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@ 118,10 +118,10 @@ to a loss of size consistency. \cite{Evangelisti_1983,Cleland_2010,Tenno_2017}




Another route to solve the Schr\"odinger equation is densityfunctional theory (DFT). \cite{Hohenberg_1964,Kohn_1999}


Presentday DFT calculations are almost exclusively done within the socalled KohnSham (KS) formalism, \cite{Kohn_1965} which


transfers the complexity of the manybody problem to the exchangecorrelation (xc) functional thanks to a judicious mapping between a noninteracting reference system and its interacting analog which both have exactly the same oneelectron density.


transfers the complexity of the manybody problem to the \manu{universal and yet unknown} exchangecorrelation (xc) functional thanks to a judicious mapping between a noninteracting reference system and its interacting analog which both have exactly the same oneelectron density.


KSDFT \cite{Hohenberg_1964,Kohn_1965} is now the workhorse of electronic structure calculations for atoms, molecules and solids thanks to its very favorable accuracy/cost ratio. \cite{ParrBook}


As compared to WFT, DFT has the indisputable advantage of converging much faster with respect to the size of the basis set. \cite{FraMusLupTouJCP15,Loos_2019d,Giner_2020}


\titou{However, there is no systematic way of refining the approximation of the unknown exact xc functional.}


\manu{However, unlike WFT where manybody perturbation theory provides a precious tool to go toward the exact wave function, there is no systematic way to improve the approximated xc functionals toward the exact functional.}


Therefore, one faces, in practice, the unsettling choice of the \emph{approximate} xc functional. \cite{Becke_2014}


Moreover, because of the approximate nature of the xc functional, although the resolution of the KS equations is variational, the resulting KS energy does not have such property.




@ 202,8 +202,9 @@ orbitals.\cite{Filippi_2000,Scemama_2006,HaghighiMood_2017,Ludovicy_2019}




The description of electron correlation within DFT is very different


from correlated methods such as FCI or CC.


\titou{As mentioned above, within KSDFT, one solves a meanfield problem with a modified potential


incorporating the effects of electron correlation, whereas in


\manu{As mentioned above, within KSDFT, one solves a meanfield problem


with a modified potential incorporating the effects of electron correlation


while maintaining the exact ground state density, whereas in


correlated methods the real Hamiltonian is used and the


electronelectron interactions are considered.}


Nevertheless, as the orbitals are oneelectron functions,


@ 363,7 +364,7 @@ energy is obtained as


E_0= \mel{\Psi^{\mu}}{\hat{T}+\hat{W}_\text{{ee}}^{\text{lr},\mu}+\hat{V}_{\text{ne}}}{\Psi^{\mu}}+\bar{E}^{\text{sr},\mu}_{\text{Hxc}}[n_{\Psi^\mu}].


\end{equation}




\titou{Note that for $\mu=0$ the longrange interaction vanishes}, \ie,


\manu{Pour moi y'a pas de problèmes avec cette phrase. Note that for $\mu=0$ the longrange interaction vanishes}, \ie,


$w_{\text{ee}}^{\text{lr},\mu=0}(r) = 0$, and thus RSDFT reduces to standard


KSDFT and $\Psi^\mu$ is the KS determinant. For $\mu = \infty$, the longrange


interaction becomes the standard Coulomb interaction, \ie,



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