Double Counting Correction in LDA+U: AMF vs. FLL

In summary, the conversation is about the correction of the one electron self-interaction in LDA+U calculation, specifically through subtracting the double counting from the DFT functional. The two main possibilities for this correction are Around Mean Field (AMF) and Fully Localized Limit (FLL). The speaker is looking for a correction term for AMF, as there is one for FLL due to non-collinearity. They have searched for information on this topic but have not found anything. They also mention a paper that discusses the correction in terms of density matrices but have not been able to get the correct result.
  • #1
PascalM
2
0
Hi there,

I'm not sure if someone here can help me because the topic is quite specific.
In LDA+U Calculation one have to substract the Double Counting from the DFT functional. There are two main possibilities to do this:
1.) Around Mean Field (AMF)
2.) Fully Localized Limit (FLL)

I found out, that there's a correction term to FLL due to non-collinearity and I ask myself if there's a correction term to AMF aswell. I searched in books, papers and the internet but didn't find anything about this topic.

Maybe someone can help me.

Thanks for your help!
 
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  • #2
PascalM said:
to substract the Double Counting from the DFT functional.

When you say subtract double counting, do you mean correcting the one electron self-interaction?
 
  • #3
Hi,

yes i mean the correction of the one electron self-interaction. Sorry for that mad formulation!
I found a paper (Physical Review B 67, 153106 (2003)) where the author wrote down the correction in terms of density matrices. But if I try to evaluate these formula for FLL DC (where I know the exact result, i.e. given in http://ftp.abinit.org/ws11/bousquet.pdf), I do not get the right double-counting correction.

I will go on working on this problem today.
 

What is double counting correction in LDA+U?

Double counting correction in LDA+U is a method used in density functional theory calculations to account for the interactions between electrons in a system. This correction is necessary because the LDA+U method uses an effective on-site Coulomb interaction (U) to describe electron-electron interactions in a localized manner, while the exchange-correlation energy is described by the local density approximation (LDA). Without double counting correction, the total energy of the system would be overestimated.

What is the difference between AMF and FLL in double counting correction?

AMF (around mean field) and FLL (fully localized limit) are two different approaches for implementing double counting correction in LDA+U. In the AMF method, the U value is calculated self-consistently for each atomic site, while in the FLL method, a fixed U value is used for all atomic sites. The FLL method is more computationally efficient but may not accurately capture the electronic structure of the system.

Which method is more accurate: AMF or FLL?

The accuracy of AMF and FLL in double counting correction depends on the system being studied. In general, AMF is considered to be more accurate as it takes into account the variations in U values at different atomic sites. However, for some systems, FLL may provide reasonable accuracy while being more computationally efficient.

How do I choose between AMF and FLL for my calculations?

The choice between AMF and FLL depends on the specific system being studied. It is recommended to perform calculations using both methods and compare the results to determine which method is more appropriate for the system. Additionally, the choice may also depend on the available computational resources and the desired level of accuracy.

Are there any other methods for double counting correction in LDA+U?

Yes, there are other methods for double counting correction in LDA+U, such as the linear response (LR) method and the around mean field rotation (AMFR) method. These methods may provide different levels of accuracy and efficiency compared to AMF and FLL, and their suitability depends on the system being studied.

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