diff --git a/Manuscript/FCI2.tex b/Manuscript/FCI2.tex index f1474fa..be0ce84 100644 --- a/Manuscript/FCI2.tex +++ b/Manuscript/FCI2.tex @@ -595,37 +595,36 @@ $^i${0-0 energies from Ref.~\citenum{Jud84c}.} \end{table} \titou{HERE} -For acetone, one should clearly distinguish the valence ES, for which both methodological and basis set effects are small, and the Rydberg transitions that, not only are very -sensitive to the basis set, but are upshifted by ca.~$0.04$ eV with {\CCSDTQ} as compared to {\CCT} and {\CCSDT}. For this compound, the 1996 {\CASPT} transition energies of Merch\'an and coworkers listed on the -r.h.s. of Table \ref{Table-4} are quite clearly too small, especially for the three valence ES. \cite{Mer96b} As expected, this error can be partially ascribed to the details of the calculations, as the Urban group obtained {\CASPT} -excitation energies of $4.40$, $4.09$ and $6.22$ eV for the $^1A_2$, $^3A_2$, and $^3A_1$ ES, \cite{Pas12} in much better agreement with ours. Their estimates for the three $n \ra 3p$ transitions of $7.52$, $7.57$, and $7.53$ eV -for the $^1A_2$, $^1A_1$, and $^1B_2$ ES also systematically fall within $0.10$ eV of our current CC values, whereas for these three ES, the current {\NEV} values are quite clearly too large. +For acetone, one should clearly distinguish the valence ES, for which both methodological and basis set effects are small, and the Rydberg transitions that both very +sensitive to the basis set, and upshifted by ca.~$0.04$ eV with {\CCSDTQ} as compared to {\CCT} and {\CCSDT}. For this compound, the 1996 {\CASPT} transition energies of Merch\'an and coworkers listed on the +right panel of Table \ref{Table-4} are clearly too low, especially for the three valence ES. \cite{Mer96b} As expected, this error can be partially ascribed to the \titou{details of the calculations}, as the Urban group obtained {\CASPT} +excitation energies of $4.40$, $4.09$ and $6.22$ eV for the $^1A_2$, $^3A_2$, and $^3A_1$ ES, \cite{Pas12} in much better agreement with ours. Their estimates of the three $n \ra 3p$ transitions, $7.52$, $7.57$, and $7.53$ eV +for the $^1A_2$, $^1A_1$, and $^1B_2$ ES, also systematically fall within $0.10$ eV of our current CC values, whereas for these three ES, the current {\NEV} values are clearly too large. -In contrast to acetone, both valence and Rydberg ES of thioacetone are rather insensitive to the CC expansion, as illustrated by the maximal discrepancies of $\pm$0.02 eV between the {\CCT} and {\CCSDTQ} results -with the {\Pop} basis set. While the lowest $n \ra \pis$ transition of both spin symmetries are rather insensitive to the selected basis set, all other states need quite large bases to be correctly described (Table S4). -As expected our theoretical vertical transition energies show the same ranking but are systematically larger than the available experimental 0-0 energies. +In contrast to acetone, both valence and Rydberg ES of thioacetone are rather insensitive to the CC expansion, as illustrated by the maximal discrepancies of $\pm$0.02 eV between the {\CCT}/{\Pop} and {\CCSDTQ}/{\Pop} results. +While the lowest $n \ra \pis$ transition of both spin symmetries are rather basis set insensitive, all the other states need quite large one-electron bases to be correctly described (Table S4). +As expected, our theoretical vertical transition energies show the same ranking but are systematically larger than the available experimental 0-0 energies. -For the isoleectronic isobutene, we considered two singlet Rydberg and one triplet valence ES. For all three cases, we note very nice agreement between {\CCT} and {\CCSDT} results for all considered basis sets, the -CC results being also within or very close to the {\FCI} estimates with Pople's basis set. The match with the {\CCSD} results of Caricato and coworkers, \cite{Car10} is also very satisfying. +For the isoleectronic isobutene molecule, we have considered two singlet Rydberg state and one triplet valence ES. For these three cases, we note, for each basis, a very nice agreement between {\CCT} and {\CCSDT}, the +CC results being also very close to the {\FCI} estimates obtained with the Pople basis set. The similarity with the {\CCSD} results of Caricato and coworkers \cite{Car10} is also very satisfying. -For the three remaining compounds, namely, cyanoformaldehyde, propynal, and thiopropynal, we report low-lying valence transitions all showing a largely dominant single excitation character. The basis set -effects are clearly under control (they are only significant for the second $^1A''$ ES of cyanoformaldehyde) and we could not detect any variation larger than $0.03$ eV between the {\CCT} and {\CCSDT} values for -a given basis, hinting that the CC values should be close to the spot, as confirmed by the {\FCI} data. +For the three remaining compounds, namely, cyanoformaldehyde, propynal, and thiopropynal, we report low-lying valence transitions with a definite single excitation character. The basis set +effects are clearly under control (they are only significant for the second $^1A''$ ES of cyanoformaldehyde) and we could not detect any variation larger than $0.03$ eV between the {\CCT} and {\CCSDT} values for +a given basis, alluding that the CC values are very accurate. +This is further confirmed by the {\FCI} data. \subsubsection{Intermediate conclusions} \label{sec-ic} -As we have seen for the 15 four-atom molecules considered here, we found extremely consistent transition energies between the tested CC approaches and the {\FCI} estimates in the vast majority of cases, -Importantly, we confirm the previous conclusions obtained on smaller compounds:\cite{Loo18a} i) {\CCSDTQ} values systematically fall within, or are extremely close from, the {\FCI} error bar, -ii) both {\CCT} and {\CCSDT} are also highly trustable when the considered ES does not show a very strong double excitation character. Indeed, considering all the 54 ``single transitions'' -for which {\CCSDTQ} estimates could be obtained (only excluding the lowest $^1A_g$ ES of butadiene and glyoxal), we determined trifling mean signed errors (MSE of 0.00 eV), tiny +As we have seen for the 15 four-atom molecules considered here, we found extremely consistent transition energies between CC and {\FCI} estimates in the vast majority of the cases. +Importantly, we confirm our previous conclusions obtained on smaller compounds: \cite{Loo18a} i) {\CCSDTQ} values systematically fall within (or are extremely close to) the {\FCI} error bar, +ii) both {\CCT} and {\CCSDT} are also highly trustable when the considered ES does not exhibit a strong double excitation character. Indeed, considering the 54 ``single'' excitations +for which {\CCSDTQ} estimates could be obtained (only excluding the lowest $^1A_g$ ES of butadiene and glyoxal), we determined negligible mean signed errors (MSE of $0.00$ eV), tiny MAE ($0.01$ and $0.02$ eV), and small maximal deviations ($0.05$ and $0.04$ eV) for {\CCT} and {\CCSDT}, respectively. This clearly indicates that these two approaches provide chemically-accurate -estimates (errors $< 1$ kcal.mol$^{-1}$ or $0.043$ eV) for most electronic transitions. Interestingly, some of us have shown that {\CCT} also provides chemically-accurate 0-0 energies as compared -to experimental values for most valence transitions. \cite{Loo18b,Loo19a,Sue19} When comparing the {\NEV} and {\CCT} ({\CCSDT}) results obtained with {\AVTZ} for all transitions in four-atom molecules, -one obtains a mean signed deviation of $+0.09$ ($+0.09$) eV and a mean absolute deviation of $0.11$ ($0.12$) eV, considering all 91 (65) ES for which comparisons are possible, again excluding only -the lowest $^1A_g$ states of butadiene and glyoxal. Although the error cannot be fully ascribed to the multi-reference method, that is additionally dependent of the selected active space, it seems to -indicate that {\NEV}, as applied here, has a slight tendency to overestimate the transition energies. This contrasts with the {\CASPT} approach that, from the comparisons discussed above, -generally undershoots the transition energies. +estimates (errors below $1$ kcal.mol$^{-1}$ or $0.043$ eV) for most electronic transitions. Interestingly, some of us have shown that {\CCT} also provides chemically-accurate 0-0 energies as compared +to experimental values for most valence transitions. \cite{Loo18b,Loo19a,Sue19} When comparing the {\NEV} and {\CCT} ({\CCSDT}) results obtained with {\AVTZ} for the 91 (65) ES for which comparisons are possible (again excluding only the lowest $^1A_g$ states of butadiene and glyoxal), +one obtains a mean signed deviation of $+0.09$ ($+0.09$) eV and a mean absolute deviation of $0.11$ ($0.12$) eV. +This seems to indicate that {\NEV}, as applied here, has a slight tendency to overestimate the transition energies. This contrasts with {\CASPT} that is known to generally underestimate transition energies, as further illustrated and discussed above. \subsection{Five-atom molecules} @@ -688,7 +687,7 @@ $^c${MR-CC results from Ref.~\citenum{Li10c};} $^d${{\AT} results from Ref.~\citenum{Hol15};} $^e${{\CCT} results from Ref.~\citenum{Sch17};} $^f${Various experiments summarized in Ref.~\citenum{Wan00};} -$^g${Electron impact from Ref.~\citenum{Vee76b}: for the $^1A_1$ state two values (6.44 and 6.61 eV) are reported, whereas for the two lowest triplet states, 3.99 eV and 5.22 eV values can be found in Ref.~\citenum{Fli76};} +$^g${Electron impact from Ref.~\citenum{Vee76b}: for the $^1A_1$ state two values (6.44 and 6.61 eV) are reported, whereas for the two lowest triplet states, Two values (3.99 eV and 5.22 eV) can be found in Ref.~\citenum{Fli76};} $^h${{\NEV} results from Ref.~\citenum{Pas06c};} $^i${Best estimate from Ref.~\citenum{Chr99}, based on CC calculations;} $^j${XMS-{\CASPT} results from Ref.~\citenum{Hei19};} @@ -768,7 +767,7 @@ $^c${MR-MP results from Ref.~\citenum{Nak96};} $^d${{\CCT} results from Ref.~\citenum{Sch17};} $^e${Electron impact from Ref.~\citenum{Fru79};} $^f${Gas phase absorption from Ref.~\citenum{McD91b};} -$^g${Energy loss from Ref.~\citenum{McD85} for the two valence state; two-photon resonant experiment from Ref.~\citenum{Sab92} for the $^1A_2$ Rydberg ES;} +$^g${Energy loss from Ref.~\citenum{McD85} for the two valence states; two-photon resonant experiment from Ref.~\citenum{Sab92} for the $^1A_2$ Rydberg ES;} $^h${{\CASPT} results from Ref.~\citenum{Ser96b};} $^i${{\CCT} results from Ref.~\citenum{Sil10c};} $^j${Gas-phase experimental estimates from Ref.~\citenum{Dev06};} @@ -777,7 +776,7 @@ $^l${SAC-CI results from Ref.~\citenum{Wan01};} $^m${CCSDR(3) results from Ref.~\citenum{Pas07};}%, this work also contains {\NEV} estimates;} $^n${TBE from Ref.~\citenum{Hol14}, based on EOM-CCSD for singlet and ADC(2) for triplets;} $^o${0-0 energies from Ref.~\citenum{Dil72};} -$^p${0-0 energies from Ref.~\citenum{Var82} for the singlets and energy loss experiment from Ref.~\citenum{Hab03} for the triplet ES;} +$^p${0-0 energies from Ref.~\citenum{Var82} for the singlets and energy loss experiment from Ref.~\citenum{Hab03} for the triplets;} $^q${0-0 energies from Ref.~\citenum{Hol14}.} \end{footnotesize} \end{flushleft} @@ -854,7 +853,7 @@ $^b${{\CCT} results from Ref.~\citenum{Chr96c};} $^c${SAC-CI results from Ref.~\citenum{Li07b};} $^d${RASPT2(18,18) results from Ref.~\citenum{Sha19};} $^e${Electron impact from Ref.~\citenum{Doe69};} -$^f${Jet-cooled experiment from Ref.~\citenum{Hir91} for the two lowest states, multi-photon experiments from Refs.~ \citenum{Joh76} and \citenum{Joh83} for the Rydberg states.} +$^f${Jet-cooled experiment from Ref.~\citenum{Hir91} for the two lowest states, multi-photon experiments from Refs.~\citenum{Joh76} and \citenum{Joh83} for the Rydberg states.} \end{footnotesize} \end{flushleft} \end{table} @@ -922,14 +921,14 @@ $^a${{\CASPT} results from Ref.~\citenum{Web99};} $^b${{\STEOM} results from Ref.~\citenum{Noo99};} $^c${SAC-CI results from Ref.~\citenum{Li07b};} $^d${{\CCT} results from Ref.~\citenum{Sch17};} -$^e${Dip spectroscopy from Ref.~\citenum{Oku90} ($B_{3u}$ and $B_{2g}$ states) and EEL from Ref.~\citenum{Wal91} (other states);} +$^e${\titou{Dip} spectroscopy from Ref.~\citenum{Oku90} ($B_{3u}$ and $B_{2g}$ states) and EEL from Ref.~\citenum{Wal91} (other states);} $^f${UV max from Ref.~\citenum{Bol84};} $^g${{\CASPT} results from Ref.~\citenum{Rub99};} $^h${Ext-{\STEOM} results from Ref.~\citenum{Noo00};} $^i${GVVPT2 results from Ref.~\citenum{Dev08};} $^j${{\NEV} results from Ref.~\citenum{Ang09};} $^k${{\CCT} results from Ref.~\citenum{Sil10c};} -$^l${From Ref.~\citenum{Pal97}, the singlets are from EEL, but for the 4.97 and 5.92 eV values that are from VUV; the triplets are from EEL, and other triplet peaks are mentioned at 4.21, 4.6, and 5.2 eV but not identified;} +$^l${From Ref.~\citenum{Pal97}, the singlets are from EEL, except for the $4.97$ and $5.92$ eV values that are from VUV; the triplets are from EEL, and other triplet peaks are mentioned at $4.21$, $4.6$, and $5.2$ eV but not identified;} $^m${all these doubly ES have a $(n,n \ra \pis, \pis)$ character.} \end{footnotesize} \end{flushleft} @@ -1089,7 +1088,7 @@ $^d${EOM-CCSD({$\tilde{{T}}$}) from Ref.~\citenum{Del97b};} $^e${UV max from Ref.~\citenum{Bol84};} $^f${EEL from Ref.~\citenum{Lin15};} $^g${{\CASPT} from Ref.~\citenum{Oli05};} -$^h${CC3-ext. from Ref.~\citenum{Sil10c}.} +$^h${CC3-ext.~from Ref.~\citenum{Sil10c}.} \end{footnotesize} \end{flushleft} \end{table} @@ -1381,12 +1380,12 @@ Triazine &$^1A_1'' (\Val; n \ra \pis)$ & & 88.3 & 4.72 & {\CCSDT}/AVTZ \begin{flushleft}\begin{footnotesize}\begin{singlespace} \vspace{-0.6 cm} $^a${ -Method A: {\CCSDT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\AVDZ} and {\CCSDT}/{\AVDZ} results; -Method B: {\CCSDT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\Pop} and {\CCSDT}/{\Pop} results; -Method C: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\Pop} and {\CCT}/{\Pop} results; -Method D: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDT}/{\AVDZ} and {\CCT}/{\AVDZ} results; -Method E: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDT}/{\Pop} and {\CCT}/{\Pop} results; -Method F: {exCI}/{\AVDZ} value (from Ref.~\citenum{Loo19c}) corrected by the difference between {\CCSDT}/{\AVTZ} and {\CCSDT}/{\AVDZ} results. +Method A: {\CCSDT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\AVDZ} and {\CCSDT}/{\AVDZ}; +Method B: {\CCSDT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\Pop} and {\CCSDT}/{\Pop}; +Method C: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDTQ}/{\Pop} and {\CCT}/{\Pop}; +Method D: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDT}/{\AVDZ} and {\CCT}/{\AVDZ}; +Method E: {\CCT}/{\AVTZ} value corrected by the difference between {\CCSDT}/{\Pop} and {\CCT}/{\Pop}; +Method F: {\FCI}/{\AVDZ} value (from Ref.~\citenum{Loo19c}) corrected by the difference between {\CCSDT}/{\AVTZ} and {\CCSDT}/{\AVDZ}. } \end{singlespace}\end{footnotesize}\end{flushleft}