diff --git a/Manuscript/Ex-srDFT.tex b/Manuscript/Ex-srDFT.tex index 3cbb66c..5e68031 100644 --- a/Manuscript/Ex-srDFT.tex +++ b/Manuscript/Ex-srDFT.tex @@ -20,9 +20,11 @@ \newcommand{\mc}{\multicolumn} \newcommand{\fnm}{\footnotemark} \newcommand{\fnt}{\footnotetext} -\newcommand{\mcc}[1]{\multicolumn{1}{c}{#1}} +\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} \newcommand{\mr}{\multirow} \newcommand{\SI}{\textcolor{blue}{supporting information}} + +\newcommand{\br}{\mathbf{r}} % energies \newcommand{\EHF}{E_\text{HF}} @@ -33,8 +35,10 @@ \newcommand{\EDMC}{E_\text{DMC}} \newcommand{\EexFCI}{E_\text{exFCI}} \newcommand{\EexDMC}{E_\text{exDMC}} +\newcommand{\Ead}{\Delta E_\text{ad}} \newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$} +\newcommand{\ra}{\rightarrow} % units \newcommand{\IneV}[1]{#1 eV} @@ -45,98 +49,169 @@ \newcommand{\si}{\sigma} \newcommand{\sis}{\sigma^\star} + + \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} \begin{document} -\title{Prout} +\title{Excitation Energies Near The Complete Basis Set Limit} -%\author{Pierre-Fran\c{c}ois Loos} -%\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr} -%\affiliation{\LCPQ} -%\author{Anthony Scemama} -%\affiliation{\LCPQ} +\author{Emmanuel Giner} +\affiliation{\LCT} +\author{Anthony Scemama} +\affiliation{\LCPQ} +\author{Julien Toulouse} +\affiliation{\LCT} +\author{Pierre-Fran\c{c}ois Loos} +\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr} +\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., J.~Chem.~Phys.~149, 194301 (2018)}], we show that one can obtain vertical and adiabatic excitation energies with chemical accuracy with a small basis set. \end{abstract} -%\maketitle +\maketitle +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Introduction} +\label{sec:intro} +%%%%%%%%%%%%%%%%%%%%%%%% +One of the most fundamental problem of conventional electronic structure methods is their slow energy convergence with respect to the size of the one-electron basis set. +This problem was already noticed thirty years ago by Kutzelnigg \cite{Kutzelnigg_1985} who proposed to introduce explicitly the correlation between electrons via the introduction of the interelectronic distance $r_{12} = \abs{\br_1 - \br_2}$ as a basis function. \cite{Kutzelnigg_1991, Termath_1991, Klopper_1991a, Klopper_1991b, Noga_1994} +This yields a prominent improvement of the energy convergence from $O(L^{-3})$ to $O(L^{-7})$ (where $L$ is the maximum angular momentum of the one-electron basis). +This idea was later generalised to more accurate correlation factors $f_{12} \equiv f(r_{12})$. \cite{Persson_1996, Persson_1997, May_2004, Tenno_2004b, Tew_2005, May_2005} +The resulting F12 methods achieve chemical accuracy for small organic molecules with relatively small Gaussian basis sets. \cite{Tenno_2012a, Tenno_2012b, Hattig_2012, Kong_2012} +For example, as illustrated by Tew and coworkers, one can obtain, at the CCSD(T) level, quintuple-zeta quality correlation energies with a triple-zeta basis. \cite{Tew_2007b} + +In the present study, we rely on the recently proposed short-range density-functional functional correction for basis set incompleteness. \cite{Giner_2018} + +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Computational details} +\label{sec:compdetails} +%%%%%%%%%%%%%%%%%%%%%%%% + + +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Results} +\label{sec:res} +%%%%%%%%%%%%%%%%%%%%%%%% +%======================= +\subsection{Water} +\label{sec:H2O} +%======================= + +%======================= +\subsection{Formaldehyde} +\label{sec:CH2O} +%======================= + +%======================= +\subsection{Methylene} +\label{sec:CH2} +%======================= %%% TABLE 1 %%% \begin{squeezetable} - \begin{table} + \begin{table*} \caption{ - Total energies (in hartree) and adiabatic transition energies (in eV) of excited states of methylene for various methods and basis sets.} + Total energies $E$ (in hartree) and adiabatic transition energies $\Ead$ (in eV) of excited states of methylene for various methods and basis sets.} \begin{ruledtabular}{} - \begin{tabular}{lccdd} - Method & Basis set & State & \mcc{Total energy (a.u.)} & \mcc{Excitation energy (eV)} \\ + \begin{tabular}{llddddddd} + & & \mc{1}{c}{$1\,^{3}B_1$} + & \mc{2}{c}{$1\,^{3}B_1 \ra 1\,^{1}A_1$} + & \mc{2}{c}{$1\,^{3}B_1 \ra 1\,^{1}B_1$} + & \mc{2}{c}{$1\,^{3}B_1 \ra 2\,^{1}A_1$} \\ + \cline{3-3} \cline{4-5} + \cline{6-7} \cline{8-9} + Method & Basis set & \tabc{$E$ (a.u.)} + & \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)} + & \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)} + & \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)} \\ \hline - CIPSI & AVDZ & $1\,^{3}B_1$ & -39.04846(1) & \\ - & & $1\,^{1}A_1$ & -39.03225(1) & 0.441 \\ - & & $1\,^{1}B_1$ & -38.99203(1) & 1.536 \\ - & & $2\,^{1}A_1$ & -38.95076(1) & 2.659 \\ - CIPSI & AVTZ & $1\,^{3}B_1$ & -39.08064(3) & \\ - & & $1\,^{1}A_1$ & -39.06565(2) & 0.408 \\ - & & $1\,^{1}B_1$ & -39.02833(1) & 1.423 \\ - & & $2\,^{1}A_1$ & -38.98709(1) & 2.546 \\ - CIPSI & AVQZ & $1\,^{3}B_1$ & -39.08854(1) & \\ - & & $1\,^{1}A_1$ & -39.07402(2) & 0.395 \\ - & & $1\,^{1}B_1$ & -39.03711(1) & 1.399 \\ - & & $2\,^{1}A_1$ & -38.99607(1) & 2.516 \\ - CIPSI & AV5Z & $1\,^{3}B_1$ & -39.09079(1) & \\ - & & $1\,^{1}A_1$ & -39.07647(1) & 0.390 \\ - & & $1\,^{1}B_1$ & -39.03964(3) & 1.392 \\ - & & $2\,^{1}A_1$ & -38.99867(1) & 2.507 \\ - CIPSI+srLDA & AVDZ & $1\,^{3}B_1$ & & \\ - & & $1\,^{1}A_1$ & & 0.347 \\ - & & $1\,^{1}B_1$ & & 1.431 \\ - & & $2\,^{1}A_1$ & & 2.590 \\ - CIPSI+srLDA & AVTZ & $1\,^{3}B_1$ & & \\ - & & $1\,^{1}A_1$ & & 0.360 \\ - & & $1\,^{1}B_1$ & & 1.377 \\ - & & $2\,^{1}A_1$ & & 2.513 \\ - CIPSI+srLDA & AVQZ & $1\,^{3}B_1$ & & \\ - & & $1\,^{1}A_1$ & & 0.371 \\ - & & $1\,^{1}B_1$ & & 1.376 \\ - & & $2\,^{1}A_1$ & & 2.498 \\ - CIPSI+srPBE & AVDZ & $1\,^{3}B_1$ & & \\ - & & $1\,^{1}A_1$ & & 0.358 \\ - & & $1\,^{1}B_1$ & & 1.420 \\ - & & $2\,^{1}A_1$ & & 2.529 \\ - CIPSI+srPBE & AVTZ & $1\,^{3}B_1$ & & \\ - & & $1\,^{1}A_1$ & & 0.373 \\ - & & $1\,^{1}B_1$ & & 1.383 \\ - & & $2\,^{1}A_1$ & & 2.496 \\ - CIPSI+srPBE & AVQZ & $1\,^{3}B_1$ & & \\ - & & $1\,^{1}A_1$ & & 0.380 \\ - & & $1\,^{1}B_1$ & & 1.381 \\ - & & $2\,^{1}A_1$ & & 2.492 \\ - SHCI & AVQZ & $1\,^{3}B_1$ & -39.08849(1) & \\ - & & $1\,^{1}A_1$ & -39.07404(1) & 0.393 \\ - & & $1\,^{1}B_1$ & -39.03711(1) & 1.398 \\ - & & $2\,^{1}A_1$ & -38.99603(1) & 2.516 \\ - CR-EOMCC (2,3)D& AVQZ & $1\,^{3}B_1$ & -39.08817 & \\ - & & $1\,^{1}A_1$ & -39.07303 & 0.412 \\ - & & $1\,^{1}B_1$ & -39.03450 & 1.460 \\ - & & $2\,^{1}A_1$ & -38.99457 & 2.547 \\ - FCI & TZ2P & $1\,^{3}B_1$ & -39.066738 & \\ - & & $1\,^{1}A_1$ & -39.048984 & 0.483 \\ - & & $1\,^{1}B_1$ & -39.010059 & 1.542 \\ - & & $2\,^{1}A_1$ & -38.968471 & 2.674 \\ - DMC & & $1\,^{3}B_1$ & & \\ - & & $1\,^{1}A_1$ & & 0.406 \\ - & & $1\,^{1}B_1$ & & 1.416 \\ - & & $2\,^{1}A_1$ & & 2.524 \\ - Exp. & & $1\,^{3}B_1$ & & \\ - & & $1\,^{1}A_1$ & & 0.400 \\ - & & $1\,^{1}B_1$ & & 1.411 \\ + exFCI & AVDZ & -39.04846(1) + & -39.03225(1) & 0.441 + & -38.99203(1) & 1.536 + & -38.95076(1) & 2.659 \\ + & AVTZ & -39.08064(3) + & -39.06565(2) & 0.408 + & -39.02833(1) & 1.423 + & -38.98709(1) & 2.546 \\ + & AVQZ & -39.08854(1) + & -39.07402(2) & 0.395 + & -39.03711(1) & 1.399 + & -38.99607(1) & 2.516 \\ + & AV5Z & -39.09079(1) + & -39.07647(1) & 0.390 + & -39.03964(3) & 1.392 + & -38.99867(1) & 2.507 \\ + exFCI+srLDA & AVDZ & + & & 0.347 + & & 1.431 + & & 2.590 \\ + & AVTZ & + & & 0.360 + & & 1.377 + & & 2.513 \\ + & AVQZ & + & & 0.371 + & & 1.376 + & & 2.498 \\ + exFCI+srPBE & AVDZ & + & & 0.358 + & & 1.420 + & & 2.529 \\ + & AVTZ & + & & 0.373 + & & 1.383 + & & 2.496 \\ + & AVQZ & + & & 0.380 + & & 1.381 + & & 2.492 \\ + HBCI & AVQZ & -39.08849(1) + & -39.07404(1) & 0.393 + & -39.03711(1) & 1.398 + & -38.99603(1) & 2.516 \\ + CR-EOMCC (2,3)D& AVQZ & -39.08817 + & -39.07303 & 0.412 + & -39.03450 & 1.460 + & -38.99457 & 2.547 \\ + FCI & TZ2P & -39.066738 + & -39.048984 & 0.483 + & -39.010059 & 1.542 + & -38.968471 & 2.674 \\ + DMC & & + & & 0.406 + & & 1.416 + & & 2.524 \\ + Exp. & & + & & 0.400 + & & 1.411 \end{tabular} \end{ruledtabular} - \end{table} + \end{table*} \end{squeezetable} %%% %%% %%% +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Conclusion} +\label{sec:ccl} +%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%% +\section*{Supporting Information} +%%%%%%%%%%%%%%%%%%%%%%%% +See {\SI} for geometries and additional information (including total energies). + +%%%%%%%%%%%%%%%%%%%%%%%% +\begin{acknowledgements} +This work was performed using HPC resources from +i) GENCI-TGCC (Grant No. 2018-A0040801738), +ii) CALMIP (Toulouse) under allocations 2018-0510 and 2018-12158. +\end{acknowledgements} +%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/References/Booth_2012.pdf b/References/Booth_2012.pdf new file mode 100644 index 0000000..b136f25 Binary files /dev/null and b/References/Booth_2012.pdf differ diff --git a/References/Kong_2010.pdf b/References/Kong_2010.pdf new file mode 100644 index 0000000..ba129ad Binary files /dev/null and b/References/Kong_2010.pdf differ diff --git a/References/Kong_2011.pdf b/References/Kong_2011.pdf new file mode 100644 index 0000000..3156df9 Binary files /dev/null and b/References/Kong_2011.pdf differ diff --git a/References/Torheyden_2009.pdf b/References/Torheyden_2009.pdf new file mode 100644 index 0000000..7bdde33 Binary files /dev/null and b/References/Torheyden_2009.pdf differ diff --git a/References/Wiles_2018.pdf b/References/Wiles_2018.pdf new file mode 100644 index 0000000..a507cc8 Binary files /dev/null and b/References/Wiles_2018.pdf differ