# What correlation effects are included in DFT?

In wavefunction methods the accuracy of the description of a system of electrons can be improved systematically starting from a reference, usually a Hartree-Fock wavefunction. This difference between the HF energy and the true non-relativistic energy is called (Coulomb) correlation energy and, as far as I know, it can be divided in, at least, two types: static correlation and dynamic correlation.

Dynamic correlation can be described by perturbative methods or Coupled Cluster theory, while static correlation needs multi-reference descriptions. Although the definition of dynamic and static correlation can be ambiguous, in some cases the effects of static correlation can be "separated" from dynamic effects and it becomes important to know what correlated method is needed.

In DFT, however, it seems that the amount of dynamic correlation, introduced by the exchange-correlation (XC) potential, is unspecified. Moreover, Kohn-Sham orbitals are constructed such that they reproduce the real electron density, which means that KS orbitals account some correlation effects. Also, the KS exchange energy is based only on a single determinant, thus, one can think that static effects are neglected. However, I'm not really sure about that sentence.

So, the question is, what correlation effects are included in DFT?

• A small comment: Kohn-Sham DFT is not based on a single determinant for the wavefunction, the wavefunction is a product state. Nov 16, 2020 at 11:52
• @PhilHasnip Could you expound a bit more on that comment? I was under the impression that they worked with a single slater determinant in practice Dec 24, 2020 at 0:17

By definition all of them, because Density Functional Theory is in principle exact.

Becke states:[1]

Density-functional theory (DFT) is a subtle, seductive, provocative business. Its basic premise, that all the intricate motions and pair correlations in a many-electron system are somehow contained in the total electron density alone, is so compelling it can drive one mad.
[...]
Let us introduce the acronym DFA at this point for “density-functional approximation.” If you attend DFT meetings, you will know that Mel Levy often needs to remind us that DFT is exact. The failures we report at meetings and in papers are not failures of DFT, but failures of DFAs.

DFT does model the exact electron density, hence all electron correlation. The problem becomes which of part of correlation is treated by the particular DFA, and how. Given the large number of approaches and parameterisations, this is probably too much to handle on this platform.[2]

As you also state that the definition of dynamic and static correlation can be ambiguous, it is at first only really meaningful for wave-function based approaches. As you separate the electron density differently in DFA, you have even more ambiguity.

You can see that in real life, when you calculate 'strongly-correlated' systems with DFT, and surprisingly they manage quite well, where wave-function based methods completely fail.
Another point in favour of this is the broken symmetry approach often taken, see for example in the popular Orca input library: broken symmetry DFT.

### References:

1. Becke, A. D. Perspective: Fifty years of density-functional theory in chemical physics. J. Chem. Phys. 2014, 140 (18), 18A301. DOI: 10.1063/1.4869598.

2. I have written a bit more about functionals, their shortcomings and advantages, etc. at Chemistry.se: DFT Functional Selection Criteria.

• If one considers only the DFT in LDA, what's the correlation effect included in that?
– Jack
Jan 23, 2021 at 0:15
• @Jack In the sense of this anser: LDA is not DFT. Everything that is not currently covered in the little text is probably worthwhile a separate answer. I'm certain this cannot be elucidated in a comment. Jan 23, 2021 at 0:29