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Manuscript/srDFT_SC.tex
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@ -251,14 +251,15 @@
\newcommand{\PBEspin}{PBEspin}
\newcommand{\PBEueg}{PBE-UEG-{$\tilde{\zeta}$}}
\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France}
\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France}
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique, Universit\'e Pierre et Marie Curie, Sorbonne Universit\'e, CNRS, Paris, France}
\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France}
\newcommand{\IUF}{Institut Universitaire de France, Paris, France}
\begin{document}
\title{A density-based basis set correction for strong correlation}
\title{A density-based basis-set correction for strong correlation}
\author{Emmanuel Giner}
\email{emmanuel.giner@lct.jussieu.fr}
@ -274,16 +275,13 @@
\author{Julien Toulouse}
\email{toulouse@lct.jussieu.fr}
\affiliation{\LCT}
\affiliation{\IUF}
\begin{abstract}
The present work proposes an application and extension to strongly correlated systems of the recently proposed basis set correction based on density functional theory (DFT).
We study the potential energy surfaces (PES) of the H$_{10}$, C$_2$, N$_2$, O$_2$ and F$_2$ molecules up to full dissociation limit in increasing basis sets at near full configuration interaction (FCI) level with and without the present basis set correction.
Such basis set correction relies on a mapping between range-separated DFT (RSDFT) and wave function calculations in a finite basis set through the definition of an effective non-divergent interaction mimicking the coulomb operator projected in a finite basis set. From that mapping, RSDFT-types functionals are used to recover the dominant part of the short-range correlation effects missing in a finite basis set.
The scope of the present work is to develop new approximations for the complementary functionals which are suited to describe strong correlation regimes and which fulfill two very desirable properties: $S_z$ invariance and size extensivity.
In that context, we investigate the dependence of the functionals on different flavours of on-top pair densities and spin-polarizations. An important result is that the explicit dependence on the on-top pair density allows one to completely remove the dependence on any form of spin-polarization without any significant loss of accuracy.
In the general context of multi-configurational DFT, such findings show that one can avoid the effective spin polarization whose mathematical definition is rather \textit{ad hoc} and which can become complex valued.
Quantitatively, we show that the basis set correction allows chemical accuracy on atomization energies in a triple-zeta quality for most of the systems studied. Also, the present basis set correction provides smooth curves all along the PES.
We extend to strongly correlated systems the recently introduced basis-set correction based on density-functional theory (DFT) [E. Giner \textit{et al.}, J. Chem. Phys. \textbf{149}, 194301 (2018)]. This basis-set correction relies on a mapping between wave-function calculations in a finite basis set and range-separated DFT (RSDFT) through the definition of an effective non-divergent interaction corresponding to the Coulomb electron-electron interaction projected in the finite basis set, allowing one to use RSDFT-type complementary functionals to recover the dominant part of the short-range correlation effects missing in a finite basis set. Using as test cases the potential energy curves of the H$_{10}$, C$_2$, N$_2$, O$_2$, and F$_2$ molecules up to the dissociation limit, we systematically explore different approximations for the complementary functionals which are suited to describe strong-correlation regimes and which fulfill two very desirable properties: $S_z$ invariance and size consistency. Specifically, we investigate the dependence of the functionals on different flavours of on-top pair densities and spin polarizations. An important result is that the explicit dependence on the on-top pair density allows one to completely remove the dependence on any form of spin polarization without any significant loss of accuracy.
In the general context of multiconfigurational DFT, this finding shows that one can avoid the effective spin polarization whose mathematical definition is rather \textit{ad hoc} and which can become complex valued. Quantitatively, we show that the basis-set correction reaches chemical accuracy on atomization energies with triple-zeta quality basis sets for most of the systems studied. Also, the present basis-set correction provides smooth curves along the whole potential energy curves.
%We study the potential energy surfaces (PES) of the H$_{10}$, C$_2$, N$_2$, O$_2$, and F$_2$ molecules up to the dissociation limit using increasing basis sets at near full configuration interaction (FCI) level with and without the present basis-set correction.
\end{abstract}
\maketitle