Calculation of U for an alloy (DFT+U)

[rishikanta_m]

Hi

For an elemental compound A, I have calculated the U parameter using the linear response ansatz of Cococcioni et al.
wiki/index.php/Calculate_U_for_LSDA%2BU. The bandgap was quite okay.

Now, I am interested in a binary alloy AxB(1-x). So, I would like to calculate the "U" parameter for the B element.
First, I fix the U parameter for A and perform the same procedure of linear response to calculate "U" for B.
Second, I set the U parameter for A to 0, and perform the same procedure for B.
But the results from both the results are not satisfactory.
Is there anything wrong with these procedures?

[fabien_tran1]

Hi,

What do you exactly mean by "not satisfactory"? Not in agreement with experiment? Can you explain more precisely what you expected from the calculations. Don't forget that since DFT is an approximate method it may or may not give good agreement with the supposedly correct results.

[rishikanta_m]

Yes, the bandgap value of the alloy is underestimated by more than 10 times.

I am very actually more interested in knowing whether the two different procedures are reasonable or not.
Thanks

[fabien_tran1]

According to the description of the method on the wiki, the value of U has to be obtained from a calculation on the system under consideration (AxB(1-x) with a chosen value of x). However, from your explanations (if I understood them correctly) it seems that you used elemental A to calculate U on A. I think that you should calculate A by considering AxB(1-x) and not elemental A (in the example on the wiki the U for Ni is calculated by considering NiO and not elemental Ni).

Besides, what are the values of U on A and B that you obtained?

[rishikanta_m]

I got Ueff for A as -2.72 (A is cubic Germanium structure).

After fixing Ueff as A to -2.72, I obtained Ueff for B as -0.2014 for AxB(1-x)
After fixing Ueff as A to 0, I obtained Ueff value for B as -0.1984 (AxB(1-x))

I got some points of clarification from your explanation, that I need to calculate U for A on the AxB(1-x) system for a fixed 'x' value.
However, does that mean that U for A will change for different 'x' values?
Another thing is how to calculate U for B.

[fabien_tran1]

I got Ueff for A as -2.72 (A is cubic Germanium structure).

After fixing Ueff as A to -2.72, I obtained Ueff for B as -0.2014 for AxB(1-x)
After fixing Ueff as A to 0, I obtained Ueff value for B as -0.1984 (AxB(1-x))

Does that mean that the obtained values of Ueff are negative? If yes then it should be unphysical.

However, does that mean that U for A will change for different 'x' values?

In principle yes.

Another thing is how to calculate U for B.

The same way as for A of course.

Besides:

• Have you tried the example of NiO from the wiki and obtained the expected result for U? If not, then I suggest that you do it.

• What type of atoms are A and B in your system AxB(1-x)? Are these transition-metal atoms? According to the literature, would it make sense to apply U in this case?

[rishikanta_m]

Hi

I would like to use "U" value in thin film calculations, especially band gap estimation. This film is a 7-layer slab: a total of 84 atoms.
Can I use a U value calculated from a 2x2x2 supercell (bulk) of the same material for the calculation of the band gap of the thin film?

[rishikanta_m]

Also, can I apply U values of s and p orbitals for same atom in INCAR?
If so, please let me know how to include tags in INCAR.

[fabien_tran1]

I would like to use "U" value in thin film calculations, especially band gap estimation. This film is a 7-layer slab: a total of 84 atoms.
Can I use a U value calculated from a 2x2x2 supercell (bulk) of the same material for the calculation of the band gap of the thin film?

Yes, this is a pragmatic way that would make sense.

Also, can I apply U values of s and p orbitals for same atom in INCAR?
If so, please let me know how to include tags in INCAR.

No. Only one angular momentum per atom can be specified. Concerning applying U on s or p orbitals, it is usually not particularly recommended. The U method is applied only inside the atomic PAW sphere, while the s and p orbitals are usually quite delocalized so that they extend well outside the PAW spheres. Have you found indications in the literature that applying U on s or p orbitals in a system similar to yours is beneficial?

[rishikanta_m]

Thank you sir for the help.

Sakata et al. in the article (https://www.sciencedirect.com/science/a ... 5615006709) mentioned that Tahini et al. Ref. [27] of the article has used U values on s and p states. Interestingly, Tahini used VASP. so I was curious.