From f58715d53c55902ee65edc27117d22bf1bc8ad13 Mon Sep 17 00:00:00 2001
From: Pierre-Francois Loos <pierrefrancois.loos@gmail.com>
Date: Thu, 30 May 2019 11:49:37 +0200
Subject: [PATCH] CH2

---
 Manuscript/CH2.pdf      | Bin 46225 -> 46222 bytes
 Manuscript/Ex-srDFT.bib |   6 +-
 Manuscript/Ex-srDFT.tex | 242 ++++++++++++----------------------------
 3 files changed, 73 insertions(+), 175 deletions(-)

diff --git a/Manuscript/CH2.pdf b/Manuscript/CH2.pdf
index b15f2a761d539abb71fb45009e9b303810289545..414ed788443c4b2de2bb7f499ca54e83cf822ef7 100644
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diff --git a/Manuscript/Ex-srDFT.bib b/Manuscript/Ex-srDFT.bib
index 8f1e26f..1de5e6a 100644
--- a/Manuscript/Ex-srDFT.bib
+++ b/Manuscript/Ex-srDFT.bib
@@ -1,7 +1,7 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2019-05-29 23:30:47 +0200 
+%% Created for Pierre-Francois Loos at 2019-05-30 11:26:43 +0200 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
@@ -12712,9 +12712,9 @@
 	Year = {2018},
 	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00591}}
 
-@article{LooBogSceCafJAc-JCTC-19,
+@article{LooBogSceCafJac-JCTC-19,
 	Author = {Loos, Pierre-Fran{\c c}ois and Boggio-Pasqua, Martial and Scemama, Anthony and Caffarel, Michel and Jacquemin, Denis},
-	Date-Modified = {2019-04-07 14:02:34 +0200},
+	Date-Modified = {2019-05-30 11:26:43 +0200},
 	Doi = {10.1021/acs.jctc.8b01205},
 	Journal = {J. Chem. Theory Comput.},
 	Number = {3},
diff --git a/Manuscript/Ex-srDFT.tex b/Manuscript/Ex-srDFT.tex
index 52b32ec..68dec94 100644
--- a/Manuscript/Ex-srDFT.tex
+++ b/Manuscript/Ex-srDFT.tex
@@ -333,11 +333,13 @@ This computationally-lighter functional will be refered to as PBE.
 In the present study, we compute the ground- and excited-state energies, one-electron and on-top densities with a selected CI method known as CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively). \cite{HurMalRan-JCP-73, GinSceCaf-CJC-13, GinSceCaf-JCP-15}
 The total energy of each state is obtained via an efficient extrapolation procedure of the sCI energies designed to reach near-FCI accuracy. \cite{QP2}
 These energies will be labeled exFCI in the following.
+Using near-FCI excitation energies (within a given basis set) has the indisputable advantage to remove the error inherent to the WFT method.
+Indeed, in the present case, the only source of error on the excitation energies is due to basis set incompleteness.
 We refer the interested reader to Refs.~\onlinecite{HolUmrSha-JCP-17, SceGarCafLoo-JCTC-18, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18, LooBogSceCafJac-JCTC-19, QP2} for more details.
 The one-electron and on-top densities are computed from a very large CIPSI expansion containing several million determinants.
 All the RS-DFT and exFCI calculations have been performed with {\QP}. \cite{QP2}
 For the numerical quadratures, we employ the SG-2 grid. \cite{DasHer-JCC-17}
-Except for methylene for which FCI/TZVP geometries have been taken from Ref.~\onlinecite{SheLeiVanSch-JCP-98}, the other geometries have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19} and have been obtained at the CC3/aug-cc-pVTZ level of theory.
+Except for methylene for which FCI/TZVP geometries have been taken from Ref.~\onlinecite{SheLeiVanSch-JCP-98}, the other geometries have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJac-JCTC-19} and have been obtained at the CC3/aug-cc-pVTZ level of theory.
 For the sake of completeness, they are also reported in the {\SI}.
 Frozen-core calculations are systematically performed and defined as such: a \ce{He} core is frozen from \ce{Li} to \ce{Ne}, while a \ce{Ne} core is frozen from \ce{Na} to \ce{Ar}.
 The frozen-core density-based correction is used consistently with the frozen-core approximation in WFT methods.
@@ -365,12 +367,18 @@ We have also computed these adiabatic energies at the exFCI/AV5Z level and used
 \end{equation}
 
 These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{tab:CH2} alongside reference values from the literature obtained with various approaches. \cite{ChiHolAdaOttUmrShaZim-JPCA-18, SheLeiVanSch-JCP-98, JenBun-JCP-88, SheLeiVanSch-JCP-98, ZimTouZhaMusUmr-JCP-09}
+Figure \ref{fig:CH2} clearly shows that, for the double-$\zeta$ basis, the exFCI adiabatic energies are far from being chemically accurate with errors as high as 0.015 eV.
+From triplet-$\zeta$ onward, the exFCI excitation energies are chemically-accurate though.
+
 
 %%% TABLE 1 %%%
+	\begin{turnpage}
 	\begin{squeezetable}
 	\begin{table*}
 	\caption{
-	Total energies $E$ (in hartree) and adiabatic transition energies $\Ead$ (in eV) of excited states of methylene for various methods and basis sets.}
+	Total energies $E$ (in hartree) and adiabatic transition energies $\Ead$ (in eV) of excited states of methylene for various methods and basis sets.
+	The value in parenthesis is an estimate on the last digit of the extrapolation error.
+	The relative difference with respect to the exFCI/CBS result is reported in square brackets.}
 	\label{tab:CH2}
 	\begin{ruledtabular}
 	\begin{tabular}{llddddddd}
@@ -386,64 +394,64 @@ These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{t
 								&	\tabc{$E$ (a.u.)}	&	\tabc{$\Ead$ (eV)}	\\
 	\hline
 	exFCI		&	AVDZ		&	-39.04846(1)				
-								&	-39.03225(1)	&	0.441	
-								&	-38.99203(1)	&	1.536	
-								&	-38.95076(1)	&	2.659	\\	
+								&	-39.03225(1)	&	0.441 [+0.053]	
+								&	-38.99203(1)	&	1.536 [+0.146]
+								&	-38.95076(1)	&	2.659 [+0.154]	\\	
 				&	AVTZ		&	-39.08064(3)				
-								&	-39.06565(2)	&	0.408	
-								&	-39.02833(1)	&	1.423	
-								&	-38.98709(1)	&	2.546	\\	
+								&	-39.06565(2)	&	0.408 [+0.020]	
+								&	-39.02833(1)	&	1.423 [+0.034]	
+								&	-38.98709(1)	&	2.546 [+0.042]	\\	
 				&	AVQZ		&	-39.08854(1)				
-								&	-39.07402(2)	&	0.395	
-								&	-39.03711(1)	&	1.399	
-								&	-38.99607(1)	&	2.516	\\	
+								&	-39.07402(2)	&	0.395 [+0.007]	
+								&	-39.03711(1)	&	1.399 [+0.010]	
+								&	-38.99607(1)	&	2.516 [+0.012]	\\	
 				&	AV5Z		&	-39.09079(1)				
-								&	-39.07647(1)	&	0.390	
-								&	-39.03964(3)	&	1.392	
-								&	-38.99867(1)	&	2.507	\\	
-				&	CBS			&	-39.09111				
-								&	-39.07682		&	0.388	
-								&	-39.04000		&	1.390	
-								&	-38.99904		&	2.504	\\	
-								\\
-	exFCI+LDA	&	AVDZ		&	-39.07450(1)				
-								&	-39.06213(1)	&	0.337	
-								&	-39.02233(1)	&	1.420	
-								&	-38.97946(1)	&	2.586	\\	
-				&	AVTZ		&	-39.09099(3)				
-								&	-39.07779(2)	&	0.359	
-								&	-39.04051(1)	&	1.374	
-								&	-38.99859(1)	&	2.514	\\	
-				&	AVQZ		&	-39.09319(1)				
-								&	-39.07959(2)	&	0.370	
-								&	-39.04267(1)	&	1.375	
-								&	-39.00135(1)	&	2.499	\\	
-								\\
-	exFCI+PBE	&	AVDZ		&	-39.07282(1)				
-								&	-39.06150(1)	&	0.308	
-								&	-39.02181(1)	&	1.388	
-								&	-38.97873(1)	&	2.560	\\	
-				&	AVTZ		&	-39.08948(3)				
-								&	-39.07639(2)	&	0.356	
-								&	-39.03911(1)	&	1.371	
-								&	-38.99724(1)	&	2.510	\\	
-				&	AVQZ		&	-39.09247(1)				
-								&	-39.07885(2)	&	0.371
-								&	-39.04193(1)	&	1.375	
-								&	-39.00066(1)	&	2.498	\\	
+								&	-39.07647(1)	&	0.390 [+0.001]	
+								&	-39.03964(3)	&	1.392 [+0.002]	
+								&	-38.99867(1)	&	2.507 [+0.003]	\\	
+				&	CBS			&	-39.09141				
+								&	-39.07715		&	0.388	
+								&	-39.04034		&	1.390	
+								&	-38.99939		&	2.504	\\	
 								\\
 	exFCI+PBEot	&	AVDZ		&	-39.06924(1)				
-								&	-39.05651(1)	&	0.347	
-								&	-39.01777(1)	&	1.401	
-								&	-38.97698(1)	&	2.511	\\	
+								&	-39.05651(1)	&	0.347 [-0.042]	
+								&	-39.01777(1)	&	1.401 [+0.011]	
+								&	-38.97698(1)	&	2.511 [+0.007]	\\	
 				&	AVTZ		&	-39.08805(3)				
-								&	-39.07430(2)	&	0.374	
-								&	-39.03742(1)	&	1.378	
-								&	-38.99652(1)	&	2.491	\\	
+								&	-39.07430(2)	&	0.374 [-0.014]	
+								&	-39.03742(1)	&	1.378 [-0.012]	
+								&	-38.99652(1)	&	2.491 [-0.013]	\\	
 				&	AVQZ		&	-39.09189(1)				
-								&	-39.07795(2)	&	0.379	
-								&	-39.04124(1)	&	1.378	
-								&	-39.00044(1)	&	2.489	\\	
+								&	-39.07795(2)	&	0.379 [-0.009]	
+								&	-39.04124(1)	&	1.378 [-0.011]	
+								&	-39.00044(1)	&	2.489 [-0.016]	\\	
+								\\
+	exFCI+PBE	&	AVDZ		&	-39.07282(1)				
+								&	-39.06150(1)	&	0.308 [-0.080]	
+								&	-39.02181(1)	&	1.388 [-0.002]	
+								&	-38.97873(1)	&	2.560 [+0.056]	\\	
+				&	AVTZ		&	-39.08948(3)				
+								&	-39.07639(2)	&	0.356 [-0.032]	
+								&	-39.03911(1)	&	1.371 [-0.019]	
+								&	-38.99724(1)	&	2.510 [+0.006]	\\	
+				&	AVQZ		&	-39.09247(1)				
+								&	-39.07885(2)	&	0.371 [-0.017]
+								&	-39.04193(1)	&	1.375 [-0.015]	
+								&	-39.00066(1)	&	2.498 [-0.006]	\\	
+								\\
+	exFCI+LDA	&	AVDZ		&	-39.07450(1)				
+								&	-39.06213(1)	&	0.337 [-0.051]	
+								&	-39.02233(1)	&	1.420 [+0.030]	
+								&	-38.97946(1)	&	2.586 [+0.082]	\\	
+				&	AVTZ		&	-39.09099(3)				
+								&	-39.07779(2)	&	0.359 [-0.029]	
+								&	-39.04051(1)	&	1.374 [-0.016]	
+								&	-38.99859(1)	&	2.514 [+0.010]	\\	
+				&	AVQZ		&	-39.09319(1)				
+								&	-39.07959(2)	&	0.370 [-0.018]	
+								&	-39.04267(1)	&	1.375 [-0.015]	
+								&	-39.00135(1)	&	2.499 [-0.005]	\\	
 								\\
 	SHCI\fnm[1]	&	AVQZ		&	-39.08849(1)				
 								&	-39.07404(1)	&	0.393	
@@ -473,13 +481,14 @@ These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{t
 	\fnt[5]{References \onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.}
 	\end{table*}
 	\end{squeezetable}
+	\end{turnpage}
 %%% %%% %%%
 
 %%% FIG 1 %%%
 \begin{figure}
 	\includegraphics[width=\linewidth]{CH2}
 	\caption{Error in adiabatic excitation energies $\Ead$ (in eV) of methylene for various basis sets and methods.
-	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
 	See Table \ref{tab:CH2} for raw data.}
 	\label{fig:CH2}
 \end{figure}
@@ -497,7 +506,7 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
 	\begin{table*}
 	\caption{
 	Vertical absorption energies $\Eabs$ (in eV) of excited states of ammonia, carbon dimer, water and ethylene for various methods and basis sets.
-	The TBEs have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19} on the same geometries.
+	The TBEs have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJac-JCTC-19} on the same geometries.
 	See the {\SI} for raw data.}
 	\begin{ruledtabular}{}
 	\begin{tabular}{lllddddddddddddd}
@@ -553,33 +562,6 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
 																								&	0.11	&	0.02	&	0.00
 	\\
 	\\
-%	Hydrogen chloride&	${}^1\Sigma \ra {}^1\Pi$	&	CT\fnm[2]	&	7.86	&	-0.04	&	-0.02	&	0.02
-%																				&	0.13	&	0.06	&	0.06
-%																				&	0.11	&	0.04	&	0.05
-%																				&	0.10	&	0.05	&	0.06
-%	\\
-%	\\
-%	Hydrogen sulfide	&	$1\,^{1}A_1 \ra 1\,^{1}A_2$		&	Ryd.	&	6.10	&	0.00	&	0.08	&	0.05
-%																					&	0.15	&	0.12	&	0.07
-%																					&	0.14	&	0.11	&	0.07
-%																					&	0.14	&	0.11	&	0.07
-%	\\
-%						&	$1\,^{1}A_1 \ra 1\,^{1}B_1$		&	Ryd.	&	6.29	&	0.00	&	-0.05	&	0.00
-%																					&	-0.12	&	0.01	&	0.03
-%																					&	-0.14	&	0.00	&	0.03
-%																					&	-0.14	&	0.01	&	0.03
-%	\\
-%						&	$1\,^{1}A_1 \ra 1\,^{3}A_2$		&	Ryd.	&	5.74	&	0.01	&	0.07	&	0.05
-%																					&	0.18	&	0.12	&	0.08
-%																					&	0.20	&	0.13	&	0.08
-%																					&	0.19	&	0.13	&	0.08
-%	\\
-%						&	$1\,^{1}A_1 \ra 1\,^{3}B_1$		&	Ryd.	&	5.94	&	-0.04	&	-0.05	&	-0.01
-%																					&	0.07	&	0.02	&	0.03
-%																					&	0.09	&	0.03	&	0.03
-%																					&	0.07	&	0.04	&	0.04
-%	\\
-%	\\
 	Water		&	$1\,^{1}A_1 \ra 1\,^{1}B_1$		&	Ryd.	&	7.70		&	-0.17	&	-0.07	&	-0.02	
 																	&	0.01	&	0.00	&	0.02	
 																	&	-0.02	&	-0.01	&	0.00	
@@ -611,32 +593,6 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
 																	&	0.06	&	0.03	&	0.04
 	\\
 	\\
-%	Acetylene	&	$1\,^{1}\Sigma_{g}^{+} \ra 1\,^{1}\Sigma_{u}^{-}$	&	Val.	&	7.10	&	0.10	&	0.00
-%																								&	0.07	&	0.00	
-%																								&	0.11	&	0.00	
-%																								&	0.11	&	0.00	
-%	\\
-%				&	$1\,^{1}\Sigma_{g}^{+} \ra 1\,^{1}\Delta_{u}$		&	Val.	&	7.44	&	0.07	&	0.00	
-%																								&	0.04	&	-0.01	
-%																								&	0.12	&	0.02	
-%																								&	0.11	&	0.02	
-%	\\
-%				&	$1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Sigma_{u}^{+}$	&	Val.	&	5.56	&	-0.06	&	-0.03		
-%																								&	0.07	&	0.02	
-%																								&	0.04	&	0.00	
-%																								&	0.02	&	0.00	
-%	\\
-%				&	$1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Delta_{u}$		&	Val.	&	6.40	&	0.06	&	0.00	
-%																								&	0.10	&	0.02	
-%																								&	0.14	&	0.03	
-%																								&	0.12	&	0.03	
-%	\\
-%				&	$1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Sigma_{u}^{-}$	&	Val.	&	7.09	&	0.05	&	-0.01
-%																								&	0.08	&	0.00	
-%																								&	0.16	&	0.04	
-%																								&	0.14	&	0.04	
-%	\\
-%	\\
 	Ethylene	&	$1\,^{1}A_{1g} \ra 1\,^{1}B_{3u}$		&	Ryd.	&	7.43	&	-0.12	&	-0.04	&	
 																					&	-0.05	&	-0.01	&	
 																					&	-0.04	&	-0.01	&	
@@ -668,55 +624,9 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
 																					&	0.05	&	0.04	&	
 	\\
 	\\
-%	Formaldehyde&	$1\,^{1}A_{1} \ra 1\,^{1}A_{2}$			&	Val.	&	3.97	&	0.02	&	0.01	&	
-%																					&	0.05	&	0.02	&	
-%																					&	0.03	&	0.02	&	
-%																					&	0.02	&	0.01	&	
-%	\\
-%				&	$1\,^{1}A_{1} \ra 1\,^{1}B_{2}$			&	Ryd.	&	7.30	&	-0.19	&	-0.07	&	
-%																					&	0.00	&	0.00	&	
-%																					&	-0.02	&	0.00	&	
-%																					&	-0.04	&	0.00	&	
-%	\\
-%				&	$1\,^{1}A_{1} \ra 2\,^{1}B_{2}$			&	Ryd.	&	8.14	&	-0.10	&	-0.01	&	
-%																					&	0.09	&	0.07	&	
-%																					&	0.08	&	0.06	&	
-%																					&	0.05	&	0.06	&	
-%	\\
-%				&	$1\,^{1}A_{1} \ra 2\,^{1}A_{1}$			&	Ryd.	&	8.27	&	-0.15	&	-0.04	&	
-%																					&	0.03	&	0.04	&	
-%																					&	0.02	&	0.03	&	
-%																					&	0.00	&	0.03	&	
-%	\\
-%				&	$1\,^{1}A_{1} \ra 1\,^{3}A_{2}$			&	Val.	&	3.58	&	0.00	&	0.00	&	
-%																					&	0.09	&	0.05	&	
-%																					&	0.11	&	0.06	&	
-%																					&	0.07	&	0.04	&	
-%	\\
-%				&	$1\,^{1}A_{1} \ra 1\,^{3}A_{1}$			&	Val.	&	6.07	&	0.03	&	0.01	&	
-%																					&	0.13	&	0.04	&	
-%																					&	0.15	&	0.05	&	
-%																					&	0.11	&	0.04	&	
-%	\\
-%				&	$1\,^{1}A_{1} \ra 1\,^{3}B_{2}$			&	Ryd.	&	7.14	&	-0.19	&	-0.08	&	
-%																					&	0.01	&	0.01	&	
-%																					&	0.02	&	0.01	&	
-%																					&	-0.01	&	0.00	&	
-%	\\
-%				&	$1\,^{1}A_{1} \ra 2\,^{3}B_{2}$			&	Ryd.	&	7.96	&	-0.09	&	-0.02	&	
-%																					&	0.13	&	0.08	&	
-%																					&	0.14	&	0.08	&	
-%																					&	0.10	&	0.07	&	
-%	\\
-%				&	$1\,^{1}A_{1} \ra 1\,^{3}A_{1}$			&	Ryd.	&	8.15	&	-0.14	&	-0.05	&	
-%																					&	0.07	&	0.05	&	
-%																					&	0.07	&	0.04	&	
-%																					&	0.04	&	0.04	&	
-%	\\
 	\end{tabular}
 	\end{ruledtabular}
 	\fnt[1]{Doubly-excited states of $(\pi,\pi) \ra (\si,\si)$ character.}
-%	\fnt[2]{CT stands for charge transfer.}
 	\end{table*}
 	\end{squeezetable}
 %%% %%% %%%
@@ -725,7 +635,7 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
 \begin{figure}
 	\includegraphics[width=\linewidth]{H2O}
 	\caption{Error in vertical excitation energies (in eV) of water for various basis sets and methods.
-	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
 	See the {\SI} for raw data.}
 	\label{fig:H2O}
 \end{figure}
@@ -735,7 +645,7 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
 \begin{figure}
 	\includegraphics[width=\linewidth]{NH3}
 	\caption{Error in vertical excitation energies (in eV) of ammonia for various basis sets and methods.
-	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
 	See the {\SI} for raw data.}
 	\label{fig:NH3}
 \end{figure}
@@ -746,13 +656,13 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
 \label{sec:C2}
 %=======================
 It is also interesting to study doubly-excited states. \cite{AbrShe-JCP-04, AbrShe-CPL-05, Var-JCP-08, PurZhaKra-JCP-09, AngCimPas-MP-12, BooCleThoAla-JCP-11, Sha-JCP-15, SokCha-JCP-16, VarRoc-PTRSMPES-18}
-In the carbon dimer, these valence states are of $(\pi,\pi) \ra (\si,\si)$ character and they have been recently studied with state-of-the-art methods. \cite{LooBogSceCafJAc-JCTC-19}
+In the carbon dimer, these valence states are of $(\pi,\pi) \ra (\si,\si)$ character and they have been recently studied with state-of-the-art methods. \cite{LooBogSceCafJac-JCTC-19}
 
 %%% FIG 4 %%%
 \begin{figure}
 	\includegraphics[width=\linewidth]{C2}
 	\caption{Error in vertical excitation energies $\Eabs$ (in eV) for two doubly-excited states of the carbon dimer for various basis sets and methods.
-	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
 	See the {\SI} for raw data.}
 	\label{fig:C2}
 \end{figure}
@@ -766,26 +676,14 @@ In the carbon dimer, these valence states are of $(\pi,\pi) \ra (\si,\si)$ chara
 
 Ethylene is an interesting molecules as it contains both valence and Rydberg excited states. \cite{SerMarNebLinRoo-JCP-93, WatGwaBar-JCP-96, WibOliTru-JPCA-02, BarPaiLis-JCP-04, Ang-JCC-08, SchSilSauThi-JCP-08, SilSchSauThi-JCP-10, SilSauSchThi-MP-10, Ang-IJQC-10, DadSmaBooAlaFil-JCTC-12, FelPetDav-JCP-14, ChiHolAdaOttUmrShaZim-JPCA-18}
 
-%\begin{figure}
-%	\includegraphics[width=\linewidth]{C2H2}
-%	\caption{Error in vertical excitation energies (in eV) of acetylene for various basis sets and methods.}
-%	\label{fig:C2H2}
-%\end{figure}
-
 \begin{figure}
 	\includegraphics[width=\linewidth]{C2H4}
 	\caption{Error in vertical excitation energies $\Eabs$ (in eV) of ethylene for various basis sets and methods.
-	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
+	The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
 	See the {\SI} for raw data.}
 	\label{fig:C2H4}
 \end{figure}
 
-%\begin{figure}
-%	\includegraphics[width=\linewidth]{CH2O}
-%	\caption{Error in vertical excitation energies $\Eabs$ (in eV) of formaldehyde for various basis sets and methods.}
-%	\label{fig:CH2O}
-%\end{figure}
-
 %%%%%%%%%%%%%%%%%%%%%%%%
 \section{Conclusion}
 \label{sec:ccl}
@@ -796,7 +694,7 @@ We are currently investigating the performance of the present basis set correcti
 %%%%%%%%%%%%%%%%%%%%%%%%
 \section*{Supporting Information Available}
 %%%%%%%%%%%%%%%%%%%%%%%%
-See {\SI} for geometries and additional information (including total energies).
+See {\SI} for geometries and additional information (including energetic correction of the various functionals).
 
 %%%%%%%%%%%%%%%%%%%%%%%%
 \begin{acknowledgements}