Intro 1st shot

Manuscript/G2-srDFT.tex

@@ -177,7 +177,7 @@
 
 \begin{document}	
 
-\title{G2 Atomization Energies With Chemical Accuracy}
+\title{A density-based basis set correction for wave function theory}
 
 \author{Bath\'elemy Pradines}
 \affiliation{\LCPQ}
@@ -192,6 +192,7 @@
 \affiliation{\LCT}
 
 \begin{abstract}
+We report a universal density-based basis set incompleteness correction that can be applied to any wave function theory method.
 \end{abstract}
 
 \maketitle
@@ -199,9 +200,37 @@
 %%%%%%%%%%%%%%%%%%%%%%%%
 \section{Introduction}
 %%%%%%%%%%%%%%%%%%%%%%%%
+Contemporary quantum chemistry has developed in two directions --- wave function theory (WFT) \cite{Pop-RMP-99} and density-functional theory (DFT). \cite{Koh-RMP-99}
+Although both spring from the same Schr\"odinger equation, each of these philosophies has its own advantages and shortcomings.
+
+WFT is attractive as it exists a well-defined path for systematic improvement.
+For example, the coupled cluster (CC) family of methods offers a powerful WFT approach for the description of weakly correlated systems and is well regarded as the gold standard of quantum chemistry. 
+By increasing the excitation degree of the CC expansion, one can systematically converge, for a given basis set, to the exact, full configuration interaction (FCI) limit, although the computational cost associated with such improvement is usually pricey.
+One of the most fundamental drawback of conventional WFT methods is the slow convergence of energies and properties with respect to the size of the one-electron basis set.
+This undesirable feature was put into light by Kutzelnigg more than thirty years ago, \cite{Kut-TCA-85}
+who proposed, to palliate this, to introduce explicitly the interelectronic distance $r_{12} = \abs{\br_1 - \br_2}$ as a basis function. \cite{Kut-TCA-85, KutKlo-JCP-91, TerKloKut-JCP-91, KloKut-JCP-91, KloRohKut-CPL-91, NogKut-JCP-94}
+The resulting F12 methods yields a prominent improvement of the energy convergence, and achieve chemical accuracy for small organic molecules with relatively small Gaussian basis sets. \cite{Ten-TCA-12, TenNog-WIREs-12, HatKloKohTew-CR-12, KonBisVal-CR-12}
+For example, at the CCSD(T) level, it is advertised that one can obtain quintuple-zeta quality correlation energies with a triple-zeta basis, \cite{TewKloNeiHat-PCCP-07} although computational overheads are introduced by the large auxiliary basis used to resolve three- and four-electron integrals.
+
+Present-day DFT calculations are almost exclusively done within the so-called Kohn-Sham (KS) formalism, which corresponds to an exact dressed one-electron theory. \cite{KohSha-PR-65}
+DFT's attractivity originates from its very favorable cost/efficient ratio as it can provide accurate energies and properties at a relatively low computational cost.
+Thanks to this, KS-DFT \cite{HohKoh-PR-64, KohSha-PR-65} has become the workhorse of electronic structure calculations for atoms, molecules and solids. \cite{ParYan-BOOK-89}
+To obtain accurate results within DFT, one only requires an exchange and correlation functionals, which can be classified in various families depending on their physical input quantities. \cite{Bec-JCP-14}
+Although there is no clear way on how to systematically improve density-functional approximations (DFAs), climbing the Jacob's ladder of DFT is potentially the most satisfactory way forward (or upward in that case). \cite{PerSch-AIPCP-01, PerRuzTaoStaScuCso-JCP-05}
+%The local-density approximation (LDA) sits on the first rung of the Jacob's ladder and only uses as input the electron density $n$. \cite{Dir-PCPRS-30, VosWilNus-CJP-80}
+%The generalized-gradient approximation (GGA) corresponds to the second rung and adds the gradient of the electron density $\nabla n$ as an extra ingredient.\cite{Bec-PRA-88, PerWan-PRA-91, PerBurErn-PRL-96}
+In the present context, one of the interesting feature of density-based methods is their much faster convergence with respect to the size of the basis set. \cite{FraMusLupTou-JCP-15}
+
+Progress toward unifying these two approaches are on-going.
+Using accurate and rigorous WFT methods, some of us have developed radical generalisations of DFT that are free of the well-known limitations of conventional DFT. 
+In that respect range-separated DFT (RS-DFT) is particularly promising as it allows to perform multi-configurational DFT calculations within a rigorous mathematical framework. 
+Range-separated hybrids, i.e.~single-determinant approximations of RS-DFT, correct for the wrong long-range behavior of the usual hybrid approximations thanks to the inclusion of the long-range part of the Hartree-Fock (HF) exchange.  
 
 
 
+The present manuscript is organised as follows.
+Unless otherwise stated, atomic used are used.
+
 %%%%%%%%%%%%%%%%%%%%%%%%
 \section{Theory}
 %%%%%%%%%%%%%%%%%%%%%%%%