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Pierre-Francois Loos 2020-05-19 17:38:29 +02:00
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BSEdyn.bib
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%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/ %% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2020-05-19 16:23:54 +0200 %% Created for Pierre-Francois Loos at 2020-05-19 17:13:25 +0200
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)

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BSEdyn.tex
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@ -67,6 +67,8 @@
\newcommand{\RPA}{\text{RPA}} \newcommand{\RPA}{\text{RPA}}
\newcommand{\BSE}{\text{BSE}} \newcommand{\BSE}{\text{BSE}}
\newcommand{\GW}{GW} \newcommand{\GW}{GW}
\newcommand{\stat}{\text{stat}}
\newcommand{\dyn}{\text{dyn}}
% energies % energies
\newcommand{\Enuc}{E^\text{nuc}} \newcommand{\Enuc}{E^\text{nuc}}
@ -86,6 +88,7 @@
\newcommand{\eevGW}[1]{\epsilon^\text{\evGW}_{#1}} \newcommand{\eevGW}[1]{\epsilon^\text{\evGW}_{#1}}
\newcommand{\eGnWn}[2]{\epsilon^\text{\GnWn{#2}}_{#1}} \newcommand{\eGnWn}[2]{\epsilon^\text{\GnWn{#2}}_{#1}}
\newcommand{\Om}[2]{\Omega_{#1}^{#2}} \newcommand{\Om}[2]{\Omega_{#1}^{#2}}
\newcommand{\tOm}[2]{\Tilde{\Omega}_{#1}^{#2}}
% Matrix elements % Matrix elements
\newcommand{\A}[2]{A_{#1}^{#2}} \newcommand{\A}[2]{A_{#1}^{#2}}
@ -171,6 +174,9 @@
\newcommand{\EgOpt}{\Eg^\text{opt}} \newcommand{\EgOpt}{\Eg^\text{opt}}
\newcommand{\EB}{E_B} \newcommand{\EB}{E_B}
\newcommand{\pis}{\pi^*}
\newcommand{\ra}{\rightarrow}
\newcommand\vari{{\varepsilon}_i} \newcommand\vari{{\varepsilon}_i}
\newcommand\vara{{\varepsilon}_a} \newcommand\vara{{\varepsilon}_a}
\newcommand\varj{{\varepsilon}_j} \newcommand\varj{{\varepsilon}_j}
@ -583,8 +589,9 @@ This correction can be renormalized by computing, at basically no extra cost, th
\end{equation} \end{equation}
which finally yields which finally yields
\begin{equation} \begin{equation}
\Om{m}{} \approx \Om{m}{(0)} + Z_{m} \Om{m}{(1)}. \Om{m}{\text{dyn}} = \Om{m}{\text{stat}} + \Delta\Om{m}{\text{dyn}} = \Om{m}{(0)} + Z_{m} \Om{m}{(1)}.
\end{equation} \end{equation}
with $\Om{m}{\text{stat}} \equiv \Om{m}{(0)}$ and $\Delta\Om{m}{\text{dyn}} = Z_{m} \Om{m}{(1)}$.
This is our final expression. This is our final expression.
%%% FIG 1 %%% %%% FIG 1 %%%
@ -618,7 +625,7 @@ Further details about our implementation of {\GOWO} and {\evGW} can be found in
As one-electron basis sets, we employ the augmented Dunning family (aug-cc-pVXZ) defined with cartesian Gaussian functions. As one-electron basis sets, we employ the augmented Dunning family (aug-cc-pVXZ) defined with cartesian Gaussian functions.
Finally, the infinitesimal $\eta$ is set to $100$ meV for all calculations. Finally, the infinitesimal $\eta$ is set to $100$ meV for all calculations.
For comparison purposes, we employ the theoretical best estimates and geometries of Ref.~\onlinecite{Loos_2018a} from which coupled cluster (CC) excitation energies, namely, CC2 \cite{Christiansen_1995}, CCSD, \cite{Purvis_1982} and CC3, \cite{Christiansen_1995b} are also extracted. For comparison purposes, we employ the theoretical best estimates and geometries of Refs.~\onlinecite{Loos_2018a,Loos_2019,Loos_2020b} from which coupled cluster (CC) excitation energies, namely, CC2 \cite{Christiansen_1995}, CCSD, \cite{Purvis_1982} and CC3, \cite{Christiansen_1995b} are also extracted.
All the BSE calculations have been performed with our locally developed $GW$ software, \texttt{QuAcK}, \cite{QuAcK} freely available on \texttt{github}, where the present perturbative correction has been implemented. All the BSE calculations have been performed with our locally developed $GW$ software, \texttt{QuAcK}, \cite{QuAcK} freely available on \texttt{github}, where the present perturbative correction has been implemented.
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
@ -626,6 +633,46 @@ All the BSE calculations have been performed with our locally developed $GW$ sof
\label{sec:resdis} \label{sec:resdis}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
\begin{table*}
\caption{
BSE excitation energies for various molecules obtained with the aug-cc-pVTZ basis set.
\label{tab:BigTab}
}
\begin{ruledtabular}
\begin{tabular}{lccccccccccc}
& & \mc{4}{c}{BSE@{\GOWO}@HF} & \mc{4}{c}{BSE@{\evGW}@HF} \\
\cline{4-7} \cline{8-11}
Mol. & State & $\Om{m}{\stat}$ & $\Om{m}{\dyn}$ & $\Delta\Om{m}{\dyn}$ & $Z_{m}$
& $\Om{m}{\stat}$ & $\Om{m}{\dyn}$ & $\Delta\Om{m}{\dyn}$ & $Z_{m}$ & CC2 & CC3 \\
\hline
\ce{HCl} & $^1\Pi$(CT)\\
\ce{H2O} & \\
\ce{N2} & $^1\Pi_g(n \ra \pis)$ \\
& $^1\Sigma_u^-(\pi \ra \pis)$ \\
& $^1\Delta_u(\pi \ra \pis)$ \\
& $^3\Sigma_u^+(\pi \ra \pis)$\\
& $^3\Pi_g(n \ra \pis)$ \\
& $^3\Delta_u(\pi \ra \pis)$ \\
& $^3\Sigma_u^-(\pi \ra \pis)$ \\
\ce{CO} & $^1\Pi(n \ra \pis)$ \\
& $^1\Sigma^-(\pi \ra \pis)$ \\
& $^1\Delta(\pi \ra \pis)$ \\
& $^3\Pi(n \ra \pis)$ \\
& $^3\Sigma^+(\pi \ra \pis)$\\
& $^3\Delta(\pi \ra \pis)$ \\
& $^3\Sigma_u^-(\pi \ra \pis)$ \\
\ce{HNO} & \\
\ce{CH2O} & \\
\ce{C2H4} & $^1B_{3u}(\pi \ra 3s)$ \\
& $^1B_{1u}(\pi \ra \pis)$ \\
& $^1B_{1g}(\pi \ra 3p)$ \\
& $^3B_{1u}(\pi \ra \pis)$ \\
& $^3B_{3u}(\pi \ra 3s)$ \\
& $^3B_{1g}(\pi \ra 3p)$ \\
\end{tabular}
\end{ruledtabular}
\end{table*}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusion} \section{Conclusion}
\label{sec:conclusion} \label{sec:conclusion}