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Vp>8=09xgr*FB(0)q>>cc{{h^p>#YC) diff --git a/Manuscript/Ex-srDFT.tex b/Manuscript/Ex-srDFT.tex index 65806da..93434b7 100644 --- a/Manuscript/Ex-srDFT.tex +++ b/Manuscript/Ex-srDFT.tex @@ -147,11 +147,11 @@ \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{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Universit\'e Pierre et Marie Curie, Sorbonne Universit\'e, CNRS, Paris, France} \begin{document} -\title{Excitation Energies Near The Complete Basis Set Limit} +\title{Chemically-Accurate Excitation Energies With a Small Basis Set} \author{Emmanuel Giner} \affiliation{\LCT} @@ -164,7 +164,8 @@ \affiliation{\LCPQ} \begin{abstract} -By combining extrapolated selected configuration interaction (sCI) calculations performed with the CIPSI algorithm with the recently proposed short-range density-functional functional correction for basis set incompleteness [\href{https://doi.org/10.1063/1.5052714}{Giner et al., \textit{J.~Chem.~Phys.}~\textbf{149}, 194301 (2018)}], we show that one can obtain vertical and adiabatic excitation energies with chemical accuracy with a small basis set. +By combining extrapolated selected configuration interaction (sCI) calculations performed with the CIPSI algorithm with the recently proposed short-range density-functional functional correction for basis set incompleteness [\href{https://doi.org/10.1063/1.5052714}{Giner et al., \textit{J.~Chem.~Phys.}~\textbf{149}, 194301 (2018)}], we show that one can obtain vertical and adiabatic excitation energies with chemical accuracy with, typically, augmented double-$\zeta$ basis sets. +The present study clearly evidences that special care has to be taken for very diffuse excited states where the present correction might not be enough to catch the radial incompleteness of the one-electron basis set. \end{abstract} \maketitle @@ -212,6 +213,195 @@ Contrary to our recent study on atomization and correlation energies, \cite{LooP %Very recently, a major step forward has been taken by some of the present authors thanks to the development of a density-based basis-set correction for WFT methods. \cite{GinPraFerAssSavTou-JCP-18} %The present work proposes an extension of this new methodological development alongside the first numerical tests on molecular systems. +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Theory} +\label{sec:theory} +%%%%%%%%%%%%%%%%%%%%%%%% + + +%Let us assume that we have reasonable approximations of the FCI energy and density of a $\Ne$-electron system in an incomplete basis set $\Bas$, say the CCSD(T) energy $\E{\CCSDT}{\Bas}$ and the Hartree-Fock (HF) density $\n{\HF}{\Bas}$. +%According to Eq.~(15) of Ref.~\citenum{GinPraFerAssSavTou-JCP-18}, the exact ground-state energy $\E{}{}$ may be approximated as +%\begin{equation} +% \label{eq:e0basis} +% \titou{\E{}{} +% \approx \E{\CCSDT}{\Bas} +% + \bE{}{\Bas}[\n{\HF}{\Bas}],} +%\end{equation} +%where +%\begin{equation} +% \label{eq:E_funcbasis} +% \bE{}{\Bas}[\n{}{}] +% = \min_{\wf{}{} \to \n{}{}} \mel*{\wf{}{}}{\hT + \hWee{}}{\wf{}{}} +% - \min_{\wf{}{\Bas} \to \n{}{}} \mel*{\wf{}{\Bas}}{\hT + \hWee{}}{\wf{}{\Bas}} +%\end{equation} +%is the basis-dependent complementary density functional, $\hT$ is the kinetic operator and $\hWee{} = \sum_{i2B}wz2CU^8_JJ8 z&zfuYUVAW}xn}7uOwTiPoFXvpHypzv=dvQ)MVUgV(%e^!50y{x<_#=3H{?enRf{#P zF7ume+zzlB;phh37*6-6=3i07E1kkHW9*4BGh2d|8S-@n!Ne_t)Gt^Q7ZnFAXS zWIW%B{9anhdExGU{`H&IMt}8X65Rb9^77bxK=$(aMY#L<@&~J1$MY@FTx8%)=4ip1 zVsGmRbVR!uG#v(#IRaTPSIvR(8g5Gmr$S(y$jwabx$C;BJi0S8uhEtYi{R|d*qvy1 z-Q+2(yV?#T)=>iq<@3RdLw^DxO%)F8z0tPBPDk_dt_l4R)mvfo>4#f@W>l;8=q(MW zh;HlW6{ZD0rj#b!N+*D(sHns3A;;e5@fPrUe6-me*rv5D9X=8HB=7JmbuPrHG0JW2 z0GR7KvJm)jo~)!%J2q0;3NPc7*AhS7 zz5v^VtJ88M7DjASd|<7R(3Q%y=fSQ9y4z>YTPB4>IFciO)KigLx966sXSEw9^+f-J 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