changes in intro

Manuscript/srDFT_SC.bbl

@@ -6,7 +6,7 @@
 %Control: page (0) single
 %Control: year (1) truncated
 %Control: production of eprint (0) enabled
-\begin{thebibliography}{57}%
+\begin{thebibliography}{60}%
 \makeatletter
 \providecommand \@ifxundefined [1]{%
  \@ifx{#1\undefined}
@@ -50,6 +50,26 @@
 \providecommand \BibitemShut  [1]{\csname bibitem#1\endcsname}%
 \let\auto@bib@innerbib\@empty
 %</preamble>
+\bibitem [{\citenamefont {Pople}(1999)}]{Pop-RMP-99}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {J.~A.}\ \bibnamefont
+  {Pople}},\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Rev.
+  Mod. Phys.}\ }\textbf {\bibinfo {volume} {{71}}},\ \bibinfo {pages} {1267}
+  (\bibinfo {year} {1999})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Kohn}(1999)}]{Koh-RMP-99}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
+  {Kohn}},\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Rev.
+  Mod. Phys.}\ }\textbf {\bibinfo {volume} {{71}}},\ \bibinfo {pages} {1253}
+  (\bibinfo {year} {1999})}\BibitemShut {NoStop}%
+\bibitem [{\citenamefont {Kohn}\ and\ \citenamefont
+  {Sham}(1965)}]{KohSha-PR-65}%
+  \BibitemOpen
+  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
+  {Kohn}}\ and\ \bibinfo {author} {\bibfnamefont {L.~J.}\ \bibnamefont
+  {Sham}},\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Phys.
+  Rev.}\ }\textbf {\bibinfo {volume} {140}},\ \bibinfo {pages} {A1133}
+  (\bibinfo {year} {1965})}\BibitemShut {NoStop}%
 \bibitem [{\citenamefont {Hylleraas}(1929)}]{Hyl-ZP-29}%
   \BibitemOpen
   \bibfield  {author} {\bibinfo {author} {\bibfnamefont {E.~A.}\ \bibnamefont

Manuscript/srDFT_SC.tex

@@ -289,23 +289,9 @@ In the general context of multiconfigurational DFT, this finding shows that one
 %%%%%%%%%%%%%%%%%%%%%%%%
 \section{Introduction}
 %%%%%%%%%%%%%%%%%%%%%%%%
-The general goal of quantum chemistry is to provide reliable theoretical tools to explore the rich area of chemistry. More specifically, developments in quantum chemistry primarily aim at accurately computing the electronic structure of molecular systems, but despite intense developments, no definitive solution to this problem has been found. The theoretical challenge to tackle belongs to the quantum many-body problem, due the intrinsic quantum nature of the electrons and the Coulomb repulsion between them. This so-called electronic correlation problem corresponds to finding a solution to the Schr\"odinger equation for a $N$-electron system, and two main roads have emerged to approximate this solution: wave-function theory (WFT) and density-functional theory (DFT). 
+The general goal of quantum chemistry is to provide reliable theoretical tools to explore the rich area of chemistry. More specifically, developments in quantum chemistry primarily aim at accurately computing the electronic structure of molecular systems, but despite intense developments, no definitive solution to this problem has been found. The theoretical challenge to tackle belongs to the quantum many-body problem, due the intrinsic quantum nature of the electrons and the Coulomb repulsion between them. This so-called electronic correlation problem corresponds to finding a solution to the Schr\"odinger equation for a $N$-electron system, and two main roads have emerged to approximate this solution: wave-function theory (WFT)~\cite{Pop-RMP-99} and density-functional theory (DFT)~\cite{Koh-RMP-99}. Although both WFT and DFT spring from the same Schr\"odinger equation, they rely on very different formalisms, as the former deals with the complicated $N$-electron wave function whereas the latter focuses on the much simpler one-electron density. In its Kohn-Sham (KS) formulation~\cite{KohSha-PR-65}, the computational cost of DFT is very appealing since it is a simple mean-field procedure. Therefore, although continued efforts have been done to reduce the computational cost of WFT, DFT still remains the workhorse of quantum chemistry. 
-Although both WFT and DFT spring from the same equation, their formalisms are very different as the former deals with the complex 
-$N$~-~body wave function whereas the latter handles the much simpler one~-~body density. 
-In its Kohn-Sham (KS) formulation, the computational cost of DFT is very appealing as it can be recast in a mean-field procedure. 
-Therefore, although constant efforts are performed to reduce the computational cost of WFT, DFT remains still the workhorse of quantum chemistry. 
 
-The complexity of a reliable theoretical description of a given chemical system can be roughly 
+The difficulty of obtaining a reliable theoretical description of a given chemical system can be roughly categorized by the strength of the electronic correlation appearing in its electronic structure. The so-called weakly correlated systems, such as closed-shell organic molecules near their equilibrium geometries, are typically dominated by correlation effects which do not affect the qualitative mean-field picture of the system. These weak correlation effects can be either short range(near the electron-electron coalescence point) or long range (London dispersion interactions). The theoretical description of weakly correlated systems is one of the most concrete achievement of quantum chemistry, and the main remaining issue for these systems is to push the limit of the size of the chemical systems that can be treated.  The case of the so-called strongly correlated systems, which are ubiquitous in chemistry, is much more problematic as they exhibit a much more complex electronic structure. For example, transition metal complexes, low-spin open-shell systems, covalent bond breaking situations have all in common that they cannot be even qualitatively described by a single electronic configuration. It is now clear that the usual semilocal density-functional approximations of KS DFT fail to accurately describe these situations and WFT is king for the treatment of strongly correlated systems. 
-categorized by the strength of the electronic correlation appearing in its electronic structure.  
-The so-called weakly correlated systems, such as closed-shell organic molecules near their equilibrium geometry, are typically dominated by correlation effects which do not affect the qualitative mean-field picture of the system. These weak correlation effects can be either short-range when electron are near the electron coalescence point, or long-range 
- with dispersion forces. The theoretical description of weakly correlated systems is one of the more concrete achievement 
-of quantum chemistry, and the main remaining issue for these systems is to push the limit in terms of the size of the chemical systems that can be treated.  
-The case of the so-called strongly correlated systems, which are ubiquitous in chemistry, is much more problematic as they exhibits 
-a much more exotic electronic structure. 
-Transition metals containing systems, low-spin open shell systems, covalent bond breaking or excited states 
-have all in common that they cannot be even qualitatively described by a single electronic configuration. 
-It is now clear that the usual semi-local approximations in KS-DFT fail in giving an accurate description of these situations and WFT has become 
-the standard for the treatment of strongly correlated systems. 
 
 In practice WFT uses a finite one-particle basis set (here referred as $\basis$) to project the Schroedinger equation whose exact solution becomes clear: the full configuration interaction (FCI) which consists in a linear algebra problem whose dimension scales exponentially with the system size. 
 Because of the exponential growth of the FCI, many approximations have appeared and in that regard the complexity of the strong correlation problem is, at least, two-fold: 
@@ -314,6 +300,8 @@ ii) the quantitative description of the systems must take into account weak corr
 other electronic configurations with typically much smaller weights in the wave function.  
 Fulfilling these two objectives is a rather complicated task for a given approximated approach, specially if one adds the requirement of satisfying formal properties, such $S_z$ invariance or additivity of the computed energy in the case of non interacting fragments. 
 
+%energy degeneracy of spin-multiplet components
+
 %To tackle this complicated problem, many methods have been proposed and an exhaustive review of the zoology of methods for strong correlation goes beyond the scope and purpose of this article. 
 
 %To tackle this problem, many WFT methods have emerged which can be categorized in two branches: the single-reference (SR)