From f68c0ffee19886bad75990fb2252b94c9414d255 Mon Sep 17 00:00:00 2001
From: Pierre-Francois Loos <pierrefrancois.loos@gmail.com>
Date: Fri, 30 Oct 2020 13:12:56 +0100
Subject: [PATCH] Tab for Be

---
 sfBSE.tex | 29 ++++++++++++++++++++++++-----
 1 file changed, 24 insertions(+), 5 deletions(-)

diff --git a/sfBSE.tex b/sfBSE.tex
index 5deaa73..44b08ec 100644
--- a/sfBSE.tex
+++ b/sfBSE.tex
@@ -129,7 +129,7 @@ where the expressions of the matrix elements of $\bA{}{}$ and $\bB{}{}$ are spec
 The spin structure of these matrices, though, is general 
 \begin{subequations}
 \begin{align}
-\label{eq:LR-RPA-AB}
+\label{eq:LR-RPA-AB-sc}
 	\bA{}{\spc} & = \begin{pmatrix}
 		\bA{}{\upup,\upup}	&	\bA{}{\upup,\dwdw}	\\
 		\bA{}{\dwdw,\upup}	&	\bA{}{\dwdw,\dwdw}	\\
@@ -140,7 +140,7 @@ The spin structure of these matrices, though, is general
 		\bB{}{\dwdw,\upup}	&	\bB{}{\dwdw,\dwdw}	\\
 	\end{pmatrix}
 \\
-\label{eq:LR-RPA-AB}
+\label{eq:LR-RPA-AB-sf}
 	\bA{}{\spf} & = \begin{pmatrix}
 		\bA{}{\updw,\updw}	&	\bO	\\
 		\bO					&	\bA{}{\dwup,\dwup}	\\
@@ -215,6 +215,7 @@ Within the acclaimed $GW$ approximation, \cite{Hedin_1965,Golze_2019} the exchan
 \end{split}
 \end{equation}
 is, like the one-body Green's function, spin-diagonal, and its spectral representation reads
+\begin{subequations}
 \begin{gather}
 	\Sig{p_\sig q_\sig}{\x}
 	= - \sum_{i} \ERI{p_\sig i_\sig}{i_\sig q_\sig}	 
@@ -226,6 +227,7 @@ is, like the one-body Green's function, spin-diagonal, and its spectral represen
 	& + \sum_{am} \frac{\ERI{p_\sig a_\sig}{m} \ERI{q_\sig a_\sig}{m}}{\omega - \e{a_\sig} - \Om{m}{\spc,\RPA} + i \eta}			 
 \end{split}
 \end{gather}
+\end{subequations}
 where the self-energy has been split in its exchange (x) and correlation (c) contributions.
 The Dyson equation linking the Green's function and the self-energy holds separately for each spin component 
 \begin{equation}
@@ -550,9 +552,26 @@ All the static and dynamic BSE calculations have been performed with the softwar
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %%% TABLE I %%%
-%\begin{table}
-%
-%\end{table}
+\begin{squeezetable}
+\begin{table*}
+	\caption{
+	Spin-flip excitations of \ce{Be} obtained for various methods with the 6-31G basis.
+	The $GW$ calculations are performed with a HF starting point.
+	\label{tab:Be}}
+	\begin{ruledtabular}
+		\begin{tabular}{lcccccccccccc}
+			State			&	TD-BLYP		&	TD-B3LYP	&	TD-BHHLYP		&	CIS		
+							&	BSE@{\GOWO}	&	BSE@{\evGW}	&	dBSE@{\GOWO}	&	dBSE@{\evGW}	
+							&	ADC(2)		&	ADC(2)-x	&	ADC(3)			&	FCI	\\
+			\hline
+			$^3P(1s^22s2p)$	&	&	&	&	2.111	&	&	&	&	&	&	&	&	2.862	\\
+			$^1P(1s^22s2p)$	&	&	&	&	6.036	&	&	&	&	&	&	&	&	6.577	\\
+			$^3P(1s^22p^2)$	&	&	&	&	7.480	&	&	&	&	&	&	&	&	7.669	\\
+			$^1P(1s^22p^2)$	&	&	&	&	8.945	&	&	&	&	&	&	&	&	8.624	\\
+		\end{tabular}
+	\end{ruledtabular}
+\end{table*}
+\end{squeezetable}
 %%% %%% %%% %%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Conclusion}