PTEROSOR/BSEdyn
10
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

saving work

Browse Source
This commit is contained in:
Pierre-Francois Loos 2020-06-08 10:59:36 +02:00
parent cf7c8aea8d
commit 314f247236
3 changed files with 10498 additions and 98 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

207
BSEdyn.tex
View File

@ -725,38 +725,41 @@ All the static and dynamic BSE calculations have been performed with the softwar
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
%%% TABLE I %%% %%% TABLE I %%%
\begin{squeezetable}
\begin{table*} \begin{table*}
\caption{ \caption{
Singlet and triplet excitation energies (in eV) of \ce{N2} computed at the BSE@{\GOWO}@HF level for various basis sets. Singlet and triplet excitation energies (in eV) of \ce{N2} computed at the BSE@{\GOWO}@HF level for various basis sets.
\label{tab:N2} \label{tab:N2}
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lddddddddd} \begin{tabular}{llddddddddd}
& \mc{3}{c}{aug-cc-pVDZ ($\Eg^{\GW} = 19.49$ eV)} & & \mc{3}{c}{aug-cc-pVDZ ($\Eg^{\GW} = 19.49$ eV)}
& \mc{3}{c}{aug-cc-pVTZ ($\Eg^{\GW} = 19.20$ eV)} & \mc{3}{c}{aug-cc-pVTZ ($\Eg^{\GW} = 19.20$ eV)}
& \mc{3}{c}{aug-cc-pVQZ ($\Eg^{\GW} = 19.00$ eV)} \\ & \mc{3}{c}{aug-cc-pVQZ ($\Eg^{\GW} = 19.00$ eV)} \\
\cline{2-4} \cline{5-7} \cline{8-10} \cline{3-5} \cline{6-8} \cline{9-11}
State & \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$} State & Nature & \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$}
& \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$}
& \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$} \\ & \tabc{$\Om{s}{\stat}$} & \tabc{$\Delta\Om{s}{\dyn}$(dTDA)} & \tabc{$\Delta\Om{s}{\dyn}$} \\
\hline \hline
$^1\Pi_g(n \ra \pis)$ & 10.18 & -0.41 & -0.43 & 10.42 & -0.42 & -0.40 & 10.52 & -0.43 & -0.40 \\ $^1\Pi_g(n \ra \pis)$ & Val. & 10.18 & -0.41 & -0.43 & 10.42 & -0.42 & -0.40 & 10.52 & -0.43 & -0.40 \\
$^1\Sigma_u^-(\pi \ra \pis)$ & 9.95 & -0.44 & -0.44 & 10.11 & -0.45 & -0.45 & 10.20 & -0.45 & -0.45 \\ $^1\Sigma_u^-(\pi \ra \pis)$ & Val. & 9.95 & -0.44 & -0.44 & 10.11 & -0.45 & -0.45 & 10.20 & -0.45 & -0.45 \\
$^1\Delta_u(\pi \ra \pis)$ & 10.57 & -0.41 & -0.40 & 10.75 & -0.42 & -0.41 & 10.85 & -0.42 & -0.42 \\ $^1\Delta_u(\pi \ra \pis)$ & Val. & 10.57 & -0.41 & -0.40 & 10.75 & -0.42 & -0.41 & 10.85 & -0.42 & -0.42 \\
$^1\Sigma_g^+$(R) & 13.72 & -0.04 & -0.04 & 13.60 & -0.03 & -0.03 & 13.55 & -0.02 & -0.02 \\ $^1\Sigma_g^+$ & Ryd. & 13.72 & -0.04 & -0.04 & 13.60 & -0.03 & -0.03 & 13.55 & -0.02 & -0.02 \\
$^1\Pi_u$(R) & 14.07 & -0.05 & -0.05 & 13.98 & -0.04 & -0.04 & 13.96 & -0.03 & -0.04 \\ $^1\Pi_u$ & Ryd. & 14.07 & -0.05 & -0.05 & 13.98 & -0.04 & -0.04 & 13.96 & -0.03 & -0.04 \\
$^1\Sigma_u^+$(R) & 13.80 & -0.08 & -0.08 & 13.98 & -0.07 & -0.08 & 14.08 & -0.06 & -0.06 \\ $^1\Sigma_u^+$ & Ryd. & 13.80 & -0.08 & -0.08 & 13.98 & -0.07 & -0.08 & 14.08 & -0.06 & -0.06 \\
$^1\Pi_u$(R) & 14.22 & -0.04 & -0.03 & 14.24 & -0.03 & -0.03 & 14.26 & -0.03 & -0.02 \\ $^1\Pi_u$ & Ryd. & 14.22 & -0.04 & -0.03 & 14.24 & -0.03 & -0.03 & 14.26 & -0.03 & -0.02 \\
\\ \\
$^3\Sigma_u^+(\pi \ra \pis)$ & 9.21 & -1.01 & -0.71 & 9.50 & -1.04 & -0.73 & 9.61 & -1.04 & -0.71 \\ $^3\Sigma_u^+(\pi \ra \pis)$ & Val. & 9.21 & -1.01 & -0.71 & 9.50 & -1.04 & -0.73 & 9.61 & -1.04 & -0.71 \\
$^3\Pi_g(n \ra \pis)$ & 9.58 & -0.57 & -0.34 & 9.85 & -0.58 & -0.33 & 9.96 & -0.57 & -0.23 \\ $^3\Pi_g(n \ra \pis)$ & Val. & 9.58 & -0.57 & -0.34 & 9.85 & -0.58 & -0.33 & 9.96 & -0.57 & -0.23 \\
$^3\Delta_u(\pi \ra \pis)$ & 9.97 & -0.92 & -0.58 & 10.19 & -0.95 & -0.36 & 10.29 & -0.95 & -0.70 \\ $^3\Delta_u(\pi \ra \pis)$ & Val. & 9.97 & -0.92 & -0.58 & 10.19 & -0.95 & -0.36 & 10.29 & -0.95 & -0.70 \\
$^3\Sigma_u^-(\pi \ra \pis)$ & 10.71 & -0.81 & -0.68 & 10.89 & -0.82 & -0.30 & 11.00 & -0.83 & -0.53 \\ $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & 10.71 & -0.81 & -0.68 & 10.89 & -0.82 & -0.30 & 11.00 & -0.83 & -0.53 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table*} \end{table*}
\end{squeezetable}
%%%% TABLE I %%% %%%% TABLE I %%%
%\begin{squeezetable}
%\begin{table*} %\begin{table*}
% \caption{ % \caption{
% Singlet and triplet excitation energies (in eV) of \ce{N2} computed at the BSE@{\GOWO}@HF level for various basis sets. % Singlet and triplet excitation energies (in eV) of \ce{N2} computed at the BSE@{\GOWO}@HF level for various basis sets.
@ -788,6 +791,7 @@ All the static and dynamic BSE calculations have been performed with the softwar
% \end{ruledtabular} % \end{ruledtabular}
% \fnt[1]{Excitation energy larger than the fundamental gap.} % \fnt[1]{Excitation energy larger than the fundamental gap.}
%\end{table*} %\end{table*}
%\end{squeezetable}
First, we investigate the basis set dependency of the dynamical correction as well as the validity of the dTDA (which corresponds to neglecting the dynamical correction originating from the anti-resonant part of the BSE Hamiltonian). First, we investigate the basis set dependency of the dynamical correction as well as the validity of the dTDA (which corresponds to neglecting the dynamical correction originating from the anti-resonant part of the BSE Hamiltonian).
Note that, in the present calculations, the zeroth-order Hamiltonian is always the ``full'' BSE static Hamiltonian, \ie, without TDA. Note that, in the present calculations, the zeroth-order Hamiltonian is always the ``full'' BSE static Hamiltonian, \ie, without TDA.
@ -803,95 +807,95 @@ This outcome is similar to the conclusions of several benchmark studies \cite{Ja
In accordance with the success of the dTDA, the remaining calculations of the present study are performed within this approximation. In accordance with the success of the dTDA, the remaining calculations of the present study are performed within this approximation.
%%% TABLE I %%% %%% TABLE I %%%
%\begin{squeezetable} \begin{squeezetable}
\begin{table*} \begin{table*}
\caption{ \caption{
Singlet excitation energies (in eV) for various molecules obtained with the aug-cc-pVTZ basis set computed at various levels of theory. Singlet excitation energies (in eV) for various molecules obtained with the aug-cc-pVTZ basis set computed at various levels of theory.
The dynamical correction is computed in the dTDA. The dynamical correction is computed in the dTDA.
CT and R stand respectively for charge transfer and Rydberg. CT stands for charge transfer.
\label{tab:BigTabSi} \label{tab:BigTabSi}
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lldddddddddd} \begin{tabular}{llldddddddddd}
& & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\ %& \mc{5}{c}{Density-based methods} \\ & & & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\ %& \mc{5}{c}{Density-based methods} \\
\cline{3-7} \cline{8-12} %\cline{13-17} \cline{4-8} \cline{9-13} %\cline{13-17}
Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$} Mol. & State & Nature & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$}
& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{TBE} \\ & \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{TBE} \\
% & \tabc{B3LYP} & \tabc{PBE0} & \tabc{M06-2X} & \tabc{CAM-B3LYP} & \tabc{LC-$\omega$HPBE} \\ % & \tabc{B3LYP} & \tabc{PBE0} & \tabc{M06-2X} & \tabc{CAM-B3LYP} & \tabc{LC-$\omega$HPBE} \\
\hline \hline
\ce{HCl} & $^1\Pi$(CT) & 13.43 & 8.30 & 8.19 & -0.11 & 1.009 \ce{HCl} & $^1\Pi$ & CT & 13.43 & 8.30 & 8.19 & -0.11 & 1.009
& 6.07 & 7.97 & 7.91 & 7.96 & 7.84 \\ & 6.07 & 7.97 & 7.91 & 7.96 & 7.84 \\
% & 7.33 & 7.59 & 7.56 & 7.52 & 7.96 \\ % & 7.33 & 7.59 & 7.56 & 7.52 & 7.96 \\
\\ \\
\ce{H2O} & $^1B_1(n \ra 3s)$ & 13.58 & 8.09 & 8.00 & -0.09 & 1.007 \ce{H2O} & $^1B_1(n \ra 3s)$ & Ryd. & 13.58 & 8.09 & 8.00 & -0.09 & 1.007
& 7.62 & 7.18 & 7.60 & 7.23 & 7.17 \\ & 7.62 & 7.18 & 7.60 & 7.23 & 7.17 \\
% & 6.92 & 7.18 & 7.46 & 7.13 & 7.50 \\ % & 6.92 & 7.18 & 7.46 & 7.13 & 7.50 \\
& $^1A_2(n \ra 3p)$ & & 9.79 & 9.72 & -0.07 & 1.005 & $^1A_2(n \ra 3p)$ & Ryd. & & 9.79 & 9.72 & -0.07 & 1.005
& 9.41 & 8.84 & 9.36 & 8.89 & 8.92 \\ & 9.41 & 8.84 & 9.36 & 8.89 & 8.92 \\
% & 8.33 & 8.61 & 8.93 & 8.69 & 9.11 \\ % & 8.33 & 8.61 & 8.93 & 8.69 & 9.11 \\
& $^1A_1(n \ra 3s)$ & & 10.42 & 10.35 & -0.07 & 1.006 & $^1A_1(n \ra 3s)$ & Ryd. & & 10.42 & 10.35 & -0.07 & 1.006
& 9.99 & 9.52 & 9.96 & 9.58 & 9.52 \\ & 9.99 & 9.52 & 9.96 & 9.58 & 9.52 \\
% & 9.08 & 9.37 & 9.64 & 9.28 & 9.65 \\ % & 9.08 & 9.37 & 9.64 & 9.28 & 9.65 \\
\\ \\
\ce{N2} & $^1\Pi_g(n \ra \pis)$ & 19.20 & 10.42 & 9.99 & -0.42 & 1.031 \ce{N2} & $^1\Pi_g(n \ra \pis)$ & Val. & 19.20 & 10.42 & 9.99 & -0.42 & 1.031
& 9.66 & 9.48 & 9.41 & 9.44 & 9.34 \\ & 9.66 & 9.48 & 9.41 & 9.44 & 9.34 \\
& $^1\Sigma_u^-(\pi \ra \pis)$ & & 10.11 & 9.66 & -0.45 & 1.029 & $^1\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.11 & 9.66 & -0.45 & 1.029
& 10.31 & 10.26 & 10.00 & 10.32 & 9.88 \\ & 10.31 & 10.26 & 10.00 & 10.32 & 9.88 \\
& $^1\Delta_u(\pi \ra \pis)$ & & 10.75 & 10.33 & -0.42 & 1.030 & $^1\Delta_u(\pi \ra \pis)$ & Val. & & 10.75 & 10.33 & -0.42 & 1.030
& 10.85 & 10.79 & 10.44 & 10.86 & 10.29 \\ & 10.85 & 10.79 & 10.44 & 10.86 & 10.29 \\
& $^1\Sigma_g^+$(R) & & 13.60 & 13.57 & -0.03 & 1.003 & $^1\Sigma_g^+$ & Ryd. & & 13.60 & 13.57 & -0.03 & 1.003
& 13.67 & 12.99 & 13.15 & 12.83 & 12.98 \\ & 13.67 & 12.99 & 13.15 & 12.83 & 12.98 \\
& $^1\Pi_u$(R) & & 13.98 & 13.94 & -0.04 & 1.004 & $^1\Pi_u$ & Ryd. & & 13.98 & 13.94 & -0.04 & 1.004
& 13.64 & 13.32 & 13.43 & 13.15 & 13.03 \\ & 13.64 & 13.32 & 13.43 & 13.15 & 13.03 \\
& $^1\Sigma_u^+$(R) & & 13.98 & 13.91 & -0.07 & 1.008 & $^1\Sigma_u^+$ & Ryd. & & 13.98 & 13.91 & -0.07 & 1.008
& 13.75 & 13.07 & 13.26 & 12.89 & 13.09 \\ & 13.75 & 13.07 & 13.26 & 12.89 & 13.09 \\
& $^1\Pi_u$(R) & & 14.24 & 14.21 & -0.03 & 1.002 & $^1\Pi_u$ & Ryd. & & 14.24 & 14.21 & -0.03 & 1.002
& 14.52 & 14.00 & 13.67 & 13.96 & 13.46 \\ & 14.52 & 14.00 & 13.67 & 13.96 & 13.46 \\
\\ \\
\ce{CO} & $^1\Pi(n \ra \pis)$ & 16.46 & 9.54 & 9.19 & -0.34 & 1.029 & 8.78 & 8.69 & 8.59 & 8.64 & 8.49 \\ \ce{CO} & $^1\Pi(n \ra \pis)$ & Val. & 16.46 & 9.54 & 9.19 & -0.34 & 1.029 & 8.78 & 8.69 & 8.59 & 8.64 & 8.49 \\
& $^1\Sigma^-(\pi \ra \pis)$ & & 10.25 & 9.90 & -0.35 & 1.023 & 10.13 & 10.03 & 9.99 & 10.30 & 9.92 \\ & $^1\Sigma^-(\pi \ra \pis)$ & Val. & & 10.25 & 9.90 & -0.35 & 1.023 & 10.13 & 10.03 & 9.99 & 10.30 & 9.92 \\
& $^1\Delta(\pi \ra \pis)$ & & 10.71 & 10.39 & -0.32 & 1.023 & 10.41 & 10.30 & 10.12 & 10.60 & 10.06 \\ & $^1\Delta(\pi \ra \pis)$ & Val. & & 10.71 & 10.39 & -0.32 & 1.023 & 10.41 & 10.30 & 10.12 & 10.60 & 10.06 \\
& $^1\Sigma^+$(R) & & 11.88 & 11.85 & -0.03 & 1.005 & 11.48 & 11.32 & 11.22 & 11.11 & 10.95 \\ & $^1\Sigma^+$ & Ryd. & & 11.88 & 11.85 & -0.03 & 1.005 & 11.48 & 11.32 & 11.22 & 11.11 & 10.95 \\
& $^1\Sigma^+$(R) & & 12.39 & 12.37 & -0.02 & 1.003 & 11.71 & 11.83 & 11.75 & 11.63 & 11.52 \\ & $^1\Sigma^+$ & Ryd. & & 12.39 & 12.37 & -0.02 & 1.003 & 11.71 & 11.83 & 11.75 & 11.63 & 11.52 \\
& $^1\Pi$(R) & & 12.37 & 12.32 & -0.05 & 1.004 & 12.06 & 12.03 & 11.96 & 11.83 & 11.72 \\ & $^1\Pi$ & Ryd. & & 12.37 & 12.32 & -0.05 & 1.004 & 12.06 & 12.03 & 11.96 & 11.83 & 11.72 \\
\\ \\
\ce{HNO} & $^1A''(n \ra \pis)$ & 11.71 & 2.46 & 1.98 & -0.48 & 1.035 \ce{HNO} & $^1A''(n \ra \pis)$ & Val. & 11.71 & 2.46 & 1.98 & -0.48 & 1.035
& 1.80 & 1.68 & 1.76 & 1.74 & 1.74 \\ & 1.80 & 1.68 & 1.76 & 1.74 & 1.74 \\
% & 1.55 & 1.51 & 0.99 & 1.51 & 1.46 \\ % & 1.55 & 1.51 & 0.99 & 1.51 & 1.46 \\
& $^1A'$(R) & & 7.05 & 7.01 & -0.04 & 1.003 & $^1A'$ & Ryd. & & 7.05 & 7.01 & -0.04 & 1.003
& 5.81 & 5.73 & 6.30 & 5.72 & 6.27 \\ & 5.81 & 5.73 & 6.30 & 5.72 & 6.27 \\
% & 5.63 & 5.85 & 6.22 & 5.94 & 6.33 \\ % & 5.63 & 5.85 & 6.22 & 5.94 & 6.33 \\
\\ \\
\ce{C2H2} & $^1\Sigma_{u}^-(\pi \ra \pis)$ & 12.28 & 7.37 & 7.05 & -0.32 & 1.026 \ce{C2H2} & $^1\Sigma_{u}^-(\pi \ra \pis)$ & Val. & 12.28 & 7.37 & 7.05 & -0.32 & 1.026
& 7.28 & 7.24 & 7.15 & 7.26 & 7.10 \\ & 7.28 & 7.24 & 7.15 & 7.26 & 7.10 \\
& $^1\Delta_{u}(\pi \ra \pis)$ & & 7.74 & 7.46 & -0.29 & 1.025 & $^1\Delta_{u}(\pi \ra \pis)$ & Val. & & 7.74 & 7.46 & -0.29 & 1.025
& 7.62 & 7.56 & 7.48 & 7.59 & 7.44\\ & 7.62 & 7.56 & 7.48 & 7.59 & 7.44\\
\\ \\
%T2: check state ordering in BSE calculation %T2: check state ordering in BSE calculation
\ce{C2H4} & $^1B_{3u}(\pi \ra 3s)$ & 11.49 & 7.64 & 7.62 & -0.03 & 1.004 \ce{C2H4} & $^1B_{3u}(\pi \ra 3s)$ & Ryd. & 11.49 & 7.64 & 7.62 & -0.03 & 1.004
& 7.35 & 7.34 & 7.42 & 7.29 & 7.39 \\ & 7.35 & 7.34 & 7.42 & 7.29 & 7.39 \\
% & 6.63 & 6.88 & 6.94 & 6.93 & 7.57 \\ % & 6.63 & 6.88 & 6.94 & 6.93 & 7.57 \\
& $^1B_{1u}(\pi \ra \pis)$ & & 8.18 & 8.03 & -0.15 & 1.022 & $^1B_{1u}(\pi \ra \pis)$ & Val. & & 8.18 & 8.03 & -0.15 & 1.022
& 7.95 & 7.91 & 8.02 & 7.92 & 7.93 \\ & 7.95 & 7.91 & 8.02 & 7.92 & 7.93 \\
% & 8.06 & 7.51 & 7.50 & 7.46 & 7.64 \\ % & 8.06 & 7.51 & 7.50 & 7.46 & 7.64 \\
& $^1B_{1g}(\pi \ra 3p)$ & & 8.29 & 8.26 & -0.03 & 1.003 & $^1B_{1g}(\pi \ra 3p)$ & Ryd. & & 8.29 & 8.26 & -0.03 & 1.003
& 8.01 & 7.99 & 8.08 & 7.95 & 8.08 \\ & 8.01 & 7.99 & 8.08 & 7.95 & 8.08 \\
% & 7.18 & 7.45 & 7.47 & 7.54 & 8.15 \\ % & 7.18 & 7.45 & 7.47 & 7.54 & 8.15 \\
\\ \\
\ce{CH2O} & $^1A_2(n \ra \pis)$ & 12.00 & 5.03 & 4.68 & -0.35 & 1.027 & 4.04 & 3.92 & 4.01 & 4.07 & 3.98 \\ \ce{CH2O} & $^1A_2(n \ra \pis)$ & Val. & 12.00 & 5.03 & 4.68 & -0.35 & 1.027 & 4.04 & 3.92 & 4.01 & 4.07 & 3.98 \\
& $^1B_2(n \ra 3s)$ & & 7.87 & 7.85 & -0.02 & 1.001 & 6.64 & 6.50 & 7.23 & 6.56 & 7.23 \\ & $^1B_2(n \ra 3s)$ & Ryd. & & 7.87 & 7.85 & -0.02 & 1.001 & 6.64 & 6.50 & 7.23 & 6.56 & 7.23 \\
& $^1B_2(n \ra 3p)$ & & 8.76 & 8.72 & -0.04 & 1.003 & 7.56 & 7.53 & 8.12 & 7.57 & 8.13 \\ & $^1B_2(n \ra 3p)$ & Ryd. & & 8.76 & 8.72 & -0.04 & 1.003 & 7.56 & 7.53 & 8.12 & 7.57 & 8.13 \\
& $^1A_1(n \ra 3p)$ & & 8.85 & 8.84 & -0.01 & 1.000 & 8.16 & 7.47 & 8.21 & 7.52 & 8.23 \\ & $^1A_1(n \ra 3p)$ & Ryd. & & 8.85 & 8.84 & -0.01 & 1.000 & 8.16 & 7.47 & 8.21 & 7.52 & 8.23 \\
& $^1A_2(n \ra 3p)$ & & 8.87 & 8.85 & -0.02 & 1.002 & 8.04 & 7.99 & 8.65 & 8.04 & 8.67 \\ & $^1A_2(n \ra 3p)$ & Ryd. & & 8.87 & 8.85 & -0.02 & 1.002 & 8.04 & 7.99 & 8.65 & 8.04 & 8.67 \\
& $^1B_1(\si \ra \pis)$ & & 10.18 & 9.77 & -0.42 & 1.032 & 9.38 & 9.17 & 9.28 & 9.32 & 9.22 \\ & $^1B_1(\si \ra \pis)$ & Val. & & 10.18 & 9.77 & -0.42 & 1.032 & 9.38 & 9.17 & 9.28 & 9.32 & 9.22 \\
& $^1A_1(\pi \ra \pis)$ & & 10.05 & 9.81 & -0.24 & 1.026 & 9.08 & 9.46 & 9.67 & 9.54 & 9.43 \\ & $^1A_1(\pi \ra \pis)$ & Val. & & 10.05 & 9.81 & -0.24 & 1.026 & 9.08 & 9.46 & 9.67 & 9.54 & 9.43 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table*} \end{table*}
%\end{squeezetable} \end{squeezetable}
%%% TABLE II %%% %%% TABLE II %%%
%\begin{squeezetable} \begin{squeezetable}
\begin{table*} \begin{table*}
\caption{ \caption{
Triplet excitation energies (in eV) for various molecules obtained with the aug-cc-pVTZ basis set computed at various levels of theory. Triplet excitation energies (in eV) for various molecules obtained with the aug-cc-pVTZ basis set computed at various levels of theory.
@ -899,68 +903,68 @@ In accordance with the success of the dTDA, the remaining calculations of the pr
\label{tab:BigTabTr} \label{tab:BigTabTr}
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lldddddddddd} \begin{tabular}{llldddddddddd}
& & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\%& \mc{5}{c}{Density-based methods} \\ & & & \mc{5}{c}{BSE@{\GOWO}@HF} & \mc{5}{c}{Wave function-based methods} \\%& \mc{5}{c}{Density-based methods} \\
\cline{3-7} \cline{8-12} %\cline{13-17} \cline{4-8} \cline{8-13} %\cline{13-17}
Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$} Mol. & State & Nature & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$}
& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{TBE} \\ & \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{TBE} \\
% & \tabc{B3LYP} & \tabc{PBE0} & \tabc{M06-2X} & \tabc{CAM-B3LYP} & \tabc{LC-$\omega$HPBE} \\ % & \tabc{B3LYP} & \tabc{PBE0} & \tabc{M06-2X} & \tabc{CAM-B3LYP} & \tabc{LC-$\omega$HPBE} \\
\hline \hline
\ce{H2O} & $^3B_1(n \ra 3s)$ & 13.58 & 8.14 & 7.98 & -0.15 & 1.014 \ce{H2O} & $^3B_1(n \ra 3s)$ & Ryd. & 13.58 & 8.14 & 7.98 & -0.15 & 1.014
& 7.25 & 6.86 & 7.20 & 6.91 & 6.92 \\ & 7.25 & 6.86 & 7.20 & 6.91 & 6.92 \\
% & 6.55 & 6.75 & 7.12 & 6.72 & 7.04 \\ % & 6.55 & 6.75 & 7.12 & 6.72 & 7.04 \\
& $^3A_2(n \ra 3p)$ & & 9.97 & 9.89 & -0.07 & 1.008 & $^3A_2(n \ra 3p)$ & Ryd. & & 9.97 & 9.89 & -0.07 & 1.008
& 9.24 & 8.72 & 9.20 & 8.77 & 8.91 \\ & 9.24 & 8.72 & 9.20 & 8.77 & 8.91 \\
% & 8.22 & 8.45 & 8.77 & 8.54 & 8.92 \\ % & 8.22 & 8.45 & 8.77 & 8.54 & 8.92 \\
& $^3A_1(n \ra 3s)$ & & 10.28 & 10.13 & -0.15 & 1.012 & $^3A_1(n \ra 3s)$ & Ryd. & & 10.28 & 10.13 & -0.15 & 1.012
& 9.54 & 9.15 & 9.49 & 9.20 & 9.30 \\ & 9.54 & 9.15 & 9.49 & 9.20 & 9.30 \\
% & 8.60 & 8.82 & 9.24 & 8.79 & 9.11 \\ % & 8.60 & 8.82 & 9.24 & 8.79 & 9.11 \\
\\ \\
\ce{N2} & $^3\Sigma_u^+(\pi \ra \pis)$ & 19.20 & 9.50 & 8.46 & -1.04 & 1.060 & 8.20 & 8.15 & 7.66 & 8.19 & 7.70 \\ \ce{N2} & $^3\Sigma_u^+(\pi \ra \pis)$ & Val. & 19.20 & 9.50 & 8.46 & -1.04 & 1.060 & 8.20 & 8.15 & 7.66 & 8.19 & 7.70 \\
& $^3\Pi_g(n \ra \pis)$ & & 9.85 & 9.27 & -0.58 & 1.050 & 8.33 & 8.20 & 8.09 & 8.19 & 8.01 \\ & $^3\Pi_g(n \ra \pis)$ & Val. & & 9.85 & 9.27 & -0.58 & 1.050 & 8.33 & 8.20 & 8.09 & 8.19 & 8.01 \\
& $^3\Delta_u(\pi \ra \pis)$ & & 10.19 & 9.24 & -0.95 & 1.060 & 9.30 & 9.25 & 8.91 & 9.30 & 8.87 \\ & $^3\Delta_u(\pi \ra \pis)$ & Val. & & 10.19 & 9.24 & -0.95 & 1.060 & 9.30 & 9.25 & 8.91 & 9.30 & 8.87 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & & 10.89 & 10.06 & -0.82 & 1.058 & 10.29 & 10.23 & 9.83 & 10.29 & 9.66 \\ & $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.89 & 10.06 & -0.82 & 1.058 & 10.29 & 10.23 & 9.83 & 10.29 & 9.66 \\
\\ \\
\ce{CO} & $^3\Pi(n \ra \pis)$ & 16.46 & 8.10 & 7.33 & -0.77 & 1.055 & 6.51 & 6.45 & 6.36 & 6.42 & 6.28 \\ \ce{CO} & $^3\Pi(n \ra \pis)$ & Val. & 16.46 & 8.10 & 7.33 & -0.77 & 1.055 & 6.51 & 6.45 & 6.36 & 6.42 & 6.28 \\
& $^3\Sigma^+(\pi \ra \pis)$ & & 9.61 & 9.04 & -0.57 & 1.037 & 8.63 & 8.54 & 8.34 & 8.72 & 8.45 \\ & $^3\Sigma^+(\pi \ra \pis)$ & Val. & & 9.61 & 9.04 & -0.57 & 1.037 & 8.63 & 8.54 & 8.34 & 8.72 & 8.45 \\
& $^3\Delta(\pi \ra \pis)$ & & 10.20 & 9.69 & -0.50 & 1.036 & 9.44 & 9.33 & 9.23 & 9.56 & 9.27 \\ & $^3\Delta(\pi \ra \pis)$ & Val. & & 10.20 & 9.69 & -0.50 & 1.036 & 9.44 & 9.33 & 9.23 & 9.56 & 9.27 \\
& $^3\Sigma_u^-(\pi \ra \pis)$ & & 10.79 & 10.38 & -0.42 & 1.034 & 10.10 & 10.01 & 9.81 & 10.27 & 9.80 \\ & $^3\Sigma_u^-(\pi \ra \pis)$ & Val. & & 10.79 & 10.38 & -0.42 & 1.034 & 10.10 & 10.01 & 9.81 & 10.27 & 9.80 \\
& $^3\Sigma_u^+$(R) & & 11.48 & 11.38 & -0.10 & 1.010 & 10.98 & 10.83 & 10.71 & 10.60 & 10.47 \\ & $^3\Sigma_u^+$ & Ryd. & & 11.48 & 11.38 & -0.10 & 1.010 & 10.98 & 10.83 & 10.71 & 10.60 & 10.47 \\
\\ \\
\ce{HNO} & $^3A''(n \ra \pis)$ & 11.71 & 3.05 & 2.35 & -0.71 & 1.069 \ce{HNO} & $^3A''(n \ra \pis)$ & Val. & 11.71 & 3.05 & 2.35 & -0.71 & 1.069
& 0.91 & 0.78 & 0.85 & 0.84 & 0.88 \\ & 0.91 & 0.78 & 0.85 & 0.84 & 0.88 \\
% & -0.47 & -0.61 & 0.36 & -0.49 & -0.58 \\ % & -0.47 & -0.61 & 0.36 & -0.49 & -0.58 \\
& $^3A'(\pi \ra \pis)$ & & 6.69 & 6.70 & 0.01 & 1.000 & $^3A'(\pi \ra \pis)$ & Val. & & 6.69 & 6.70 & 0.01 & 1.000
& 5.72 & 5.46 & 5.49 & 5.44 & 5.61 \\ & 5.72 & 5.46 & 5.49 & 5.44 & 5.61 \\
% & 4.73 & 4.46 & 5.27 & 4.55 & 4.57 \\ % & 4.73 & 4.46 & 5.27 & 4.55 & 4.57 \\
\\ \\
\ce{C2H2} & $^3\Sigma_{u}^+(\pi \ra \pis)$ & 12.28 & 7.22 & 6.48 & -0.73 & 1.056 \ce{C2H2} & $^3\Sigma_{u}^+(\pi \ra \pis)$ & Val. & 12.28 & 7.22 & 6.48 & -0.73 & 1.056
& 5.79 & 5.75 & 5.45 & 5.76 & 5.53 \\ & 5.79 & 5.75 & 5.45 & 5.76 & 5.53 \\
& $^3\Delta_{u}(\pi \ra \pis)$ & & 7.70 & 7.08 & -0.62 & 1.053 & $^3\Delta_{u}(\pi \ra \pis)$ & Val. & & 7.70 & 7.08 & -0.62 & 1.053
& 6.62 & 6.57 & 6.41 & 6.60 & 6.40 \\ & 6.62 & 6.57 & 6.41 & 6.60 & 6.40 \\
& $^3\Sigma_{u}^-(\pi \ra \pis)$ & & 8.16 & 7.66 & -0.51 & 1.049 & $^3\Sigma_{u}^-(\pi \ra \pis)$ & Val. & & 8.16 & 7.66 & -0.51 & 1.049
& 7.31 & 7.27 & 7.12 & 7.29 & 7.08 \\ & 7.31 & 7.27 & 7.12 & 7.29 & 7.08 \\
\\ \\
\ce{C2H4} & $^3B_{1u}(\pi \ra \pis)$ & 11.49 & 6.54 & 5.85 & -0.69 & 1.065 \ce{C2H4} & $^3B_{1u}(\pi \ra \pis)$ & Val. & 11.49 & 6.54 & 5.85 & -0.69 & 1.065
& 4.62 & 4.59 & 4.46 & 4.59 & 4.54 \\ & 4.62 & 4.59 & 4.46 & 4.59 & 4.54 \\
% & 4.07 & 3.84 & 4.54 & 3.92 & 3.55 \\ % & 4.07 & 3.84 & 4.54 & 3.92 & 3.55 \\
& $^3B_{3u}(\pi \ra 3s)$ & & 7.61 & 7.55 & -0.06 & 1.008 & $^3B_{3u}(\pi \ra 3s)$ & Ryd. & & 7.61 & 7.55 & -0.06 & 1.008
& 7.26 & 7.23 & 7.29 & 7.19 & 7.23 \\ & 7.26 & 7.23 & 7.29 & 7.19 & 7.23 \\
% & 6.54 & 6.74 & 6.90 & 6.83 & 7.41 \\ % & 6.54 & 6.74 & 6.90 & 6.83 & 7.41 \\
& $^3B_{1g}(\pi \ra 3p)$ & & 8.36 & 8.31 & -0.05 & 1.006 % 4th state in BSE & $^3B_{1g}(\pi \ra 3p)$ & Ryd. & & 8.36 & 8.31 & -0.05 & 1.006 % 4th state in BSE
& 7.97 & 7.95 & 8.03 & 7.91 & 7.98 \\ & 7.97 & 7.95 & 8.03 & 7.91 & 7.98 \\
% & 7.14 & 7.34 & 7.46 & 7.45 & 7.53 \\ % & 7.14 & 7.34 & 7.46 & 7.45 & 7.53 \\
\\ \\
\ce{CH2O} & $^3A_2(n \ra \pis)$ & 12.00 & 5.53 & 5.05 & -0.47 & 1.049 & 3.58 & 3.46 & 3.56 & 3.59 & 3.58 \\ \ce{CH2O} & $^3A_2(n \ra \pis)$ & Val. & 12.00 & 5.53 & 5.05 & -0.47 & 1.049 & 3.58 & 3.46 & 3.56 & 3.59 & 3.58 \\
& $^3A_1(\pi \ra \pis)$ & & 8.15 & 7.32 & -0.83 & 1.067 & 6.27 & 6.20 & 5.97 & 6.30 & 6.06 \\ & $^3A_1(\pi \ra \pis)$ & Val. & & 8.15 & 7.32 & -0.83 & 1.067 & 6.27 & 6.20 & 5.97 & 6.30 & 6.06 \\
& $^3B_2(n \ra 3s)$ & & 7.51 & 7.54 & 0.03 & 0.994 & 6.66 & 6.39 & 7.08 & 6.44 & 7.06 \\ & $^3B_2(n \ra 3s)$ & Ryd. & & 7.51 & 7.54 & 0.03 & 0.994 & 6.66 & 6.39 & 7.08 & 6.44 & 7.06 \\
% & $^3B_2(n \ra 3p)$* & & 8.62 & 8.61 & -0.00 & 0.998 & 7.52 & 7.41 & 7.94 & 7.45 & 7.94 \\ % & $^3B_2(n \ra 3p)$* & & 8.62 & 8.61 & -0.00 & 0.998 & 7.52 & 7.41 & 7.94 & 7.45 & 7.94 \\
% & $^3A_1(n \ra 3p)$* & & 8.75 & 8.69 & -0.06 & 1.007 & 7.68 & 7.40 & 8.09 & 7.44 & 8.10 \\ % & $^3A_1(n \ra 3p)$* & & 8.75 & 8.69 & -0.06 & 1.007 & 7.68 & 7.40 & 8.09 & 7.44 & 8.10 \\
% & $^3B_1(n \ra 3d)$* & & 8.82 & 8.82 & -0.01 & 1.000 & 8.57 & 8.39 & 8.43 & 8.52 & 8.42 \\ % & $^3B_1(n \ra 3d)$* & & 8.82 & 8.82 & -0.01 & 1.000 & 8.57 & 8.39 & 8.43 & 8.52 & 8.42 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table*} \end{table*}
%\end{squeezetable} \end{squeezetable}
Tables \ref{tab:BigTabSi} and \ref{tab:BigTabTr} report, respectively, singlet and triplet excitation energies for various molecules computed at the BSE@{\GOWO}@HF level and with the aug-cc-pVTZ basis set. Tables \ref{tab:BigTabSi} and \ref{tab:BigTabTr} report, respectively, singlet and triplet excitation energies for various molecules computed at the BSE@{\GOWO}@HF level and with the aug-cc-pVTZ basis set.
For comparative purposes, excitation energies obtained with the same basis set and several second-order wave function methods [CIS(D), ADC(2), CCSD, and CC2] are also reported. For comparative purposes, excitation energies obtained with the same basis set and several second-order wave function methods [CIS(D), ADC(2), CCSD, and CC2] are also reported.
@ -975,28 +979,35 @@ Moreover, we have observed that an iterative, self-consistent resolution [where
\caption{ \caption{
Singlet excitation energies (in eV) for various molecules obtained with the aug-cc-pVDZ basis set computed at various levels of theory. Singlet excitation energies (in eV) for various molecules obtained with the aug-cc-pVDZ basis set computed at various levels of theory.
The dynamical correction is computed in the dTDA. The dynamical correction is computed in the dTDA.
V and R stand for valence and Rydberg, respectively.
\label{tab:BigTabSi} \label{tab:BigTabSi}
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lldddddd} \begin{tabular}{llldddddd}
& & \mc{5}{c}{BSE@{\GOWO}@HF} \\ & & & \mc{5}{c}{BSE@{\GOWO}@HF} \\
\cline{3-7} \cline{4-8}
Mol. & State & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$} & \tabc{TBE} \\ Mol. & State & Nature & \tabc{$\Eg^{\GW}$} & \tabc{$\Om{s}{\stat}$} & \tabc{$\Om{s}{\dyn}$} & \tabc{$\Delta\Om{s}{\dyn}$} & \tabc{$Z_{s}$} & \tabc{TBE} \\
\hline \hline
streptocyanine & $^1B_2(\pi \ra \pis)$ & 7.66 & 7.51 & -0.15 & 1.019 & 7.13 \\ acrolein & $^1A''(n \ra \pis)$ & Val. & \\
& $^3B_2(\pi \ra \pis)$ & 6.52 & 6.11 & -0.41 & 1.042 & 5.52 \\
\\ \\
diacetylene & $^1\Sigma_u^-(\pi \ra \pis)$ \\ butadiene & $^1B_u(\pi \ra \pis)$ & Val. & 9.88 & 6.25 & 6.13 & -0.12 & 1.019 \\
& $^1\Delta_u(\pi \ra \pis)$ \\ & $^1A_g(\pi \ra \pis)$ & Val. & & 6.88 & 6.86 & -0.03 & 1.003 \\
& $^3\Sigma_u^+(\pi \ra \pis)$ \\ & $^3B_u(\pi \ra \pis)$ & Val. & & 5.09 & 4.61 & -0.48 & 1.054 \\
& $^3\Delta_u(\pi \ra \pis)$ \\
\\ \\
butadiene & $^1B_u(\pi \ra \pis)$ \\ diacetylene & $^1\Sigma_u^-(\pi \ra \pis)$ & Val. \\
& $^1B_g(\pi \ra 3s)$ \\ & $^1\Delta_u(\pi \ra \pis)$ & Val. \\
& $^1A_g(\pi \ra \pis)$ \\ & $^3\Sigma_u^+(\pi \ra \pis)$ & Val. \\
acrolein & \\ & $^3\Delta_u(\pi \ra \pis)$ & Val. \\
glyoxal & \\ \\
glyoxal & $^1A_u(n \ra \pis)$ & Val. & 10.90 & 3.46 & 3.14 & -0.33 & 1.028 \\
& $^1B_g(n \ra \pis)$ & Val. & & 4.96 & 4.55 & -0.41 & 1.034 \\
& $^1B_g(n \ra \pis)$ & Val. & & & & & \\
& $^1B_u(n \ra 3p)$ & Ryd. & & & & & \\
& $^3A_u(n \ra \pis)$ & Val. & & 3.94 & 3.57 & -0.37 & 1.045 \\
& $^3B_g(n \ra \pis)$ & Val. & & 5.70 & 5.30 & -0.40 & 1.051 \\
& $^3B_u(\pi \ra \pis)$ & Val. & & 6.69 & 6.07 & -0.62 & 1.057 \\
\\
streptocyanine & $^1B_2(\pi \ra \pis)$ & Val. & 7.66 & 7.51 & -0.15 & 1.019 & 7.13 \\
& $^3B_2(\pi \ra \pis)$ & Val. & 6.52 & 6.11 & -0.41 & 1.042 & 5.52 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table*} \end{table*}

6341
Data/CH2O_aVTZ.out Normal file
View File

File diff suppressed because it is too large Load Diff

4048
Data/glyoxal_aVDZ.out Normal file
View File

File diff suppressed because it is too large Load Diff