small corrections

Manuscript/sfBSE.tex

@@ -761,7 +761,7 @@ Finally, the infinitesimal $\eta$ is set to $100$ meV for all calculations.
 All the static and dynamic BSE calculations (labeled in the following as SF-BSE and SF-dBSE respectively) are performed with the software \texttt{QuAcK}, \cite{QuAcK} developed in our group and freely available on \texttt{github}.
 The standard and extended spin-flip ADC(2) calculations [SF-ADC(2)-s and SF-ADC(2)-x, respectively] as well as the SF-ADC(3) \cite{Lefrancois_2015} are performed with Q-CHEM 5.2.1. \cite{qchem4}
 Spin-flip TD-DFT calculations \cite{Shao_2003} considering the BLYP, \cite{Becke_1988,Lee_1988} B3LYP, \cite{Becke_1988,Lee_1988,Becke_1993a} and BH\&HLYP \cite{Lee_1988,Becke_1993b} functionals with contains $0\%$, $20\%$, and $50\%$ of exact exchange are labeled as SF-TD-BLYP, SF-TD-B3LYP, and SF-TD-BH\&HLYP, respectively, and are also performed with Q-CHEM 5.2.1.
-\alert{Additionally, we have performed spin-flip TD-DFT calculations considering the following range-separated hybrid (RSH) functionals: CAM-B3LYP, \cite{Yanai_2004} LC-$\omega$HPBE, \cite{Henderson_2009} and $\omega$B97X-D. \cite{Chai_2008a,Chai_2008b}}
+\alert{Additionally, we have performed spin-flip TD-DFT calculations considering the following the range-separated hybrid (RSH) functionals: CAM-B3LYP, \cite{Yanai_2004} LC-$\omega$HPBE, \cite{Henderson_2009} and $\omega$B97X-D. \cite{Chai_2008a,Chai_2008b}}
 EOM-CCSD excitation energies \cite{Koch_1990,Stanton_1993,Koch_1994} are computed with Gaussian 09. \cite{g09}
 As a consistency check, we systematically perform SF-CIS calculations \cite{Krylov_2001a} with both \texttt{QuAcK} and Q-CHEM, and make sure that they yield identical excitation energies.
 Throughout this work, all spin-flip and spin-conserved calculations are performed with a UHF reference.
@@ -795,7 +795,7 @@ At the exception of the $^1D$ state, SF-BSE improves over SF-CIS with a rather s
 Note that the exact exchange seems to spin purified the $^3P(1s^2 2s^1 2p^1)$ state while the singlet states at the SF-BSE level are slightly more spin contaminated than their SF-CIS counterparts.
 
 \alert{Table \ref{tab:Be} and Fig.~\ref{fig:Be} also gathers results obtained at the partially self-consistent SF-(d)BSE@ev$GW$ and fully self-consistent SF-(d)BSE@qs$GW$ levels.
-The SF-(d)BSE excitation energies are quite stable with respect to the underlying $GW$ scheme which nicely illustrates that UHF eigenstates are actually an excellent starling point in this particular case.}
+The SF-(d)BSE excitation energies are quite stable with respect to the underlying $GW$ scheme which nicely illustrates that UHF eigenstates are actually an excellent starting point in this particular case.}
 
 The right side of Fig.~\ref{fig:Be} illustrates the performance of the SF-ADC methods.
 Interestingly, SF-BSE and SF-ADC(2)-s have rather similar accuracies, except again for the $^1D$ state where SF-ADC(2)-s has clearly the edge over SF-BSE.

Response_Letter/Response_Letter.tex

@@ -39,21 +39,25 @@ I recommend this manuscript for publication after the minor points addressed:}
 	\item 
 	{Figure 1/3: these show quite a relevant assessment of the performance of different SF methods. However, I think that the comparison with SF-TDDFT is unfair. None of the DFT exchange functionals is long-range corrected, whereas all other methods have the exact long-range exchange. Could the authors add the data for a long-range corrected functional?}
 	\\
-	\alert{Following the excellent advice of Reviewer \#1, we have added data for the long-range corrected CAM-B3LYP functional.
-	We believe that it is a consistent choice which fits nicely with the other functionals (BLYP, B3LYP, and BH\&HLYP) already included in the manuscript.
-	The CAM-B3LYP results have been added to the corresponding Tables and Figures.
-	As one can see...}
+	\alert{Following the excellent advice of Reviewer \#1, we have added data for the following range-separated hybrid functionals: CAM-B3LYP, LC-$\omega$HPBE, and $\omega$B97X-D.
+	These results have been added to the corresponding Tables and Figures.
+	In a nutshell, CAM-B3LYP does not really improved things and is less reliable than BH\&HLYP.}
 	
 	\item 
-	{Figure 1: The similarity between SF-dBSE and SF-ADC(2)-s is more than simply the results. I would say that the two formulations are equivalent, and should lead to the same results in Figure 1 if the authors would have used GW/SF-dBSE instead of G0W0/SF-dBSE. Could the authors add these results based on GW and comment?}
+	{Figure 1: The similarity between SF-dBSE and SF-ADC(2)-s is more than simply the results. 
+	I would say that the two formulations are equivalent, and should lead to the same results in Figure 1 if the authors would have used GW/SF-dBSE instead of G0W0/SF-dBSE.
+	Could the authors add these results based on GW and comment?}
 	\\
 	\alert{The reviewer is right to mention similarities between the SF-dBSE and SF-ADC(2)-s schemes.
 	However, they are not strictly identical as ADC(2) includes second-order exchange diagrams which are not present in SF-dBSE@$GW$, even in the case of more elaborate schemes like ev$GW$ and qs$GW$.
-	To illustrate this and accordingly to the reviewer's suggestion, we have added the partially self-consistent SF-dBSE@ev$GW$ results as well as the fully self-consistent SF-dBSE@qs$GW$ results. As one can see, in the case of Be, there is not much differences between these schemes and the original SF-dBSE@$G_0W_0$ which nicely illustrates that HF eigenstates are actually an excellent starling point in this particular case. 
+	To illustrate this and accordingly to the reviewer's suggestion, we have added the partially self-consistent SF-dBSE@ev$GW$ results as well as the fully self-consistent SF-dBSE@qs$GW$ results. 
+	As one can see, in the case of Be, there is not much differences between these schemes and the original SF-dBSE@$G_0W_0$ which nicely illustrates that HF eigenstates are actually an excellent starting point in this particular case. 
 	A discussion around these points have been also included in the revised version of the manuscript.}
  
 	\item 
-	{Figure 1: The only difference between SF-ADC(2)-s and SF-ADC(2)-x is that the energy difference in the dynamic part of the BSE equation is corrected to first order. The equivalent thing in SF-BSE would be to add in Eq. 30 the direct and exchange corrections in the orbital energy difference appearing in the denominator of the second term (i.e., similar to using the diagonal part of Eq. 29a and 29c in the orbital energy difference of Eq. 30). Could the authors verify that?}
+	{Figure 1: The only difference between SF-ADC(2)-s and SF-ADC(2)-x is that the energy difference in the dynamic part of the BSE equation is corrected to first order. 
+	The equivalent thing in SF-BSE would be to add in Eq. 30 the direct and exchange corrections in the orbital energy difference appearing in the denominator of the second term (i.e., similar to using the diagonal part of Eq. 29a and 29c in the orbital energy difference of Eq. 30). 
+	Could the authors verify that?}
 	\\
 	\alert{We thank the reviewer for mentioning this interesting fact. We were not aware of this.
 	Actually, this is already the case in SF-dBSE; the eigenvalues differences in the denominator of the second of Eq. 30 are $GW$ quasiparticle energies.
@@ -61,17 +65,18 @@ I recommend this manuscript for publication after the minor points addressed:}
 	We have performed SF-dBSE@$G_0W_0$ calculations replacing the $GW$ quasiparticle energies by the HF orbital energies in the denominator of Eq. (30) but it does not seem to alter much the results in the case of Be.}
 	
 	\item 
-	{Figure 2: Could the authors discuss the kink in G0W0/SF-BSE and G0W0/SF-dBSE (in supporting) appearing at around 1.2 Angstroms between $1\Sigma_g^+$ and $1\Sigma_u^+$. It is really puzzling. Is it due to the lack of self consistency in the G0W0 approximation? What does GW/SF-BSE gives in this case?}
+	{Figure 2: Could the authors discuss the kink in G0W0/SF-BSE and G0W0/SF-dBSE (in supporting) appearing at around 1.2 Angstroms between $1\Sigma_g^+$ and $1\Sigma_u^+$. It is really puzzling. 
+	Is it due to the lack of self consistency in the G0W0 approximation? 
+	What does GW/SF-BSE gives in this case?}
 	\\
 	\alert{The kink in the SF-BSE@$G_0W_0$ and SF-dBSE/$G_0W_0$ curves for \ce{H2} are due to the appearance of the symmetry-broken UHF solution.
 	Indeed, $R = 1.2~\AA$ corresponds to the location of the well-known Coulson-Fischer point.
 	Note that, as mentioned in our manuscript, all the calculations are performed with a UHF reference (even the ones based on a closed-shell singlet reference).
 	Of course, if one relies solely on the RHF solution, this kink disappears as illustrated by the figure below which has been also included in the Supporting Information. 
-	However, it would be inconsistent with the rest of the paper.
 	The appearance of this kink is now discussed in the revised version of the manuscript.
-	At the ev$GW$ level, this kink would certainly still exist as one does not self-consistently optimised the orbitals in this case.
+	At the ev$GW$ level, this kink would certainly still exist as one does not self-consistently optimise the orbitals in this case.
 	However, it would likely disappear at the qs$GW$ level but it remains to be confirmed (work is currently being done in this direction).
-	Unfortunately, it is extremely tedious to converge (partially) self-consistent $GW$ calculation with such large basis set (cc-pVQZ) for reasons discussed elsewhere [see, for example, V\'eril et al. JCTC 14, 5220 (2018)].}
+	Unfortunately, it is extremely tedious to converge (partially) self-consistent $GW$ calculations with such large basis set (cc-pVQZ) for reasons discussed elsewhere [see, for example, V\'eril et al. JCTC 14, 5220 (2018)].}
 	\\
 	\begin{center}
 		\includegraphics[width=0.5\textwidth]{SF-BSE-RHF}