timings
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Pierre-Francois Loos
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2058b3cd37
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587c20d629
@ -193,60 +193,15 @@ deviation of the errors (SDE), as well as largest positive and negative deviatio
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\begin{table*}
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\caption{Statistical quantities (in eV), considering the 265 ``safe'' TBEs (out of 284) as reference, for various multi-reference methods.
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All {error} values are in eV.}
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\label{tab:stat}
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\begin{ruledtabular}
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\begin{tabular}{lccccccc}
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&CASSCF\fnm[1] &CASPT2\fnm[1] &CASPT2\fnm[1] &CASPT3\fnm[1] &CASPT3\fnm[1] &SC-NEVPT2\fnm[2] &PC-NEVPT2\fnm[2]\\
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& &(IPEA) &(NOIPEA) &(IPEA) &(NOIPEA)\\
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\hline
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MSE &$0.11$ &$0.06$ &$-0.26$ &$0,10$ &$0,05$ &$0,13$ &$0,09$\\
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SDE &$0.58$ &$0.14$ &$0.21$ &$0.13$ &$0.13$ &$0.14$ &$0.14$\\
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RMSE &$0.61$ &$0.16$ &$0.33$ &$0.17$ &$0.14$ &$0.19$ &$0.17$\\
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MAE &$0.48$ &$0.11$ &$0.27$ &$0.11$ &$0.09$ &$0.15$ &$0.13$\\
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Max($+$) &$2.15$ &$0.71$ &$0.30$ &$0.93$ &$0.79$ &$0.65$ &$0.46$\\
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Max($-$) &$-1.18$ &$-0.32$ &$-1.02$ &$-0.28$ &$-0.36$ &$-0.38$ &$-0.57$\\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Values from the present study.}
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\fnt[2]{Values taken from Ref.~\onlinecite{Sarka_2022}.}
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\end{table*}
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\begin{table*}
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\caption{MAEs determined for several subsets of transitions computed with various multi-reference methods.
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Count is the number of excited states considered in each subset.}
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\label{tab:stat_class}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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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]\\
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& & &(IPEA) &(NOIPEA) &(IPEA) &(NOIPEA)\\
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\hline
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Singlet &174 &0.57 &0.14 &0.27 &0.14 &0.12 &0.16 &0.14\\
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Triplet &110 &0.34 &0.07 &0.29 &0.07 &0.06 &0.13 &0.11\\
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Valence &206 &0.45 &0.11 &0.33 &0.13 &0.10 &0.15 &0.12\\
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Rydberg &78 &0.54 &0.13 &0.13 &0.08 &0.07 &0.14 &0.15\\
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$n \to \pis$ &78 &0.44 &0.08 &0.44 &0.13 &0.10 &0.12 &0.10\\
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$\pi \to \pis$ &119 &0.46 &0.12 &0.27 &0.13 &0.10 &0.18 &0.14\\
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Double &9 &0.46 &0.11 &0.22 &0.12 &0.09 &0.14 &0.13\\
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1-3 non-H atoms &39 &0.38 &0.07 &0.21 &0.06 &0.05 &0.10 &0.08\\
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4 non-H atoms &94 &0.46 &0.11 &0.22 &0.12 &0.09 &0.14 &0.13\\
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5-6 non-H atoms &151 &0.51 &0.12 &0.33 &0.12 &0.11 &0.17 &0.15\\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Values from the present study.}
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\fnt[2]{Values taken from Ref.~\onlinecite{Sarka_2022}.}
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\end{table*}
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A detailed discussion of each individual molecule can be found in Ref.~\onlinecite{Sarka_2022} where we also report relevant values from the literature.
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A detailed discussion of each individual molecule can be found in Ref.~\onlinecite{Sarka_2022} where we also report relevant values from the literature.
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Here, we focus on global trends.
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Here, we focus on global trends.
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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}.
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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}.
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\begin{longtable*}{cllccccccccc}
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\begin{longtable*}{cllccccccccc}
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\caption{Vertical excitation energies (in \si{\eV}) computed at various levels of theory.
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\caption{Vertical excitation energies (in \si{\eV}) computed with various multi-reference methods.
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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
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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
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(V and R stand for valence and Rydberg, respectively) are also reported.
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(V and R stand for valence and Rydberg, respectively) are also reported.
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TBEs listed as ``safe'' are assumed to be chemically accurate (\ie, absolute error below \SI{0.05}{\eV}).
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[F] indicates a fluorescence transition, \ie, a vertical transition energy computed from an excited-state equilibrium geometry.
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[F] indicates a fluorescence transition, \ie, a vertical transition energy computed from an excited-state equilibrium geometry.
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\label{tab:BigTab}}
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\label{tab:BigTab}}
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\\
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\\
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@ -551,6 +506,66 @@ The reference TBEs of the QUEST database, their percentage of single excitations
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284 & &$^3A_2'(\pi,\pis)$ &V &97.6 &6.62 &Y &7.70 &6.62 &6.12 &6.76 &6.68\\
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284 & &$^3A_2'(\pi,\pis)$ &V &97.6 &6.62 &Y &7.70 &6.62 &6.12 &6.76 &6.68\\
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\end{longtable*}
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\end{longtable*}
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\begin{table*}
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\caption{Statistical quantities (in eV), considering the 265 ``safe'' TBEs (out of 284) as reference, for various multi-reference methods.
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All {error} values are in eV.}
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\label{tab:stat}
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\begin{ruledtabular}
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\begin{tabular}{lccccccc}
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&CASSCF\fnm[1] &CASPT2\fnm[1] &CASPT2\fnm[1] &CASPT3\fnm[1] &CASPT3\fnm[1] &SC-NEVPT2\fnm[2] &PC-NEVPT2\fnm[2]\\
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& &(IPEA) &(NOIPEA) &(IPEA) &(NOIPEA)\\
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\hline
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MSE &$0.11$ &$0.06$ &$-0.26$ &$0,10$ &$0,05$ &$0,13$ &$0,09$\\
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SDE &$0.58$ &$0.14$ &$0.21$ &$0.13$ &$0.13$ &$0.14$ &$0.14$\\
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RMSE &$0.61$ &$0.16$ &$0.33$ &$0.17$ &$0.14$ &$0.19$ &$0.17$\\
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MAE &$0.48$ &$0.11$ &$0.27$ &$0.11$ &$0.09$ &$0.15$ &$0.13$\\
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Max($+$) &$2.15$ &$0.71$ &$0.30$ &$0.93$ &$0.79$ &$0.65$ &$0.46$\\
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Max($-$) &$-1.18$ &$-0.32$ &$-1.02$ &$-0.28$ &$-0.36$ &$-0.38$ &$-0.57$\\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Values from the present study.}
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\fnt[2]{Values taken from Ref.~\onlinecite{Sarka_2022}.}
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\end{table*}
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\begin{table*}
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\caption{MAEs determined for several subsets of transitions computed with various multi-reference methods.
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Count is the number of excited states considered in each subset.}
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\label{tab:stat_class}
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\begin{ruledtabular}
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\begin{tabular}{lcccccccc}
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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]\\
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& & &(IPEA) &(NOIPEA) &(IPEA) &(NOIPEA)\\
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\hline
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Singlet &174 &0.57 &0.14 &0.27 &0.14 &0.12 &0.16 &0.14\\
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Triplet &110 &0.34 &0.07 &0.29 &0.07 &0.06 &0.13 &0.11\\
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Valence &206 &0.45 &0.11 &0.33 &0.13 &0.10 &0.15 &0.12\\
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Rydberg &78 &0.54 &0.13 &0.13 &0.08 &0.07 &0.14 &0.15\\
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$n \to \pis$ &78 &0.44 &0.08 &0.44 &0.13 &0.10 &0.12 &0.10\\
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$\pi \to \pis$ &119 &0.46 &0.12 &0.27 &0.13 &0.10 &0.18 &0.14\\
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Double &9 &0.46 &0.11 &0.22 &0.12 &0.09 &0.14 &0.13\\
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1-3 non-H atoms &39 &0.38 &0.07 &0.21 &0.06 &0.05 &0.10 &0.08\\
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4 non-H atoms &94 &0.46 &0.11 &0.22 &0.12 &0.09 &0.14 &0.13\\
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5-6 non-H atoms &151 &0.51 &0.12 &0.33 &0.12 &0.11 &0.17 &0.15\\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Values from the present study.}
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\fnt[2]{Values taken from Ref.~\onlinecite{Sarka_2022}.}
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\end{table*}
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\begin{table*}
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\caption{CASPT2 and CASPT3 timings (in seconds) for a selection of systems and states.}
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\begin{ruledtabular}
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\begin{tabular}{llcccccccc}
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System & State &Active &\# electrons &\# basis &\# CAS &\# contracted &\# uncontracted &CPU &CPU\\
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& &Space & &functions &det. &config. &config. &CASPT2 &CASPT3 \\
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\hline
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Acetone &$^1A_2(n,\pis)$ &(6e,6o) &32 &322 &104 &$3.86 \times 10^6$ &$1.49 \times 10^8$ &12.50 &33.25\\
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Pyrrole &$^1A_2(\pi,3s)$ &(6e,6o) &36 &345 &96 &$4.79 \times 10^6$ &$2.04 \times 10^8$ &13.24 &49.36\\
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Imidazole &$^1A''(\pi,3s)$ &(8e,7o) &36 &322 &600 &$1.46 \times 10^7$ &$1.82 \times 10^9$ &193.93 &282.62\\
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Pyrazine &$^1B_{3u}(n,\pis)$ &(10e,8o) &42 &368 &392 &$6.95 \times 10^6$ &$6.38 \times 10^8$ &29.58 &174.96\\
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\end{tabular}
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\end{ruledtabular}
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\end{table*}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Conclusion}
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\section{Conclusion}
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@ -516,9 +516,9 @@ $^1A''[F](\pi,\pis)$ &($a'$:6,$a''$:3) &($A'$:1,$A''$:1) &0.72$^a$ &0.69$^a$ &0.
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\end{tabular}
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\end{tabular}
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\end{ruledtabular}
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\end{ruledtabular}
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\flushleft
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\flushleft
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$^a$Using reference $(8e,7o)$ active space including valence $\pi$, $\nN$ and $3s$ orbitals.
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$^a$Using reference (8e,7o) active space including valence $\pi$, $\nN$ and $3s$ orbitals.
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$^b$Using reference $(6e,9o)$ active space including valence $\pi$ and four $3p_z$ orbitals.
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$^b$Using reference (6e,9o) active space including valence $\pi$ and four $3p_z$ orbitals.
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$^c$Using reference $(8e,10o)$ active space including valence $\pi$, $\nN$, $3s$ and three $3p$ orbitals.
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$^c$Using reference (8e,10o) active space including valence $\pi$, $\nN$, $3s$ and three $3p$ orbitals.
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\end{table*}
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\end{table*}
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\begin{table*}
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\begin{table*}
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