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Manuscript/CASPT3.tex

@@ -90,9 +90,9 @@
 
 % Abstract
 \begin{abstract}
-Based on 284 vertical transition energies of various natures extracted from the QUEST database, we assess the accuracy of third-order multireference perturbation theory, CASPT3, in the context of molecular excited states.
+Based on 284 vertical transition energies of various natures (singlet, triplet, valence, Rydberg, $n\to\pi^*$, $\pi\to\pi^*$, and double excitations) extracted from the QUEST database, we assess the accuracy of third-order multireference perturbation theory, CASPT3, in the context of molecular excited states.
 When one applies the infamous ionization-potential-electron-affinity (IPEA) shift, we show that CASPT3 provides a similar accuracy as its second-order counterpart, CASPT2, with the same mean absolute error of 0.11 eV.
-However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespectively of the type of the transitions, with a small reduction of the mean absolute errors to 0.09 eV when the IPEA shift is switched off
+However, as already reported, we also observe that the accuracy of CASPT3 is almost insensitive to the IPEA shift, irrespectively of the type of the transitions and the system size, with a small reduction of the mean absolute errors to 0.09 eV when the IPEA shift is switched off.
 %\bigskip
 %\begin{center}
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@@ -564,7 +564,7 @@ TBEs listed as ``safe'' are assumed to be chemically accurate (\ie, absolute err
 A detailed discussion of each individual molecule can be found in Ref.~\onlinecite{Sarka_2022} where we also report relevant values from the literature.
 Here, we focus on global trends.
 The exhaustive list of CASPT2 and CASPT3 transitions can be found in Table \ref{tab:BigTab} and the distribution of the errors are represented in Fig.~\ref{fig:PT2_vs_PT3}.
-Various statistical indictors are given in Table \ref{tab:stat} while MAEs determined for several subsets of transitions (singlet, triplet, valence, Rydberg, $n\to\pis$, $\pi\to\pis$, and double excitations) and system sizes (3 non-H atoms, 4 non-H atoms, and 5-6 non-H atoms) are reported in Table \ref{tab:stat_subset}.
+Various statistical indictors are given in Table \ref{tab:stat} while MAEs determined for several subsets of transitions (singlet, triplet, valence, Rydberg, $n\to\pis$, $\pi\to\pis$, and double excitations) and system sizes (3 non-H atoms, 4 non-H atoms, and 5-6 non-H atoms) are reported in Table \ref{tab:stat_subset}. (The error distributions for some of these subsets are reported in {\SupInf}.)
 
 From the different statistical quantities reported in Table \ref{tab:stat}, one can highlight the two following trends.
 First, as previously reported, \cite{Werner_1996,Grabarek_2016} CASPT3 vertical excitation energies are much less sensitive to the IPEA shift, which drastically alter the accuracy of CASPT2. 

Manuscript/sup_CASPT3.tex

@@ -94,6 +94,17 @@
 % Title
 \maketitle
 
+In Fig.~\ref{fig:subsets}, we report the error distributions obtained for CASPT2 and CASPT3 with and without IPEA shift for various subsets of transitions.
+
+%%% FIGURE S1 %%%
+\begin{figure}
+	\includegraphics[width=0.8\linewidth]{subsets}
+	\caption{Histograms of the errors (in \si{\eV}) obtained for CASPT2 and CASPT3 with and without IPEA shift for various subsets of transitions and system sizes.
+	See main text for raw data.}
+	\label{fig:subsets}
+\end{figure}
+%%% %%% %%% %%%
+
 In the following Tables, we report the vertical transition energies (in eV) obtained with the aug-cc-pVTZ basis and computed with state-averaged CASSCF, state-specific CASPT2 and CASPT3 using a level shift of \SI{0.30}{\hartree} with or without an IPEA shift of \SI{0.25}{\hartree}.
 The symbol $[F]$ indicates the calculation of emission from the lowest $S_1$ geometry, i.e., a vertical fluorescence.
 The composition of the active space is specified in terms of number of active orbitals per irreducible representation.