diff --git a/Manuscript/CASPT3.tex b/Manuscript/CASPT3.tex index 28210b7..e289e00 100644 --- a/Manuscript/CASPT3.tex +++ b/Manuscript/CASPT3.tex @@ -193,60 +193,15 @@ deviation of the errors (SDE), as well as largest positive and negative deviatio \end{figure} %%% %%% %%% %%% -\begin{table*} -\caption{Statistical quantities (in eV), considering the 265 ``safe'' TBEs (out of 284) as reference, for various multi-reference methods. -All {error} values are in eV.} -\label{tab:stat} - \begin{ruledtabular} - \begin{tabular}{lccccccc} - &CASSCF\fnm[1] &CASPT2\fnm[1] &CASPT2\fnm[1] &CASPT3\fnm[1] &CASPT3\fnm[1] &SC-NEVPT2\fnm[2] &PC-NEVPT2\fnm[2]\\ - & &(IPEA) &(NOIPEA) &(IPEA) &(NOIPEA)\\ - \hline - MSE &$0.11$ &$0.06$ &$-0.26$ &$0,10$ &$0,05$ &$0,13$ &$0,09$\\ - SDE &$0.58$ &$0.14$ &$0.21$ &$0.13$ &$0.13$ &$0.14$ &$0.14$\\ - RMSE &$0.61$ &$0.16$ &$0.33$ &$0.17$ &$0.14$ &$0.19$ &$0.17$\\ - MAE &$0.48$ &$0.11$ &$0.27$ &$0.11$ &$0.09$ &$0.15$ &$0.13$\\ - Max($+$) &$2.15$ &$0.71$ &$0.30$ &$0.93$ &$0.79$ &$0.65$ &$0.46$\\ - Max($-$) &$-1.18$ &$-0.32$ &$-1.02$ &$-0.28$ &$-0.36$ &$-0.38$ &$-0.57$\\ - \end{tabular} - \end{ruledtabular} - \fnt[1]{Values from the present study.} - \fnt[2]{Values taken from Ref.~\onlinecite{Sarka_2022}.} -\end{table*} - -\begin{table*} -\caption{MAEs determined for several subsets of transitions computed with various multi-reference methods. -Count is the number of excited states considered in each subset.} -\label{tab:stat_class} - \begin{ruledtabular} - \begin{tabular}{lcccccccc} - Transitions & Count &CASSCF\fnm[1] &CASPT2\fnm[1] &CASPT2\fnm[1] &CASPT3\fnm[1] &CASPT3\fnm[1] &SC-NEVPT2\fnm[2] &PC-NEVPT2\fnm[2]\\ - & & &(IPEA) &(NOIPEA) &(IPEA) &(NOIPEA)\\ - \hline - Singlet &174 &0.57 &0.14 &0.27 &0.14 &0.12 &0.16 &0.14\\ - Triplet &110 &0.34 &0.07 &0.29 &0.07 &0.06 &0.13 &0.11\\ - Valence &206 &0.45 &0.11 &0.33 &0.13 &0.10 &0.15 &0.12\\ - Rydberg &78 &0.54 &0.13 &0.13 &0.08 &0.07 &0.14 &0.15\\ - $n \to \pis$ &78 &0.44 &0.08 &0.44 &0.13 &0.10 &0.12 &0.10\\ - $\pi \to \pis$ &119 &0.46 &0.12 &0.27 &0.13 &0.10 &0.18 &0.14\\ - Double &9 &0.46 &0.11 &0.22 &0.12 &0.09 &0.14 &0.13\\ - 1-3 non-H atoms &39 &0.38 &0.07 &0.21 &0.06 &0.05 &0.10 &0.08\\ - 4 non-H atoms &94 &0.46 &0.11 &0.22 &0.12 &0.09 &0.14 &0.13\\ - 5-6 non-H atoms &151 &0.51 &0.12 &0.33 &0.12 &0.11 &0.17 &0.15\\ - \end{tabular} - \end{ruledtabular} - \fnt[1]{Values from the present study.} - \fnt[2]{Values taken from Ref.~\onlinecite{Sarka_2022}.} -\end{table*} - 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 are represented in Fig.~\ref{fig:PT2_vs_PT3}. \begin{longtable*}{cllccccccccc} -\caption{Vertical excitation energies (in \si{\eV}) computed at various levels of theory. +\caption{Vertical excitation energies (in \si{\eV}) computed with various multi-reference methods. The reference TBEs of the QUEST database, their percentage of single excitations $\%T_1$ involved in the transition (computed at the CC3 level), their nature (V and R stand for valence and Rydberg, respectively) are also reported. +TBEs listed as ``safe'' are assumed to be chemically accurate (\ie, absolute error below \SI{0.05}{\eV}). [F] indicates a fluorescence transition, \ie, a vertical transition energy computed from an excited-state equilibrium geometry. \label{tab:BigTab}} \\ @@ -551,6 +506,66 @@ The reference TBEs of the QUEST database, their percentage of single excitations 284 & &$^3A_2'(\pi,\pis)$ &V &97.6 &6.62 &Y &7.70 &6.62 &6.12 &6.76 &6.68\\ \end{longtable*} +\begin{table*} + \caption{Statistical quantities (in eV), considering the 265 ``safe'' TBEs (out of 284) as reference, for various multi-reference methods. + All {error} values are in eV.} + \label{tab:stat} + \begin{ruledtabular} + \begin{tabular}{lccccccc} + &CASSCF\fnm[1] &CASPT2\fnm[1] &CASPT2\fnm[1] &CASPT3\fnm[1] &CASPT3\fnm[1] &SC-NEVPT2\fnm[2] &PC-NEVPT2\fnm[2]\\ + & &(IPEA) &(NOIPEA) &(IPEA) &(NOIPEA)\\ + \hline + MSE &$0.11$ &$0.06$ &$-0.26$ &$0,10$ &$0,05$ &$0,13$ &$0,09$\\ + SDE &$0.58$ &$0.14$ &$0.21$ &$0.13$ &$0.13$ &$0.14$ &$0.14$\\ + RMSE &$0.61$ &$0.16$ &$0.33$ &$0.17$ &$0.14$ &$0.19$ &$0.17$\\ + MAE &$0.48$ &$0.11$ &$0.27$ &$0.11$ &$0.09$ &$0.15$ &$0.13$\\ + Max($+$) &$2.15$ &$0.71$ &$0.30$ &$0.93$ &$0.79$ &$0.65$ &$0.46$\\ + Max($-$) &$-1.18$ &$-0.32$ &$-1.02$ &$-0.28$ &$-0.36$ &$-0.38$ &$-0.57$\\ + \end{tabular} + \end{ruledtabular} + \fnt[1]{Values from the present study.} + \fnt[2]{Values taken from Ref.~\onlinecite{Sarka_2022}.} +\end{table*} + +\begin{table*} + \caption{MAEs determined for several subsets of transitions computed with various multi-reference methods. + Count is the number of excited states considered in each subset.} + \label{tab:stat_class} + \begin{ruledtabular} + \begin{tabular}{lcccccccc} + Transitions & Count &CASSCF\fnm[1] &CASPT2\fnm[1] &CASPT2\fnm[1] &CASPT3\fnm[1] &CASPT3\fnm[1] &SC-NEVPT2\fnm[2] &PC-NEVPT2\fnm[2]\\ + & & &(IPEA) &(NOIPEA) &(IPEA) &(NOIPEA)\\ + \hline + Singlet &174 &0.57 &0.14 &0.27 &0.14 &0.12 &0.16 &0.14\\ + Triplet &110 &0.34 &0.07 &0.29 &0.07 &0.06 &0.13 &0.11\\ + Valence &206 &0.45 &0.11 &0.33 &0.13 &0.10 &0.15 &0.12\\ + Rydberg &78 &0.54 &0.13 &0.13 &0.08 &0.07 &0.14 &0.15\\ + $n \to \pis$ &78 &0.44 &0.08 &0.44 &0.13 &0.10 &0.12 &0.10\\ + $\pi \to \pis$ &119 &0.46 &0.12 &0.27 &0.13 &0.10 &0.18 &0.14\\ + Double &9 &0.46 &0.11 &0.22 &0.12 &0.09 &0.14 &0.13\\ + 1-3 non-H atoms &39 &0.38 &0.07 &0.21 &0.06 &0.05 &0.10 &0.08\\ + 4 non-H atoms &94 &0.46 &0.11 &0.22 &0.12 &0.09 &0.14 &0.13\\ + 5-6 non-H atoms &151 &0.51 &0.12 &0.33 &0.12 &0.11 &0.17 &0.15\\ + \end{tabular} + \end{ruledtabular} + \fnt[1]{Values from the present study.} + \fnt[2]{Values taken from Ref.~\onlinecite{Sarka_2022}.} +\end{table*} + +\begin{table*} + \caption{CASPT2 and CASPT3 timings (in seconds) for a selection of systems and states.} + \begin{ruledtabular} + \begin{tabular}{llcccccccc} + System & State &Active &\# electrons &\# basis &\# CAS &\# contracted &\# uncontracted &CPU &CPU\\ + & &Space & &functions &det. &config. &config. &CASPT2 &CASPT3 \\ + \hline + Acetone &$^1A_2(n,\pis)$ &(6e,6o) &32 &322 &104 &$3.86 \times 10^6$ &$1.49 \times 10^8$ &12.50 &33.25\\ + Pyrrole &$^1A_2(\pi,3s)$ &(6e,6o) &36 &345 &96 &$4.79 \times 10^6$ &$2.04 \times 10^8$ &13.24 &49.36\\ + Imidazole &$^1A''(\pi,3s)$ &(8e,7o) &36 &322 &600 &$1.46 \times 10^7$ &$1.82 \times 10^9$ &193.93 &282.62\\ + Pyrazine &$^1B_{3u}(n,\pis)$ &(10e,8o) &42 &368 &392 &$6.95 \times 10^6$ &$6.38 \times 10^8$ &29.58 &174.96\\ + \end{tabular} + \end{ruledtabular} +\end{table*} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusion} diff --git a/Manuscript/sup_CASPT3.tex b/Manuscript/sup_CASPT3.tex index 19291ac..587ae7b 100644 --- a/Manuscript/sup_CASPT3.tex +++ b/Manuscript/sup_CASPT3.tex @@ -516,9 +516,9 @@ $^1A''[F](\pi,\pis)$ &($a'$:6,$a''$:3) &($A'$:1,$A''$:1) &0.72$^a$ &0.69$^a$ &0. \end{tabular} \end{ruledtabular} \flushleft - $^a$Using reference $(8e,7o)$ active space including valence $\pi$, $\nN$ and $3s$ orbitals. - $^b$Using reference $(6e,9o)$ active space including valence $\pi$ and four $3p_z$ orbitals. - $^c$Using reference $(8e,10o)$ active space including valence $\pi$, $\nN$, $3s$ and three $3p$ orbitals. + $^a$Using reference (8e,7o) active space including valence $\pi$, $\nN$ and $3s$ orbitals. + $^b$Using reference (6e,9o) active space including valence $\pi$ and four $3p_z$ orbitals. + $^c$Using reference (8e,10o) active space including valence $\pi$, $\nN$, $3s$ and three $3p$ orbitals. \end{table*} \begin{table*}