modification in abstract and conclusion

Manuscript/rsdft-cipsi-qmc.tex

@@ -71,11 +71,11 @@
 
 \begin{abstract}
 By combining density-functional theory (DFT) and wave function theory (WFT) via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions.
-These compact trial wave functions are generated via the diagonalization of the RS-DFT Hamiltonian.
-In particular, we combine here short-range correlation functionals with selected configuration interaction (SCI).
-As the WFT method is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional SCI calculation.
-Having low energies does not mean that they are good for chemical properties.
-\titou{T2: work in progress.}
+In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction (SCI) known as \emph{configuration interaction using a perturbative selection made iteratively} (CIPSI), a scheme that we label RS-DFT-CIPSI.
+One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansion than CIPSI.
+Indeed, as the CIPSI method is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation.
+Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects.  
+Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of $\mu=0.5$~bohr$^{-1}$ provides an effective cancellation of errors as well as compact trial wave functions, making the present method a good candidate for the accurate description of large systems.
 \end{abstract}
 
 \maketitle
@@ -547,7 +547,7 @@ Accordingly, all the RS-DFT calculations are performed with the srPBE functional
 
 Another important aspect here is the compactness of the trial wave functions $\Psi^\mu$:
 at $\mu=1.75$~bohr$^{-1}$, $\Psi^{\mu}$ has \textit{only} $54\,540$ determinants at the srPBE/VDZ-BFD level, while the FCI wave function contains $200\,521$ determinants (see Table \ref{tab:h2o-dmc}). Even at the srPBE/VTZ-BFD level, we observe a reduction by a factor two in the number of determinants between the optimal $\mu$ value and $\mu = \infty$.
-The take-home message of this first numerical study is that RS-DFT trial wave functions can yield a lower fixed-node energy with more compact multi-determinant expansion as compared to FCI.
+The take-home message of this first numerical study is that RS-DFT-CIPSI trial wave functions can yield a lower fixed-node energy with more compact multi-determinant expansion as compared to FCI.
 This is a key result of the present study.
 
 %======================================================
@@ -654,7 +654,7 @@ Also, it is interesting to notice that the FN-DMC energy of $\Psi^J$ is compatib
 with that of $\Psi^\mu$ for $0.5 < \mu < 1$~bohr$^{-1}$, as shown by the overlap between the red and blue bands.
 This confirms that introducing short-range correlation with DFT has
 an impact on the CI coefficients similar to a Jastrow factor.
-This is yet another key result of the present study.
+This is another key result of the present study.
 
 %%% FIG 4 %%%
 \begin{figure*}
@@ -728,6 +728,7 @@ produce a reasonable one-body density.
 
 %============================
 \subsection{Intermediate conclusions}
+\label{sec:int_ccl}
 %============================
 
 As conclusions of the first part of this study, we can highlight the following observations:
@@ -912,7 +913,7 @@ are even lower than those obtained with the optimal value of
 $\mu$. Although the FN-DMC energies are higher, the numbers show that
 they are more consistent from one system to another, giving improved
 cancellations of errors.
-This is another key result of the present study, and it can be explained by the lack of size-consistency when one considers different $\mu$ values for the molecule and the isolated atoms.
+This is yet another key result of the present study, and it can be explained by the lack of size-consistency when one considers different $\mu$ values for the molecule and the isolated atoms.
 This observation was also mentioned in the context of optimally-tune range-separated hybrids. \cite{Stein_2009,Karolewski_2013,Kronik_2012}
 
 %%% FIG 6 %%%
@@ -965,7 +966,8 @@ on the determinant expansion is similar to the effect of re-optimizing
 the CI coefficients in the presence of a Jastrow factor, but without
 the burden of performing a stochastic optimization.
 
-Varying the range-separation parameter $\mu$ and approaching the
+In addition to the intermediate conclusions drawn in Sec.~\ref{sec:int_ccl}, 
+we can affirm that varying the range-separation parameter $\mu$ and approaching
 RS-DFT-FCI with CIPSI provides a way to adapt the number of
 determinants in the trial wave function, leading always to
 size-consistent FN-DMC energies.
@@ -975,7 +977,7 @@ energy via the variation of the parameter $\mu$.
 The second method is for the computation of energy differences, where
 the target is not the lowest possible FN-DMC energies but the best
 possible cancellation of errors. Using a fixed value of $\mu$
-increases the consistency of the trial wave functions, and we have found
+increases the (size-)consistency of the trial wave functions, and we have found
 that $\mu=0.5$~bohr$^{-1}$ is the value where the cancellation of
 errors is the most effective.
 Moreover, such a small value of $\mu$ gives extremely