied. So I imagine step 1 through 4 is repeated until U_in = U_out
3) If step 1 through 4 is repeated, for step 2, do you use the calculated U value?
4) if step 1 through 4 is repeated, for step 3, do you apply pertubations around the calculated U value?
U=J= [-0.20+U ... +0.20+U]

Lastly, I think there are some typos in the wiki concerning the values for the number of d-electrons, every value in the tabel for d of Ni starts with 8, like 8.488, while in the calculations shown the same floats are used but starting with 4 (4.488 instead of 8.488). The difference is the exact same, such that the result of the equation is correct, but it is quite confusing when reading it for the first time where the tabulated 4.488, 4.438, etc. come from.

Kind regards,

Jeffrey

[marie-therese.huebsch]

Hi Jeffrey,

Very good point. Regarding the MAGMOM setting, I strongly advice against the default MAGMOM. It corresponds to the ferromagnetic (FM) initial guess. Even disabling symmetry with ISYM=-1, the electronic minimization will have a hard time to converge to the magnetic ground state if the magnetic order is far away from FM. Do you have any experimental evidence whether the material has a finite total magnetization? Do you know if the magnetic and the crystal unit cell is the same? Often there are certain probable magnetic configurations. They arise from the symmetry of the system. You can then try to start from different MAGMOM and see which yields the lowest total energy.

Fir the workflow of the linear-response U, I unfortunately have no experience, but I will look into it and let you know my finding. I will also ask around if any of the team members has experience with it. I agree that the tutorial needs to be polished.

Best regards,
Marie-Therese

[marie-therese.huebsch]

Okay, here are some more comments:

Regarding the ionic relaxation, yes you are absolutely rigth that the U value changes the value for the relaxed lattice constant. So including the relaxation as a first step is a good idea. See also this related discussion for NiO https://vasp.at/wiki/Choosing_pseudopot ... ium_volume.

Regarding the question if the workflow needs to be iterated until self-consistency is reached. It was originally proposed as a sigle shot method but in recent publications it seems most use an scf linear response U. These are two different scientific approaches that you can select amongst. To add a layer of complexity, there is consrtained random phase approximation (https://vasp.at/wiki/CRPA_of_SrVO3) that one can use to approximate U.

If one chooses to iterate U, the workflow would be:

• Cycle 1: pure DFT ground state → compute U1
• Cycle 2: DFT+U1 ground state (with LDAUTYPE=2, LDAUU=U1) → compute U2 from linear response perturbations of this new ground state
• Continue until U converges.

So yes, in subsequent cycles the ground state would include the previously computed U.

Does this answer your question?

Best regards,
Marie-Therese

[jeffrey_zom]

Hi Marie,

Thank you for looking into this!

It was originally proposed as a sigle shot method but in recent publications it seems most use an scf linear response U. These are two different scientific approaches that you can select amongst.

Ah okay, I believe the single shot parameter is often referred to as "self consistent U", despite that the U parameter is not iteratively updated in that case to show self consistency, which is quite confusing. I assume that the iteratively updated U would give a better result (closer to experiment), similar to G0W0 vs GW0. I haven't been able to find a publication that confirms this however, although a quite recent publication from 2024 does mention this sentiment [10.1103/PhysRevLett.97.103001]: "While in the original derivation U was calculated from the GGA groundstate, we argue here that U should be consistently obtained from the GGA+U ground state itself.". In my own testing on different systems I have consistently found that the self consistent U is often significantly (a few 10%) larger than the single shot U.

Do you have any experimental evidence whether the material has a finite total magnetization? Do you know if the magnetic and the crystal unit cell is the same?

Unfortunately I don't. I would like to use DFT+U to predict polaron formation in novel materials, and I am not interested in the magnetic properties. Nevertheless, I can imagine that the magnetic configuration influences the calculated U parameter to a certain extent, as well as the polaron stability. Without experimental work, I would then need to find a way to find the lowest energy MAGMOM configuration ab. initio., which I am sure is possible but would require quite some computational work. Calculating the energy of the systems as function of the initial MAGMOM input parameter works to a certain extent for small systems, but for larger unit cells, there are many configurations possible. It might also be the case that the unit cell chosen can not describe the magnetic system accurately, like can be the case for NiO.

Thank you again for answering my questions,

Kind regards,

Jeffrey