response letter first draft and manuscript corrections

BSEdyn.tex

@@ -818,7 +818,7 @@ One key result of the present investigation is that the dynamical correction is
 It is only for the smallest basis set (cc-pVDZ) that one can observe significant differences. 
 We can then safely conclude that the dynamical correction converges rapidly with respect to the size of the one-electron basis set, a triple-$\zeta$ or an augmented double-$\zeta$ basis being enough to obtain near complete basis set limit values.
 This is quite a nice feature as it means that one does not need to compute the dynamical correction in a very large basis to get a meaningful estimate of its magnitude.
-\titou{The difference between the values of the $GW$ gap, $\Eg^{\GW}$, obtained with cc-pVQZ and aug-cc-pVQZ can be explained by the additional radial completeness brought the set of diffuse functions in the latter one. \cite{Loos_2019c}}
+\titou{The difference between the values of the $GW$ gap, $\Eg^{\GW}$, obtained with cc-pVQZ and aug-cc-pVQZ can be explained by the additional radial completeness brought by the set of diffuse functions in the latter one. \cite{Loos_2019c}}
 
 
 
@@ -1139,12 +1139,12 @@ The BSE formalism is quickly gaining momentum in the electronic structure commun
 It now stands as a genuine cost-effective excited-state method and is regarded as a valuable alternative to the popular TD-DFT method.
 However, the vast majority of the BSE calculations are performed within the static approximation in which, in complete analogy with the ubiquitous adiabatic approximation in TD-DFT, the dynamical BSE kernel is replaced by its static limit.
 One key consequence of this static approximation is the absence of higher excitations from the BSE optical spectrum.
-Following Strinati's footsteps \titou{who originally derived the dynamical correction to the BSE}, \cite{Strinati_1982,Strinati_1984,Strinati_1988} several groups have explored the BSE formalism beyond the static approximation by retaining (or reviving) the dynamical nature of the screened Coulomb potential \cite{Sottile_2003,Romaniello_2009b,Sangalli_2011} or via a perturbative approach coupled with the plasmon-pole approximation. \cite{Rohlfing_2000,Ma_2009a,Ma_2009b,Baumeier_2012b}
+Following Strinati's footsteps \titou{who originally derived the dynamical BSE equations}, \cite{Strinati_1982,Strinati_1984,Strinati_1988} several groups have explored the BSE formalism beyond the static approximation by retaining (or reviving) the dynamical nature of the screened Coulomb potential \cite{Sottile_2003,Romaniello_2009b,Sangalli_2011} or via a perturbative approach coupled with the plasmon-pole approximation. \cite{Rohlfing_2000,Ma_2009a,Ma_2009b,Baumeier_2012b}
 
 In the present study, we have computed exactly the dynamical screening of the Coulomb interaction within the random-phase approximation, going effectively beyond both the usual static approximation and the plasmon-pole approximation.
 \titou{Dynamical corrections have been calculated using a renormalized first-order perturbative correction to the static BSE excitation energies following the work of Rohlfing and coworkers. \cite{Rohlfing_2000,Ma_2009a,Ma_2009b,Baumeier_2012b}
 Note that, although the present study goes beyond the static approximation of BSE, we do not recover additional excitations as the perturbative treatment accounts for dynamical effects only on excitations already present in the static limit. 
-However, we hope to report results on a genuinely dynamical approach in the near future in order to access double excitations within the BSE formalism.}
+However, we hope to report results on a genuine dynamical approach in the near future in order to access double excitations within the BSE formalism.}
 In order to assess the accuracy of the present scheme, we have reported a significant number of calculations for various molecular systems.
 Our calculations have been benchmarked against high-level CC calculations, allowing to clearly evidence the systematic improvements brought by the dynamical correction for both singlet and triplet excited states.
 We have found that, although $n \ra \pis$ and $\pi \ra \pis$ transitions are systematically red-shifted by $0.3$--$0.6$ eV thanks to dynamical effects, their magnitude is much smaller for CT and Rydberg states.

Response_Letter/Response_Letter.tex

@@ -50,7 +50,7 @@ I believe the paper is worth publishing.}
  
 	\item
 {Nonetheless I have a general comment: 
-Concerning the significance of screenign dynamics, I am not really sure 
+Concerning the significance of screening dynamics, I am not really sure 
 if the authors go beyond what others have already done. They go beyond 
 plasmon-pole modelling, which is a very good concept since plasmon-pole 
 models have always been questioned concerning their reliability - however, 
@@ -58,7 +58,7 @@ the authors do not compare their results with data obtained from
 plasmon-pole modelling. If they have such data readily available, 
 they might want to include them in the manuscript.}
 	\\
-	\alert{Sadly, it is hard to compare Rohlfing's results with ours as the molecules considered in Rohlfing's works are much larger than ours, and the calculations are performed in non-conventional basis sets [CHECK]. 
+	\alert{Sadly, it is hard to compare Rohlfing's results to ours as the molecules considered in Rohlfing's works are much larger than ours, the calculations are performed in non-conventional basis sets, and the underlying $GW$ calculations do not use the same starting point. 
 	We agree that, ultimately, it would be very interesting to test the performances of both approaches on the very same systems with the very same settings, but we feel this is outside the scope of the present study.}
 	
 	\item
@@ -82,7 +82,7 @@ be helpful to have all this in one paragraph. }
 	``It is important to note that, although all the studies mentioned above are clearly going beyond the static approximation of BSE, they are not able to recover additional excitations as the perturbative treatment accounts for dynamical effects only on excitations already present in the static limit. However, it does permit to recover, for transitions with a dominant single-excitation character, additional relaxation effects coming from higher excitations.''
 	To answer the reviewer's comment we have added a new paragraph to the concluding section, which reads: ``Dynamical corrections have been calculated using a renormalized first-order perturbative correction to the static BSE excitation energies following the work of Rohlfing and coworkers.
 Note that, although the present study goes beyond the static approximation of BSE, we do not recover additional excitations as the perturbative treatment accounts for dynamical effects only on excitations already present in the static limit. 
-However, we hope to report results on a genuinely dynamical approach in the near future in order to access double excitations within the BSE formalism.''
+However, we hope to report results on a genuine dynamical approach in the near future in order to access double excitations within the BSE formalism.''
 We have also added in Sec.~II.E. the following statement: ``As mentioned in Sec.~I, the present perturbative scheme does not allow to access double excitations as one loses the dynamical nature of the screening by applying perturbation theory. 
 We hope to report a genuine dynamical treatment of the BSE in a forthcoming work.''}
 
@@ -98,14 +98,14 @@ that somewhere (unless I missed it). }
 	\item 
 	{The authors use two different types of basis sets, cc-pVXZ and 
 aux-cc-pVXZ, both of which can be improved towards convergence by 
-choosig X=D, T, Q (etc.). However, Tab. I shows that the nitrogen $GW$ 
+choosing X=D, T, Q (etc.). However, Tab. I shows that the nitrogen $GW$ 
 quasiparticle gap does not converge towards the same value for the two 
 families (cc-pVQZ: 20.05 eV, aux-cc-pQVZ: 19.00 eV). 
 This seems to be a substantial difference. Why is that? }
 	\\
 	\alert{This is completely normal. 
 	To reach the complete basis set limit, one must have a basis set which is angularly complete as well as radially complete.
-	When X goes up, one improves the angular completeness of the basis set, while diffuse functions takes care of the radial completeness.
+	When X goes up, one improves the angular completeness of the basis set, while diffuse functions take care of the radial completeness.
 	For excited states and HOMO-LUMO gaps, because of the special importance of diffuse functions in these cases, the limit that one reaches with these two families of basis functions is indeed different. 
 	We refer the reviewer to [J. Chem. Phys. 151, 144118 (2019)] where the present observation is clearly illustrated.
 	We have mentioned this fact in the revised version near the beginning of the Results section.}
@@ -141,7 +141,7 @@ The work is rigorous, carefully done and well presented. The dynamical correctio
 	For example, in Section E are equations 32 to 42 new or were they already derived by Rohlfing and others? }
 	\\
 	\alert{Equations 32 to 42 aren't new.
-	Originally, the dynamical correction has been derived by Strinati [see Ref.~(2) for a detailed derivation].
+	Originally, the dynamical correction has been derived by Strinati [see Ref.~(2) for a detailed derivation] but we have gone further by deriving also the anti-resonant term (see Sec. II.D.).
 	We have clarified this point in two places in the revised manuscript (Introduction and Conclusion).}
 
 	\item 
@@ -159,7 +159,7 @@ The work is rigorous, carefully done and well presented. The dynamical correctio
 	``It is important to note that, although all the studies mentioned above are clearly going beyond the static approximation of BSE, they are not able to recover additional excitations as the perturbative treatment accounts for dynamical effects only on excitations already present in the static limit. However, it does permit to recover, for transitions with a dominant single-excitation character, additional relaxation effects coming from higher excitations.''
 	Nonetheless, to make it extra clear, we have added a new paragraph to the concluding section, which reads: ``Dynamical corrections have been calculated using a renormalized first-order perturbative correction to the static BSE excitation energies following the work of Rohlfing and coworkers.
 Note that, although the present study goes beyond the static approximation of BSE, we do not recover additional excitations as the perturbative treatment accounts for dynamical effects only on excitations already present in the static limit. 
-However, we hope to report results on a genuinely dynamical approach in the near future in order to access double excitations within the BSE formalism.''
+However, we hope to report results on a genuine dynamical approach in the near future in order to access double excitations within the BSE formalism.''
 We have also added in Sec.~II.E. the following statement: ``As mentioned in Sec.~I, the present perturbative scheme does not allow to access double excitations as one loses the dynamical nature of the screening by applying perturbation theory. 
 We hope to report a genuine dynamical treatment of the BSE in a forthcoming work.''}
 
@@ -168,19 +168,18 @@ We hope to report a genuine dynamical treatment of the BSE in a forthcoming work
 	Is this derivative easy to compute? 
 	Is $A^{(1)}(\Omega_S)$ available in analytic form or is the derivative performed numerically? }
 	\\
-	\alert{Yes, this derivative is straightforward to compute, and it is computed at no extra cost basically (as mentioned in the original manuscript, see Sec.~II.E.).
+	\alert{Yes, this derivative is straightforward to compute analytically, and it is computed at no extra cost basically (as mentioned in the original manuscript, see Sec.~II.E.).
 	The situation is very similar to the computation of the derivative of the $GW$ self-energy $\Sigma$ which is involved in the calculation of the spectral weight $Z$.}
-%	In the revised version of the manuscript, we have mentioned that this derivative can be computed easily at no extra cost.}
 
 	\item 
 	{Following up on my previous point, why does equation 40 have to be renormalised? 
 	It could be solve iteratively, as is done for the quasiparticle equation in $GW$. 
 	Then the aforementioned derivative would not have to be calculated. }
 	\\
-	\alert{Yes, the referee is right. There's two possibilities to solve this equation: renormalization or self-consistency.
-	As mentioned on page 6 of our original manuscript: "Moreover, we have observed that an iterative, self-consistent resolution [where the dynamically-corrected excitation energies are re-injected in Eq. (39)] yields basically the same results as its (cheaper) renormalized version."
-	In other words, we have tested both strategies and they basically yield similar results.
-	However, as mentioned, the renormalized version is much cheaper as one does not have to recompute all these quantities.}
+	\alert{Yes, the referee is right. There are two possibilities to solve this equation: renormalization or self-consistency.
+	As mentioned on page 6 of our original manuscript: ``Moreover, we have observed that an iterative, self-consistent resolution [where the dynamically-corrected excitation energies are re-injected in Eq. (39)] yields basically the same results as its (cheaper) renormalized version.''
+	In other words, we have tested both strategies and they basically yield identical results.
+	However, as mentioned above, the renormalized version is much cheaper as the derivative of the screening is basically free and one does not have to recompute several quantities that must be updated in the self-consistent version.}
 
 	\item 
 	{First paragraph of the introduction: "In recent years, it has been shown to be a valuable tool for computational chemists with a large number os systematic benchmark studies on large families of molecular systems appearing the literature [11-20] (see Ref. 21 for a recent review)." Maybe one could reference also the following, recent all-electron BSE implementation and benchmark study here: C. Liu, J. Kloppenburg, Y. Yao, X. Ren, H. Appel, Y. Kanai, and V. Blum, J. Chem. Phys. 152, 044105 (2020) }
@@ -193,7 +192,7 @@ We hope to report a genuine dynamical treatment of the BSE in a forthcoming work
 	These should also be visible in the optical transition energies. 
 	Such a conical intersection would be a good test for a theory that goes beyond standard BSE and can tackle more correlated systems, as recently demonstrated, for example, for dynamical configuration interaction (DCI) theory, which also includes GW and BSE elements (see e.g. M. Dvorak, D. Golze, and P. Rinke, Physical Review Materials 3, 070801(R) (2019)). }
 	\\
-	\alert{This is an interesting comment. Although outside the scope of the present study, we hope to be able to check the existence of this conical intersection in the near future while working with a fully dynamical scheme (i.e., nor perturbatively).}
+	\alert{This is an interesting comment. Although outside the scope of the present study, we hope to be able to check the existence of this conical intersection at the dynamical BSE level in the near future while working with a fully dynamical scheme (i.e., not perturbatively).}
 
 	\item 
 	{At the end of the Results and Discussion section the authors present an equation for a two level model (that does not have an equation number) to estimate when dynamical corrections are large and when not.