That is right. While Hartree-Fock does have problems, electron self-interaction is not one of them. For example, Hartree-Fock is exact for the H_2^+ cation, unlike all real world density functionals.bsmile said:Thanks for the message. Does this mean the full Hartree-Fock does not have self-interaction error while local DFT has?
This self-interaction correction does indeed reduce a major part of the self-interaction error of KS (but not all of it--only a part of the 1e parts). The problem with this correction is two-fold: (1) It massively deteriorates the practical performance of DFT. For example, thermochemical results obtained with DFT protocols modified as such are even worse than HF's. (2) Whether the resulting method should still be called "DFT" is debatable. They claim it is a theory. I would call it a hack.Meanwhile, in the paper I cited above, it specifically mentioned " A thorough analysis in the framework of
DFT was performed by Perdew and Zunger [43], who suggested an explicit correction term that makes any XC-functional SIE-free.(...)
I do not quite get what they mean with this. The CS functional is indeed parameterized on correlation energies which are self-interaction free[1] (it is fitted to correlation energies of noble atoms). This also applies for LYP, which is maybe best described as a reparameterization of CS to make it easier to apply in actual calculations. However, this SIE-freeness of the correlation functional does not actually say much: First, it is highly debatable whether in strict DFT you can separate XC contributions into C and X contributions (and n-representability contributions, which are often omitted). This is often done for practical reasons, but there is no strict basis for this in theory---in theory there is only one XC functional. Second, one would always expect the dominant self-interaction error contribution to come from the X functional, not the C functional. So even if CS/LYP, which are pure C-functionals, would be strictly self-interaction free, this would not help at all, as you still need a X from somewhere. As a result, for example, BLYP has massive self-interaction errors---even if they come from B instead of LYP. (and if you add CS or LYP to Hartree-Fock, the results are bad again)(...)An alternative way of avoiding the SIE of approximate XC-functionals was suggested by Colle and Salvetti already in 1975 who used wave function theory (WFT) to develop the first SIE-free C-functional [23]. The Colle–Salvetti (CS) functional laid the basis for the work of Lee et al. to develop the LYP correlation functional, [9] which is also SIE-free." How to possibly understand that?
I was in the same boat :). The foundations of DFT can be very confusing, and they are often misrepresented. To be honest, I have since adopted the more practical approach of completely ignoring them and treating DFT as some kind of hacked up Hartree-Fock---which indeed is how it is used in practice in >99% of the cases, even if DFT evangelists would tell you otherwise.I know of Aron Cohen's work. I enter the DFT field quite recently. Too much information flushes to me which sometimes is quite confusing.
Self-interaction error occurs in DFT calculations when the electrons in a system interact with themselves, leading to inaccurate predictions of electronic properties. This is because DFT assumes that the electrons only interact with the average electron density, rather than with themselves directly.
No, self-interaction error is not easily detected in DFT calculations because it is a subtle error that can only be identified through careful analysis of the results. It is often only apparent when comparing DFT predictions with experimental data or more accurate theoretical methods.
There are various methods for correcting self-interaction error in DFT calculations. These include the use of hybrid functionals that incorporate a fraction of exact exchange, as well as the use of self-interaction correction (SIC) methods that explicitly remove the self-interaction term from the DFT calculations.
Yes, there can be drawbacks to correcting self-interaction error in DFT calculations. The most significant drawback is that it can significantly increase the computational cost of the calculations, as more accurate methods tend to be more computationally demanding. Additionally, some methods may not be applicable to certain systems or may introduce other sources of error.
The best method for correcting self-interaction error in DFT calculations can vary depending on the system and the desired level of accuracy. It is important to carefully consider the strengths and limitations of each method and select the one that is most suitable for the specific problem at hand. Consulting with experts in the field and conducting benchmark calculations can also aid in choosing the best method.