Most of the conventional DFT codes or software use LDA, GGA, meta-GGA, PBE, etc. exchange-correlation functionals, but I'm wondering if there is any DFT code or software that uses the new generation of exchange-correlation functionals called Exact Exchange-Correlation Potentials? Particularly, I recently came across the exact Hartree-Fock exchange energy functional and potential that neglects the correlation and defined as:
$$E_{X}[n] = -\frac{1}{2}\sum_{i,j} \int d^{3}\mathbf{r} d^{3}\mathbf{r}^{'} \frac{\phi^{*}_{i}(\mathbf{r})\phi_{j}^{*}(\mathbf{r}^{'})\phi_{j}(\mathbf{r})\phi_{i}(\mathbf{r}^{'})}{|\mathbf{r}-\mathbf{r}^{'}|}$$
$$v_{X}[n]=\frac{\delta E_{X}[n]}{\delta n(\mathbf{r})}$$
and I see that this exact exchange-energy functional is able to calculate magnetic moment of $\text{FeAl}$, $\text{Ni}_{3}\text{Ga}$, $\text{Ni}_{3}\text{Al}$ with much higher accuracy in comparison to FP-LDA for example described here. So my question is: Is thisAre these sort of exact exchange-correlation energy functionals are incorporated into open-source DFT codes and are they worth to useusing in comparison to conventional XC potentials due to the fact they seem to be more complicated and more difficult to implement? Also, when we say these are exact exchange-correlation energy functionalfunctionals, what do we mean by exact? The purpose is that there is no approximation here or something else?
