tables for Enzo

Manuscript/sfBSE.tex

@@ -595,7 +595,7 @@ The TD-DFT calculations have been performed with Q-CHEM 5.2.1 \cite{qchem4} and
 \begin{table*}
 	\caption{
 	Spin-flip excitations (in  eV) of \ce{Be} obtained for various methods with the 6-31G basis.
-	The $GW$ calculations are performed with a HF starting point.
+	The $GW$ calculations are performed with an UHF starting point.
 	\label{tab:Be}}
 	\begin{ruledtabular}
 		\begin{tabular}{lcccccccccccc}
@@ -729,13 +729,73 @@ The TD-DFT calculations have been performed with Q-CHEM 5.2.1 \cite{qchem4} and
 \label{sec:CBD}
 %===============================
 
-Cyclobutadiene (CBD) is an interesting example as its electronic character of its ground state can be tune via geometrical deformation. \cite{Balkova_1994,Manohar_2008,Lefrancois_2015}
+Cyclobutadiene (CBD) is an interesting example as its electronic character of its ground state can be tune via geometrical deformation. \cite{Balkova_1994,Manohar_2008,Lefrancois_2015,Casanova_2020}
 %with potential large spin contamination.
-In its $D_{2h}$ rectangular $^1 A_g$ ground-state equilibrium geometry, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are non-degenerate, and the singlet ground state can be safely labeled as single-reference with well-defined doubly-occupied orbitals
+In its $D_{2h}$ rectangular $^1 A_g$ singlet ground-state equilibrium geometry, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are non-degenerate, and the singlet ground state can be safely labeled as single-reference with well-defined doubly-occupied orbitals
-However, in its $D_{4h}$ square-planar $^3 A_{2g}$ ground-state equilibrium geometry, the HOMO and LUMO are strictly degenerate, and the electronic ground state (which is still of singlet nature with $B_{1g}$ spatial symmetry, hence violating Hund's rule) is strongly multi-reference with singly occupied orbitals.
+However, in its $D_{4h}$ square-planar $^3 A_{2g}$ triplet round-state equilibrium geometry, the HOMO and LUMO are strictly degenerate, and the electronic ground state (which is still of singlet nature with $B_{1g}$ spatial symmetry, hence violating Hund's rule) is strongly multi-reference with singly occupied orbitals.
 In this case, single-reference methods notoriously fail.
 Nonetheless, the lowest triplet state of symmetry $^3 A_{2g}$ remains of single-reference character and is then a perfect starting point for spin-flip calculations.
 
+The $D_{2h}$ and $D_{4h}$ optimized geometries of the $^1 A_g$ and $^3 A_{2g}$ states of CBD have been extracted from Ref.~\onlinecite{Manohar_2008} and have been obtained at the CCSD(T)/cc-pVTZ level.
+EOM-CCSD and SF-ADC calculations have been taken from Refs.~\onlinecite{Manohar_2008} and Ref.~\onlinecite{Lefrancois_2015}.
+All of them have been obtained with a UHF reference like the SF-BSE calculations performed here.
+
+%%% TABLE ?? %%%
+\begin{table}
+	\caption{
+	Vertical excitation energies (with respect to the singlet $X\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{1g}$ states at the $D_{2h}$ rectangular equilibrium geometry of the $X\,{}^1 A_{g}$ singlet  ground state.
+	\label{tab:CBD_D2h}}
+	\begin{ruledtabular}
+		\begin{tabular}{lccc}
+									&	\mc{3}{c}{Excitation energies (eV)}	\\
+									\cline{2-4}
+			Method					&	$1\,{}^3B_{1g}$	&	$1\,{}^1B_{1g}$	&	$2\,{}^1A_{1g}$	\\
+			\hline
+			EOM-SF-CIS\fnm[1]			&	&	&	\\
+			EOM-SF-CCSD\fnm[1]			&	&	&	\\
+			EOM-SF-CCSD(fT)\fnm[1]		&	&	&	\\
+			EOM-SF-CCSD(dT)\fnm[1]		&	&	&	\\
+			SF-ADC(2)-s\fnm[2]			&	&	&	\\
+			SF-ADC(2)-x\fnm[2]			&	&	&	\\
+			SF-ADC(3)\fnm[2]			&	&	&	\\
+			SF-BSE@{\GOWO}@UHF\fnm[3]	&	&	&	\\
+			SF-dBSE@{\GOWO}@UHF\fnm[3]	&	&	&	\\
+		\end{tabular}
+	\end{ruledtabular}
+	\fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.}
+	\fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015} using a UHF reference.}
+	\fnt[3]{This work.}
+\end{table}
+%%% %%% %%% %%%
+
+%%% TABLE ?? %%%
+\begin{table}
+	\caption{
+	Vertical excitation energies (with respect to the singlet $X\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states at the $D_{4h}$ square-planar equilibrium geometry of the $X\,{}^1B_{1g}$ singlet ground state.
+	\label{tab:CBD_D2h}}
+	\begin{ruledtabular}
+		\begin{tabular}{lccc}
+									&	\mc{3}{c}{Excitation energies (eV)}	\\
+									\cline{2-4}
+			Method					&	$1\,{}^3A_{2g}$	&	$2\,{}^1A_{1g}$	&	$1\,{}^1B_{2g}$	\\
+			\hline
+			EOM-SF-CIS\fnm[1]			&	&	&	\\
+			EOM-SF-CCSD\fnm[1]			&	&	&	\\
+			EOM-SF-CCSD(fT)\fnm[1]		&	&	&	\\
+			EOM-SF-CCSD(dT)\fnm[1]		&	&	&	\\
+			SF-ADC(2)-s\fnm[2]			&	&	&	\\
+			SF-ADC(2)-x\fnm[2]			&	&	&	\\
+			SF-ADC(3)\fnm[2]			&	&	&	\\
+			SF-BSE@{\GOWO}@UHF\fnm[3]	&	&	&	\\
+			SF-dBSE@{\GOWO}@UHF\fnm[3]	&	&	&	\\
+		\end{tabular}
+	\end{ruledtabular}
+	\fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.}
+	\fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015} using a UHF reference.}
+	\fnt[3]{This work.}
+\end{table}
+%%% %%% %%% %%%
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Conclusion}
 \label{sec:ccl}