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20 votes
Accepted

Can DFT be 'exact' in the limit of the uniform electron gas?

Let us represent the exact exchange-correlation (xc) energy as a sum of an exchange term (x) and a correlation term (c): $$ \tag{1} E_{xc} = E_x + E_c~ . $$ For a uniform electron gas (UEG), we do ...
Nike Dattani - No Free Time's user avatar
15 votes

Hartree-Fock density vs Kohn-Sham density

Kieron Burke and co-workers have shown that in many cases one can get better results by using the HF density as input to a DFT-XC evaluation of the energy, as opposed to using the DFT-XC to generate a ...
Frank Jensen's user avatar
  • 1,806
8 votes

Hartree-Fock density vs Kohn-Sham density

I guess this will go in the answer slot, it is a bit long for a comment. DFT typically has quite a bit less spin contamination than HF (attributed to the inclusion of correlation). One issue however ...
B. Kelly's user avatar
  • 4,376
5 votes
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Self-interaction in density functional approximations for many-electron systems

No self-interaction in the exact functional The electronic structure Hamiltonian in real space is $$\tag{1} H = T + V_{ee} + V_{\text{ext}} = -\frac12 \sum_i \nabla_i^2 + \sum_{i<j} \frac{1}{\lvert ...
elutionary's user avatar
  • 1,006
5 votes
Accepted

What's the physics contained in the exchange-correlation functional in the framework of KS-DFT?

You have already detailed what the physics contained in the exchange-correlation functional is. Self-interaction error is not physical; it is an artifact in density functional approximations that ...
Susi Lehtola's user avatar
  • 19.7k
4 votes

Self-interaction in density functional approximations for many-electron systems

The way I like to think about this is the Levy-Lieb functional. The universal functional takes the following form: $F[\rho] = \underset{\substack{\Psi \mapsto \rho(\vec{r}) \\ \rho \in \mathcal{D}}}{...
lex2763's user avatar
  • 391
4 votes

Is there a relation between self-interaction errors and integer-discontinuities in Kohn-Sham-DFT?

Yes and no. The exact functional should have a piecewise linear behavior in the number of electrons Phys. Rev. Lett. 49, 1691 (1982), but this is not true for common density functional approximations,...
Susi Lehtola's user avatar
  • 19.7k

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