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Pierre-Francois Loos 2021-01-21 13:02:33 +01:00
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1
Manuscript/sfBSE-SI.tex
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@ -212,7 +212,6 @@
Excitation energies with respect to the $\text{X}\,{}^1 \Sigma_g^+$ ground state of the $\text{B}\,{}^1\Sigma_u^+$ (red), $\text{E}\,{}^1\Sigma_g^+$ (black), and $\text{F}\,{}^1\Sigma_g^+$ (blue) states of \ce{H2} obtained with the cc-pVQZ basis at the (SF-)TD-B3LYP (top), (SF-) TD-BLYP (middle), and (SF-)dBSE (bottom) levels of theory. Excitation energies with respect to the $\text{X}\,{}^1 \Sigma_g^+$ ground state of the $\text{B}\,{}^1\Sigma_u^+$ (red), $\text{E}\,{}^1\Sigma_g^+$ (black), and $\text{F}\,{}^1\Sigma_g^+$ (blue) states of \ce{H2} obtained with the cc-pVQZ basis at the (SF-)TD-B3LYP (top), (SF-) TD-BLYP (middle), and (SF-)dBSE (bottom) levels of theory.
The reference EOM-CCSD excitation energies are represented as solid lines, while the results obtained with and without spin-flip are represented as dashed and dotted lines, respectively. The reference EOM-CCSD excitation energies are represented as solid lines, while the results obtained with and without spin-flip are represented as dashed and dotted lines, respectively.
All the spin-conserved and spin-flip calculations have been performed with an unrestricted reference. All the spin-conserved and spin-flip calculations have been performed with an unrestricted reference.
The raw data are reported in the {\SI}.
\label{fig:H2}} \label{fig:H2}}
\end{figure} \end{figure}
%%% %%% %%% %%% %%% %%%

18
Manuscript/sfBSE.tex
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@ -208,7 +208,7 @@ Dynamical corrections to the static BSE optical excitations are taken into accou
The performance of the present spin-flip BSE formalism is illustrated by computing excited-state energies of the beryllium atom, the hydrogen molecule at various bond lengths, and cyclobutadiene in its rectangular and square-planar geometries. The performance of the present spin-flip BSE formalism is illustrated by computing excited-state energies of the beryllium atom, the hydrogen molecule at various bond lengths, and cyclobutadiene in its rectangular and square-planar geometries.
\bigskip \bigskip
\begin{center} \begin{center}
\boxed{\includegraphics[width=0.5\linewidth]{TOC}} \boxed{\includegraphics[width=0.4\linewidth]{TOC}}
\end{center} \end{center}
\bigskip \bigskip
\end{abstract} \end{abstract}
@ -802,12 +802,12 @@ Finally, both SF-ADC(2)-x and SF-ADC(3) yield excitation energies very close to
%\begin{squeezetable} %\begin{squeezetable}
\begin{table*} \begin{table*}
\caption{ \caption{
Excitation energies (in eV) with respect to the $^1S(1s^2 2s^2)$ singlet ground state of \ce{Be} obtained for various methods with the 6-31G basis set. Excitation energies (in eV) with respect to the $^1S(1s^2 2s^2)$ singlet ground state of \ce{Be} obtained at various methods with the 6-31G basis set.
All the spin-flip calculations have been performed with a UHF reference. All the spin-flip calculations have been performed with an unrestricted reference.
The $\expval{\hS^2}$ value associated with each state is reported in parenthesis (when available). The $\expval{\hS^2}$ value associated with each state is reported in parenthesis (when available).
\label{tab:Be}} \label{tab:Be}}
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lcccccccccc} \begin{tabular}{llllll}
& \mc{5}{c}{Excitation energies (eV)} \\ & \mc{5}{c}{Excitation energies (eV)} \\
% & \mc{5}{c}{6-31G} & \mc{5}{c}{aug-cc-pVQZ} \\ % & \mc{5}{c}{6-31G} & \mc{5}{c}{aug-cc-pVQZ} \\
\cline{2-6} %\cline{7-11} \cline{2-6} %\cline{7-11}
@ -841,9 +841,9 @@ Finally, both SF-ADC(2)-x and SF-ADC(3) yield excitation energies very close to
\begin{figure} \begin{figure}
\includegraphics[width=\linewidth]{fig1} \includegraphics[width=\linewidth]{fig1}
\caption{ \caption{
Excitation energies (in eV) with respect to the $^1S(1s^2 2s^2)$ singlet ground state of \ce{Be} obtained with the 6-31G basis for various levels of theory: Excitation energies (in eV) with respect to the $^1S(1s^2 2s^2)$ singlet ground state of \ce{Be} obtained with the 6-31G basis at various levels of theory:
SF-TD-DFT \cite{Casanova_2020} (red), SF-CIS \cite{Krylov_2001a} (purple), SF-BSE (blue), SF-ADC (orange), and FCI \cite{Krylov_2001a} (black). SF-TD-DFT \cite{Casanova_2020} (red), SF-CIS \cite{Krylov_2001a} (purple), SF-BSE (blue), SF-ADC (orange), and FCI \cite{Krylov_2001a} (black).
All these spin-flip calculations have been performed with a UHF reference. All the spin-flip calculations have been performed with an unrestricted reference.
\label{fig:Be}} \label{fig:Be}}
\end{figure} \end{figure}
%%% %%% %%% %%% %%% %%% %%% %%%
@ -957,7 +957,7 @@ This issue does not appear at the SF-BSE, SF-ADC, and SF-EOM-SF-CCSD levels.
Vertical excitation energies of CBD. Vertical excitation energies of CBD.
Left: $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{1g}$ states at the $D_{2h}$ rectangular equilibrium geometry of the $\text{X}\,{}^1 A_{g}$ ground state (see Table \ref{tab:CBD_D2h} for the raw data). Left: $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{1g}$ states at the $D_{2h}$ rectangular equilibrium geometry of the $\text{X}\,{}^1 A_{g}$ ground state (see Table \ref{tab:CBD_D2h} for the raw data).
Right: $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states at the $D_{4h}$ square-planar equilibrium geometry of the $1\,{}^3 A_{2g}$ state (see Table \ref{tab:CBD_D4h} for the raw data). Right: $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states at the $D_{4h}$ square-planar equilibrium geometry of the $1\,{}^3 A_{2g}$ state (see Table \ref{tab:CBD_D4h} for the raw data).
All the spin-flip calculations have been performed with a UHF reference and the cc-pVTZ basis set. All the spin-flip calculations have been performed with an unrestricted reference and the cc-pVTZ basis set.
\label{fig:CBD}} \label{fig:CBD}}
\end{figure*} \end{figure*}
%%% %%% %%% %%% %%% %%%
@ -966,7 +966,7 @@ This issue does not appear at the SF-BSE, SF-ADC, and SF-EOM-SF-CCSD levels.
\begin{table} \begin{table}
\caption{ \caption{
Vertical excitation energies (with respect to the singlet $\text{X}\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{g}$ states of CBD at the $D_{2h}$ rectangular equilibrium geometry of the $\text{X}\,{}^1 A_{g}$ ground state. Vertical excitation energies (with respect to the singlet $\text{X}\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{g}$ states of CBD at the $D_{2h}$ rectangular equilibrium geometry of the $\text{X}\,{}^1 A_{g}$ ground state.
All the spin-flip calculations have been performed with a UHF reference and the cc-pVTZ basis set. All the spin-flip calculations have been performed with an unrestricted reference and the cc-pVTZ basis set.
\label{tab:CBD_D2h}} \label{tab:CBD_D2h}}
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lrrr} \begin{tabular}{lrrr}
@ -998,7 +998,7 @@ This issue does not appear at the SF-BSE, SF-ADC, and SF-EOM-SF-CCSD levels.
\begin{table} \begin{table}
\caption{ \caption{
Vertical excitation energies (with respect to the singlet $\text{X}\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states of CBD at the $D_{4h}$ square-planar equilibrium geometry of the $1\,{}^3A_{2g}$ state. Vertical excitation energies (with respect to the singlet $\text{X}\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states of CBD at the $D_{4h}$ square-planar equilibrium geometry of the $1\,{}^3A_{2g}$ state.
All the spin-flip calculations have been performed with a UHF reference and the cc-pVTZ basis set. All the spin-flip calculations have been performed with an unrestricted reference and the cc-pVTZ basis set.
\label{tab:CBD_D4h}} \label{tab:CBD_D4h}}
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lrrr} \begin{tabular}{lrrr}