new tables with errors

Manuscript/Ec.tex

@@ -365,8 +365,10 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
 	\label{fig:vsEPT2}}
 \end{figure*}
 
+\begin{squeezetable}
 \begin{table*}
 	\caption{Total energy $E$ (in \SI{}{\hartree}) and correlation energy $\Delta E$ (in \SI{}{\milli\hartree}) for the frozen-core ground state of five-membered rings in the cc-pVDZ basis set.
+	For the CIPSI estimates of the correlation energy, the fitting error associated with the 4-point linear fit is reported in parenthesis.
 	\label{tab:Tab5-VDZ}}
 	\begin{ruledtabular}
 	\begin{tabular}{lcccccccccc}
@@ -392,14 +394,16 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
 		CCSD(T)	&	$-193.5439$	&	$-735.6$	&	$-229.4073$	&	$-764.0$	&	$-225.6099$	&	$-774.5$	&	$-209.5836$	&	$-754.9$	&	$-552.0458$	&	$-724.8$
 \\
 		\hline
-		CIPSI	&					&	$-739.3$			&					&	$-768.1$		&					&	$-778.3$				&					&	$-758.4$			&			&	$-729.1$\\	
+		CIPSI	&					&	$-739.3(1)$			&					&	$-768.1(2)$		&					&	$-778.3(1)$				&					&	$-758.4(2)$			&			&	$-729.1(3)$\\	
 	\end{tabular}
 	\end{ruledtabular}
 \end{table*}
+\end{squeezetable}
 
 \begin{squeezetable}
 \begin{table*}
 	\caption{Total energy $E$ (in \SI{}{\hartree}) and correlation energy $\Delta E$ (in \SI{}{\milli\hartree}) for the frozen-core ground state of six-membered rings in the cc-pVDZ basis set.
+	For the CIPSI estimates of the correlation energy, the fitting error associated with the 4-point linear fit is reported in parenthesis.
 	\label{tab:Tab6-VDZ}}
 	\begin{ruledtabular}
 	\begin{tabular}{lcccccccccccccc}
@@ -425,18 +429,127 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
 		\hline
 		CCSD(T)	&	$-231.5798$	&	$-857.5$	&	$-263.6024$		&	$-899.4$	&	$-263.5740$	&	$-904.1$	&	$-247.5929$	&	$-877.7$	&	$-263.6099$	&	$-896.2$	&	$-295.5680$		&	$-952.2$	&	$-279.6305$		&	$-913.1$	\\
 		\hline
-		CIPSI	&				&	$-863.0$		&				&	$-904.6$		&				&	$-908.8$		&				&	$-883.4$		&				&	$-900.4$		&		&	$-957.3$		&		&	$-918.5$\\
+		CIPSI	&				&	$-863.0(4)$		&				&	$-904.6(6)$		&				&	$-908.8(2)$		&				&	$-883.4(0)$		&				&	$-900.4(4)$		&		&	$-957.3(2)$		&		&	$-918.5(5)$\\
 	\end{tabular}
 	\end{ruledtabular}
 \end{table*}
 \end{squeezetable}    
 
+
+\begin{squeezetable}    
+\begin{table}
+	\caption{
+	\label{tab:fit}}
+	\begin{ruledtabular}
+	\begin{tabular}{lccc}
+	Molecule	&	Number		&	\mc{2}{c}{Fitting parameter}	\\
+									\cline{3-4}
+				&	 of points	&	$\Delta \Evar$	&	Standard error	\\	
+	\hline
+	Cyclopentadiene	&	3	&	$-739.295$	&	$0.199$	\\
+					&	4	&	$-739.309$	&	$0.088$	\\
+					&	5	&	$-739.230$	&	$0.074$	\\
+					&	6	&	$-739.304$	&	$0.072$	\\
+					&	7	&	$-739.292$	&	$0.055$	\\
+					&	8	&	$-739.119$	&	$0.131$	\\
+	\hline
+	Furan			&	3	&	$-767.790$	&	$0.064$	\\
+					&	4	&	$-768.104$	&	$0.196$	\\
+					&	5	&	$-768.194$	&	$0.135$	\\
+					&	6	&	$-768.060$	&	$0.131$	\\
+					&	7	&	$-768.086$	&	$0.101$	\\
+					&	8	&	$-767.904$	&	$0.154$	\\
+	\hline
+	Imidazole		&	3	&	$-778.295$	&	$0.356$	\\
+					&	4	&	$-778.270$	&	$0.150$	\\
+					&	5	&	$-778.178$	&	$0.105$	\\
+					&	6	&	$-778.174$	&	$0.072$	\\
+					&	7	&	$-778.051$	&	$0.099$	\\
+					&	8	&	$-777.992$	&	$0.089$	\\
+	\hline
+	Pyrrole			&	3	&	$-758.650$	&	$0.321$	\\
+					&	4	&	$-758.389$	&	$0.174$	\\
+					&	5	&	$-758.460$	&	$0.110$	\\
+					&	6	&	$-758.352$	&	$0.100$	\\
+					&	7	&	$-758.347$	&	$0.075$	\\
+					&	8	&	$-758.357$	&	$0.059$	\\
+	\hline
+	Thiophene		&	3	&	$-728.744$	&	$0.691$	\\
+					&	4	&	$-729.052$	&	$0.331$	\\
+					&	5	&	$-728.948$	&	$0.203$	\\
+					&	6	&	$-728.987$	&	$0.140$	\\
+					&	7	&	$-729.067$	&	$0.117$	\\
+					&	8	&	$-728.876$	&	$0.162$	\\
+	\hline
+	Benzene			&	3	&	$-862.325$	&	$0.279$	\\
+					&	4	&	$-863.024$	&	$0.424$	\\
+					&	5	&	$-862.890$	&	$0.266$	\\
+					&	6	&	$-862.360$	&	$0.383$	\\
+					&	7	&	$-862.083$	&	$0.339$	\\
+					&	8	&	$-861.711$	&	$0.370$	\\
+	\hline
+	Pyrazine		&	3	&	$-904.867$	&	$1.420$	\\
+					&	4	&	$-904.588$	&	$0.650$	\\
+					&	5	&	$-904.550$	&	$0.385$	\\
+					&	6	&	$-903.982$	&	$0.439$	\\
+					&	7	&	$-903.746$	&	$0.359$	\\
+					&	8	&	$-903.549$	&	$0.311$	\\
+	\hline
+	Pyridazine		&	3	&	$-909.292$	&	$0.024$	\\
+					&	4	&	$-908.808$	&	$0.230$	\\
+					&	5	&	$-908.820$	&	$0.133$	\\
+					&	6	&	$-908.342$	&	$0.303$	\\
+					&	7	&	$-908.368$	&	$0.224$	\\
+					&	8	&	$-908.229$	&	$0.198$	\\
+	\hline
+	Pyridine		&	3	&	$-883.363$	&	$0.047$	\\
+					&	4	&	$-883.413$	&	$0.029$	\\
+					&	5	&	$-882.700$	&	$0.405$	\\
+					&	6	&	$-882.361$	&	$0.341$	\\
+					&	7	&	$-882.023$	&	$0.330$	\\
+					&	8	&	$-881.732$	&	$0.322$	\\
+	\hline
+	Pyrimidine		&	3	&	$-900.817$	&	$0.726$	\\
+					&	4	&	$-900.383$	&	$0.356$	\\
+					&	5	&	$-900.496$	&	$0.214$	\\
+					&	6	&	$-900.698$	&	$0.190$	\\
+					&	7	&	$-900.464$	&	$0.206$	\\
+					&	8	&	$-900.226$	&	$0.227$	\\
+	\hline
+	Tetrazine		&	3	&	$-957.559$	&	$0.246$	\\
+					&	4	&	$-957.299$	&	$0.160$	\\
+					&	5	&	$-957.869$	&	$0.349$	\\
+					&	6	&	$-957.744$	&	$0.247$	\\
+					&	7	&	$-957.709$	&	$0.183$	\\
+					&	8	&	$-957.558$	&	$0.176$	\\
+	\hline
+	Triazine		&	3	&	$-919.596$	&	$0.105$	\\
+					&	4	&	$-918.457$	&	$0.538$	\\
+					&	5	&	$-918.355$	&	$0.312$	\\
+					&	6	&	$-918.206$	&	$0.226$	\\
+					&	7	&	$-917.876$	&	$0.267$	\\
+					&	8	&	$-917.533$	&	$0.308$	\\
+	\end{tabular}
+	\end{ruledtabular}
+\end{table}
+\end{squeezetable}    
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{CIPSI estimates}
+\label{sec:cipsi_res}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
 We first study the convergence of the variational energy as a function of the number of determinants.
 For the natural and optimized orbital sets we report, in Fig.~\ref{fig:vsNdet}, the evolution of the variational correlation energy $\Delta \Evar$ with respect to the number of determinants for the set of twelve cyclic molecules represented in Fig.~\ref{fig:mol}. 
 As one can see, the use of optimized orbitals greatly facilitate the convergence towards the FCI limit.
 This is further evidenced in Fig.~\ref{fig:vsEPT2} where we show the behavior of $\Delta \Evar$ as a function of $\EPT$ as well as its 4-point linear fit using the four largest variational wave functions.
 In both cases, the CCSDTQ correlation energy is also represented for comparison purposes.
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Benchmark of CC and MP methods}
+\label{sec:cc_mp_res}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
 %%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Conclusion}
 %%%%%%%%%%%%%%%%%%%%%%%%%

data_AS/benzene_opt.dat

@@ -24,4 +24,3 @@
   20971520   -231.5252061140  -0.0406298392   0.0000791195  -0.0403887454   0.0000786500
   41943040   -231.5337886859  -0.0346957844   0.0000668061  -0.0345247390   0.0000664767
   83886080   -231.5413391318  -0.0256659821   0.0001461668  -0.0294457584   0.0001455696
- 167772160

data_AS/cyclopentadiene_opt.dat

@@ -24,4 +24,3 @@
   20971520   -193.5126035896  -0.0246344737   0.0000479428  -0.0245465962   0.0000477718
   41943040   -193.5183426226  -0.0206049053   0.0000402624  -0.0205451654   0.0000401457
   83886080   -193.5232476384  -0.0170993616   0.0000813000  -0.0170594255   0.0000811101
- 167772160

data_AS/furan_opt.dat

@@ -24,4 +24,3 @@
   20971520   -229.3797442530  -0.0224998381   0.0000423186  -0.0224333245   0.0000421935
   41943040   -229.3852109522  -0.0185751065   0.0000362444  -0.0185311719   0.0000361586
   83886080   -229.3897820101  -0.0152739899   0.0000641000  -0.0152452221   0.0000639793
- 167772160