saving work in Sec IV
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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 \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.


transfers the complexity of the manybody problem to the 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}


\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.}


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 approximate 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.




@ 194,11 +194,11 @@ 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.


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


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.}


electronelectron interaction is explicitly considered.


Nevertheless, as the orbitals are oneelectron functions,


the procedure of orbital optimization in the presence of a


Jastrow factor can be interpreted as a selfconsistent field procedure


@ 356,7 +356,7 @@ 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}




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


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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