saving work in Sec IV

Manuscript/rsdft-cipsi-qmc.tex

@@ -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 density-functional theory (DFT). \cite{Hohenberg_1964,Kohn_1999} 
 Present-day DFT calculations are almost exclusively done within the so-called Kohn-Sham (KS) formalism, \cite{Kohn_1965} which
-transfers the complexity of the many-body problem to the \manu{universal and yet unknown} exchange-correlation (xc) functional thanks to a judicious mapping between a non-interacting reference system and its interacting analog which both have exactly the same one-electron density.
+transfers the complexity of the many-body problem to the universal and yet unknown exchange-correlation (xc) functional thanks to a judicious mapping between a non-interacting reference system and its interacting analog which both have exactly the same one-electron density.
 KS-DFT \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{FraMusLupTou-JCP-15,Loos_2019d,Giner_2020}
-\manu{However, unlike WFT where many-body 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 many-body 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 KS-DFT, one solves a mean-field problem 
+As mentioned above, within KS-DFT, one solves a mean-field 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
-electron-electron interactions are considered.}
+electron-electron interaction is explicitly considered.
 Nevertheless, as the orbitals are one-electron functions,
 the procedure of orbital optimization in the presence of a
 Jastrow factor can be interpreted as a self-consistent 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 long-range interaction vanishes}, \ie,
+Note that for $\mu=0$ the long-range interaction vanishes, \ie,
 $w_{\text{ee}}^{\text{lr},\mu=0}(r) = 0$, and thus RS-DFT reduces to standard
 KS-DFT and $\Psi^\mu$ is the KS determinant. For $\mu = \infty$, the long-range
 interaction becomes the standard Coulomb interaction, \ie,