first iteration of Sec II done

Manuscript/rsdft-cipsi-qmc.tex

@@ -121,8 +121,8 @@ Present-day DFT calculations are almost exclusively done within the so-called Ko
 transfers the complexity of the many-body problem to the 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}
-However, there is no systematic way of refining the approximation of the unknown exact xc functional, and therefore in practice 
-one faces the unsettling choice of the \emph{approximate} xc functional. \cite{Becke_2014}
+\titou{However, there is no systematic way of refining the approximation of the unknown exact xc functional, and therefore in practice 
+one faces 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.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -280,20 +280,11 @@ to the FCI wave function. At each iteration, the lowest eigenpair is
 extracted from the CI matrix expressed in the determinant subspace,
 and the FCI energy can be estimated by adding up to the variational energy 
 a second-order perturbative correction (PT2), $\EPT$.
-The magnitude of $\EPT$ is a
-measure of the distance to the FCI energy and a diagnostic of the the quality of the wave function.
-\titou{Within the CIPSI algorithm originally developed by Huron \textit{et al.} in Ref.~\onlinecite{Huron_1973} and efficiently implemented as described in Ref.~\onlinecite{Garniron_2019}, the PT2
-correction is computed along with the determinant selection. So the
-magnitude of $\EPT$ can be made the only parameter of the algorithm,
-and we choose this parameter as the convergence criterion of the CIPSI
-algorithm.}
-
-\titou{Considering that the perturbatively corrected energy is a reliable
-estimate of the FCI energy, using a fixed value of the PT2 correction
-as a stopping criterion enforces a constant distance of all the
-calculations to the FCI energy. In this work, we target the chemical
-accuracy so all the CIPSI selections were made such that $\abs{\EPT} <
-1$ m\hartree{}.}
+The magnitude of $\EPT$ is a measure of the distance to the FCI energy 
+and a diagnostic of the the quality of the wave function.
+Within the CIPSI algorithm originally developed by Huron \textit{et al.} in Ref.~\onlinecite{Huron_1973} and efficiently implemented as described in Ref.~\onlinecite{Garniron_2019}, the PT2
+correction is computed simultaneously to the determinant selection at no extra cost. 
+$\EPT$ is then the sole parameter of the CIPSI algorithm and is chosen to be its convergence criterion.
 
 %=================================
 \subsection{Range-separated DFT}
@@ -444,7 +435,8 @@ of the local-density approximation (LDA)\cite{Sav-INC-96a,TouSavFla-IJQC-04} and
 and correlation functionals defined in
 Ref.~\onlinecite{GolWerStoLeiGorSav-CP-06} (see also
 Refs.~\onlinecite{TouColSav-JCP-05,GolWerSto-PCCP-05}).
-The convergence criterion for stopping the CIPSI calculations
+In this work, we target chemical accuracy, so 
+the convergence criterion for stopping the CIPSI calculations
 has been set to $\EPT < 10^{-3}$ \hartree{} or $ \Ndet > 10^7$.
 All the wave functions are eigenfunctions of the $\Hat{S}^2$ spin operator, as
 described in Ref.~\onlinecite{Applencourt_2018}.