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

This question is inspired by this post. In the Kohn-Sham framework of density functional theory, the total energy is expressed as: $$E=E_{kin}^{non}+E_{ext}+E_{H}+E_{xc}$$ in which

• The first term is the kinetic energy of the non-interacting system: $$E^{non}_{kin}=-\dfrac{1}{2}\sum_i^{n}\phi_i^*(\vec{r})\nabla^2\phi_i(\vec{r})$$

• The second term is the external energy: $$E_{ext}=\int\phi^*(\vec{r})U_{ext}(\vec{r})\phi(\vec{r}) d\vec{r}=\int U_{ext}(\vec{r})\rho(\vec{r})d\vec{r}$$

• The third term is the Hartree energy: $$E_H=\dfrac{1}{2}\int \int \dfrac{\rho(\vec{r})\rho(\vec{r}')}{|\vec{r}-\vec{r}'|}d\vec{r}d\vec{r}'$$

• The last term is the exchange-correlation term needs to be approximated, such as LDA, which includes:

• Exchange energy;
• Correlation energy;
• The kinetic energy difference between the interacting system and the non-interacting system;
• The self-interaction error in the Hartree energy.

In this post, Phil Hasnip has claimed that including a Hubbard U potential within a Kohn-Sham density functional theory (DFT) calculation is to study a material for which you expect a significant self-interaction error.

So is there any other interesting physics contained in the exchange-correlation functional in the framework of KS-DFT?