abstract

Manuscript/G2-srDFT.tex

@@ -113,7 +113,7 @@
 
 \begin{document}	
 
-\title{A Density-Based Basis-Set Correction For Wave-Function Theory}
+\title{A Density-Based Basis Set Correction For Wave Function Theory}
 
 \author{Bath\'elemy Pradines}
 \affiliation{\LCT}
@@ -131,11 +131,12 @@
 \affiliation{\LCT}
 
 \begin{abstract}
-We report a universal density-based basis-set incompleteness correction that can be applied to any wave-function method while keeping the correct limit when reaching the complete basis set (CBS).
-The present correction relies on a short-range correlation density functional (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis-set incompleteness error.
-Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range-separation \textit{parameter} $\mu$, the key ingredient here is a range-separation \textit{function} $\mu(\bf{r})$ which automatically adapts to the basis-set used in a wave-function calculation and accounts for the non-homogeneity of the incompleteness error in real space. 
+We report a universal density-based basis set incompleteness correction that can be applied to any wave function method.
+The present correction relies on short-range correlation density functionals (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis set incompleteness error and appropriately vanishes in the complete basis set (CBS) limit.
+Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range separation \textit{parameter} $\mu$, the key ingredient here is a range separation \textit{function} $\mu(\bf{r})$ which automatically adapts to the spatial non-homogeneity of the basis set incompleteness error.
 As illustrative examples, we show how this density-based correction allows us to obtain CCSD(T) atomization energies near the CBS limit for the G2-1 set of molecules with compact Gaussian basis sets. 
-For example, while the CCSD(T)/cc-pVTZ model shows a mean deviation of 7.79 kcal/mol compared to CCSD(T)/CBS atomization energies, our basis-set corrected CCSD(T)+LDA and CCSD(T)+PBE methods performed in the same basis return 2.89 and 2.46 kcal/mol, respectively, while these values drop below 1 {\kcal} with the cc-pVQZ basis set.
+For example, while CCSD(T)/cc-pVTZ yields a mean absolute deviation (MAD) of 7.79 kcal/mol compared to CCSD(T)/CBS atomization energies, the CCSD(T)+LDA and CCSD(T)+PBE corrected methods return MAD of 2.89 and 2.46 kcal/mol (respectively) with the same basis. 
+These values drop below 1 {\kcal} with the cc-pVQZ basis set.
 \end{abstract}
 
 \maketitle
@@ -166,7 +167,7 @@ Although there is no clear way on how to systematically improve density-function
 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 thanks to a more general formulation of DFT, the so-called range-separated DFT (RS-DFT) (see Ref.~\onlinecite{TouColSav-PRA-04} and references therein) which rigorously combines WFT and DFT.
-In such a formalism the electron-electron interaction is split into a non divergent long-range part which is treated using WFT and a complementary short-range part treated with DFT. As the wave-function part only deals with a non-diverging electron-electron interaction, it is free from the problematic electron cusp condition and the convergence with respect to the one-particle basis set is greatly improved\cite{FraMusLupTou-JCP-15}. Therefore, a number of approximate RS-DFT schemes have been developed using either single-reference WFT approaches (such as M{\o}ller-Plesset perturbation theory\cite{AngGerSavTou-PRA-05}, coupled cluster\cite{GolWerSto-PCCP-05}, random-phase approximations\cite{TouGerJanSavAng-PRL-09,JanHenScu-JCP-09}) or multi-reference WFT approaches (such as multi-reference CI\cite{LeiStoWerSav-CPL-97}, multiconfiguration self-consistent field\cite{FroTouJen-JCP-07}, multi-reference perturbation theory\cite{FroCimJen-PRA-10}, density-matrix renormalization group\cite{HedKneKieJenRei-JCP-15}, selected CI\cite{FerGinTou-JCP-18}).
+In such a formalism the electron-electron interaction is split into a non divergent long-range part which is treated using WFT and a complementary short-range part treated with DFT. As the wave function part only deals with a non-diverging electron-electron interaction, it is free from the problematic electron cusp condition and the convergence with respect to the one-particle basis set is greatly improved\cite{FraMusLupTou-JCP-15}. Therefore, a number of approximate RS-DFT schemes have been developed using either single-reference WFT approaches (such as M{\o}ller-Plesset perturbation theory\cite{AngGerSavTou-PRA-05}, coupled cluster\cite{GolWerSto-PCCP-05}, random-phase approximations\cite{TouGerJanSavAng-PRL-09,JanHenScu-JCP-09}) or multi-reference WFT approaches (such as multi-reference CI\cite{LeiStoWerSav-CPL-97}, multiconfiguration self-consistent field\cite{FroTouJen-JCP-07}, multi-reference perturbation theory\cite{FroCimJen-PRA-10}, density-matrix renormalization group\cite{HedKneKieJenRei-JCP-15}, selected CI\cite{FerGinTou-JCP-18}).
 
 The present work proposes the extension of a recently proposed basis set correction scheme based on RS-DFT\cite{GinPraFerAssSavTou-JCP-18} together with the first numerical tests on molecular systems. 
 
@@ -327,7 +328,7 @@ In the final step, we employ short-range density functionals\cite{TouGorSav-TCA-
 
 
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-%\subsection{Definition of a real-space representation of the coulomb operator truncated in a basis-set $\Bas$}
+%\subsection{Definition of a real-space representation of the coulomb operator truncated in a basis set $\Bas$}
 %\label{sec:weff}
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