saving work in Sec II

Manuscript/rsdft-cipsi-qmc.tex

@@ -269,35 +269,31 @@ Beyond the single-determinant representation, the best
 multi-determinant wave function one can wish for --- in a given basis set --- is the FCI wave function.
 FCI is the ultimate goal of post-HF methods, and there exists several systematic
 improvements on the path from HF to FCI:
-increasing the maximum degree of excitation of CI methods (CISD, CISDT,
-CISDTQ, \ldots), or increasing the complete active space
-(CAS) wave functions until all the orbitals are in the active space.
+i) increasing the maximum degree of excitation of CI methods (CISD, CISDT,
+CISDTQ, \ldots), or ii) expanding the size of a complete active space
+(CAS) wave function until all the orbitals are in the active space.
 Selected CI methods take a shortcut between the HF
 determinant and the FCI wave function by increasing iteratively the
 number of determinants on which the wave function is expanded,
 selecting the determinants which are expected to contribute the most
-to the FCI eigenvector. At every iteration, the lowest eigenpair is
+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 computing a second-order
-perturbative correction (PT2) to the variational energy, $\EPT$.
+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 exact eigenvalue, and is an adjustable
-parameter controlling the quality of the wave function.
-Within the \emph{Configuration interaction using a perturbative
-selection made iteratively} (CIPSI)\cite{Huron_1973} method, the PT2
+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.
+algorithm.}
 
-Considering that the perturbatively corrected energy is a reliable
+\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{}.
-
-
+1$ m\hartree{}.}
 
 %=================================
 \subsection{Range-separated DFT}