diff --git a/BSEdyn.bib b/BSEdyn.bib index b503245..00bb7f2 100644 --- a/BSEdyn.bib +++ b/BSEdyn.bib @@ -1,7 +1,7 @@ %% This BibTeX bibliography file was created using BibDesk. %% 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) diff --git a/BSEdyn.tex b/BSEdyn.tex index 37c7f31..4d73be4 100644 --- a/BSEdyn.tex +++ b/BSEdyn.tex @@ -67,6 +67,8 @@ \newcommand{\RPA}{\text{RPA}} \newcommand{\BSE}{\text{BSE}} \newcommand{\GW}{GW} +\newcommand{\stat}{\text{stat}} +\newcommand{\dyn}{\text{dyn}} % energies \newcommand{\Enuc}{E^\text{nuc}} @@ -86,6 +88,7 @@ \newcommand{\eevGW}[1]{\epsilon^\text{\evGW}_{#1}} \newcommand{\eGnWn}[2]{\epsilon^\text{\GnWn{#2}}_{#1}} \newcommand{\Om}[2]{\Omega_{#1}^{#2}} +\newcommand{\tOm}[2]{\Tilde{\Omega}_{#1}^{#2}} % Matrix elements \newcommand{\A}[2]{A_{#1}^{#2}} @@ -171,6 +174,9 @@ \newcommand{\EgOpt}{\Eg^\text{opt}} \newcommand{\EB}{E_B} +\newcommand{\pis}{\pi^*} +\newcommand{\ra}{\rightarrow} + \newcommand\vari{{\varepsilon}_i} \newcommand\vara{{\varepsilon}_a} \newcommand\varj{{\varepsilon}_j} @@ -583,8 +589,9 @@ This correction can be renormalized by computing, at basically no extra cost, th \end{equation} which finally yields \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} +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. %%% 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. 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. %%%%%%%%%%%%%%%%%%%%%%%% @@ -626,6 +633,46 @@ All the BSE calculations have been performed with our locally developed $GW$ sof \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} \label{sec:conclusion}