SF-EOM-CCSD

Manuscript/CBD.tex

@@ -409,12 +409,12 @@ We note that SF-ADC(2)-x [which scales as $\order*{N^6}$] is probably not worth
 This behavior was previously reported by Dreuw's group. \cite{Wormit_2014,Harbach_2014,Dreuw_2015}
 Overall, even with the best exchange-correlation functional, SF-TD-DFT is clearly outperformed by the more expensive SF-ADC models.
 
-\alert{We observe that SF-EOM-CCSD tends to underestimate by about \SI{1.5}{\kcalmol} the energy barrier compared to the TBE. 
-This can be alleviated by including the triples correction with SF-EOM-CCSD(fT) and SF-EOM-CCSD(dT) (see {\SupInf}). 
-We also note that the SF-EOM-CCSD values for the energy barrier are close to the CC3 ones. 
-Our results are in agreement with previous studies \cite{Manohar_2008,Lefrancois_2015} and justify to avoid the more expensive calculations of the triples correction as we can expect a similar trend. 
-Note that contrary to a previous statement \cite{Manohar_2008} the (fT) correction performs better than the (dT) correction for the energy barrier. 
-However, for the excited states, we retrieve the same statement (see below).}
+\alert{We observe that SF-EOM-CCSD/aug-cc-pVTZ tends to underestimate by about \SI{1.5}{\kcalmol} the energy barrier compared to the TBE, a observation in agreement with previous results by Manohar and Krylov. \cite{Manohar_2008}
+This can be alleviated by including the triples correction with SF-EOM-CCSD(fT) and SF-EOM-CCSD(dT) (see {\SupInf} where we have reported the data from Ref.~\onlinecite{Manohar_2008}). 
+We also note that the SF-EOM-CCSD values for the energy barrier are close to the ones obtained with the more expensive (standard) CC3 method, yet less accurate than values computed with the cheaper SF-ADC(2)-s formalism. 
+%Our results are in agreement with previous studies \cite{Manohar_2008,Lefrancois_2015} and justify to avoid the more expensive calculations of the triples correction as we can expect a similar trend. 
+Note that, contrary to a previous statement, \cite{Manohar_2008} the (fT) correction performs better than the (dT) correction for the energy barrier. 
+However, for the excited states, the situation is reversed (see below).}
 
 Concerning the multi-reference approaches with the minimal (4e,4o) active space, the TBEs are bracketed by the CASPT2 and NEVPT2 values that differ by approximately \SI{1.5}{\kcalmol} for all bases.
 In this case, the NEVPT2 values are fairly accurate with differences below half a \si{\kcalmol} compared to the TBEs.
@@ -640,9 +640,12 @@ This further motivates the ``pyramidal'' extrapolation scheme that we have emplo
 Again, the extended version, SF-ADC(2)-x, does not seem to be relevant in the present context with much larger errors than the other schemes.
 Also, as reported previously, \cite{Loos_2020d} SF-ADC(2)-s and SF-ADC(3) have mirror error patterns making SF-ADC(2.5) particularly accurate except for the doubly-excited state {\twoAg} where the error with respect to the TBE (\SI{0.140}{\eV}) is larger than the SF-ADC(2)-s error (\SI{0.093}{\eV}). 
 
-\alert{We observe that SF-EOM-CCSD excitation energies are closer to the SF-ADC(2)-s, with an energy difference of about \SI{0.1}{\eV}, than the other schemes as it was already noticed by LeFrançois and co-workers. \cite{Lefrancois_2015}
-We see that the SF-EOM-CCSD excitations energies for the triplet state are larger of about (\SI{0.3}{\eV} compared to the CCSD ones, this was also present in the study of Manohar and Krylov. \cite{Manohar_2008}
-Again, we have similar results, with SF-EOM-CCSD, than previous studies \cite{Manohar_2008,Lefrancois_2015} for the excited states. We can logically expect similar trend for SF-EOM-CCSD(fT) and SF-EOM-CCSD(dT) that lower the excitation energies and tend to be in a better agreement with respect to the TBE (see {\SupInf}). Note that the (dT) correction demonstrates better performance than the (fT) one as previously observed. \cite{Manohar_2008}}
+\alert{Interestingly, we observe that the SF-EOM-CCSD excitation energies are systematically larger than the TBEs by approximately \SI{0.2}{\eV} with a nice consistency throughout the various (singly- and doubly-) excited states. 
+Moreover, SF-EOM-CCSD excitation energies are somehow closer to their SF-ADC(2)-s analogs (with an energy difference of about \SI{0.1}{\eV}) than the other schemes as already noticed by LeFrançois and co-workers. \cite{Lefrancois_2015}
+We see that the SF-EOM-CCSD excitations energies for the triplet state are larger of about (\SI{0.3}{\eV} compared to the CCSD ones, this was also pointed out in the study of Manohar and Krylov. \cite{Manohar_2008}
+Again, our SF-EOM-CCSD results are very similar than the ones obtained in previous studies \cite{Manohar_2008,Lefrancois_2015}. 
+We can logically expect similar trend for SF-EOM-CCSD(fT) and SF-EOM-CCSD(dT) that lower the excitation energies and tend to be in better agreement with respect to the TBE (see {\SupInf}). 
+Note that the (dT) correction slightly outperforms the (fT) correction as previously observed \cite{Manohar_2008} and theoretically expected.}
 
 Let us now move to the discussion of the results obtained with standard wave function methods that are reported in Table \ref{tab:D2h}.
 Regarding the \alert{multi-reference} calculations, the most striking result is the poor description of the {\sBoneg} ionic state, especially with the (4e,4o) active space where CASSCF predicts this state higher in energy than the {\twoAg} state. 
@@ -849,8 +852,7 @@ Concerning the singlet-triplet gap, each scheme predicts it to be positive.
 Although it provides a decent singlet-triplet gap value, SF-ADC(2)-x seems to particularly struggle with the singlet excited states ({\Aoneg} and {\Btwog}), especially for the doubly-excited state {\Aoneg} where it underestimates the vertical excitation energy by \SI{0.4}{\eV}. 
 Again, averaging the SF-ADC(2)-s and SF-ADC(3) transition energies is beneficial in most cases at the exception of {\Aoneg}.
 Although the basis set effects are larger than at the SF-TD-DFT level, they remain quite moderate at the SF-ADC level, and this holds for wave function methods in general.
-
-\alert{Again, the SF-EOM-CCSD excitation energies are closer to the SF-ADC(2)-s ones than the other schemes and (dT) and (fT) corrections tend to give a better agreement with respect to the TBE (see {\SupInf}). As for the {\Dtwo} excitation energies, the (dT) correction performs better than the (fT) one.}
+\alert{Concerning the SF-EOM-CCSD excitation energies at the {\Dfour} square planar equilibrium geometry, very similar conclusions to the ones stated in the previous  section dealing with the excitation energies at the {\Dtwo} rectangular equilibrium geometry can be drawn: (i) SF-EOM-CCSD systematically and consistently overestimates the TBEs by approximately \SI{0.2}{\eV} and are less accurate than SF-ADC(2)-s, (ii) the non-iterative triples corrections tend to give a better agreement with respect to the TBE (see {\SupInf}), and (iii) the (dT) correction performs better than the (fT) one.}
 
 Let us turn to the multi-reference results (Table \ref{tab:D4h}).
 For both active spaces, expectedly, CASSCF does not provide a quantitive energetic description, although it is worth mentioning that the right state ordering is preserved.

Manuscript/sup-CBD.tex

@@ -252,7 +252,7 @@ Literature & $8.53$\fnm[3] & $1.573$\fnm[3] & $3.208$\fnm[3] & $4.247$\fnm[3] &
 	\fnt[3]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(2)-s/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
 	\fnt[4]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(2)-x/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
 	\fnt[5]{Value obtained from Ref.~\onlinecite{Lefrancois_2015} at the SF-ADC(3)/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
-	\fnt[6]{Value obtained from Ref.~\onlinecite{Manohar_2008} at the SF-EOM-CCSD/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
+	\fnt[6]{\alert{Value obtained from Ref.~\onlinecite{Manohar_2008} at the SF-EOM-CCSD/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}}
 	\fnt[7]{\alert{Value obtained from Ref.~\onlinecite{Manohar_2008} at the SF-EOM-CCSD(fT)/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}}
 	\fnt[8]{\alert{Value obtained from Ref.~\onlinecite{Manohar_2008} at the SF-EOM-CCSD(dT)/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}}
 	\fnt[9]{\alert{Value obtained from Ref.~\onlinecite{Gulania_2021} at the EOM-DEA-CCSD/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}}