minor corrections

Manuscript/ExPerspective.bib

@@ -1,8 +1,7 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-
+%% Created for Pierre-Francois Loos at 2019-11-19 20:03:52 +0100 
-%% Created for Denis Jacquemin at 2019-11-19 19:32:14 +0100 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
@@ -83,6 +82,28 @@
 @string{theo = {J. Mol. Struct. (THEOCHEM)}}
 
 
+@article{Odd78,
+	Author = {J. Oddershede},
+	Date-Added = {2019-11-19 19:58:44 +0100},
+	Date-Modified = {2019-11-19 19:59:44 +0100},
+	Journal = {Adv. Quantum Chem.},
+	Pages = {275--352},
+	Title = {Polarization Propagator Calculations},
+	Volume = {11},
+	Year = {1978}}
+
+@article{Pac96,
+	Author = {M. J. Packer and E. K. Dalskov and T. Enevoldsen and H. J. A. Jensen and J. Oddershede},
+	Date-Added = {2019-11-19 19:55:57 +0100},
+	Date-Modified = {2019-11-19 20:03:41 +0100},
+	Doi = {10.1063/1.472430},
+	Journal = {J. Chem. Phys.},
+	Pages = {5886},
+	Title = {A new Implementation of the Second-Order Polarization Propagator Approximation (SOPPA): The Excitation Spectra of Benzene and Naphthalene},
+	Volume = {105},
+	Year = {1996},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.472430}}
+
 @article{Loo19b,
 	Author = {Loos, Pierre-Francois and Jacquemin, Denis},
 	Date-Added = {2019-11-19 19:26:28 +0100},

Manuscript/ExPerspective.tex

@@ -92,7 +92,7 @@ First of all (and maybe surprisingly), it is, in most cases, tricky to obtain re
 do not usually correspond to theoretical values as one needs to take into account both geometric relaxation and zero-point vibrational energy motion. Even more problematic, experimental spectra might not be available in gas phase, and, in the worst-case scenario, no clear 
 assignment could be made. For a more faithful comparison between theory and experiment, although more computationally demanding, the so-called 0-0 energies are definitely a safer playground. \cite{Die04b,Win13,Fan14b,Loo19b}
 
-Second, developing theories suited for excited states is usually more complex than their ground-state equivalent as a variational principle may not be available for excited states.
+Second, developing theories suited for excited states is usually more complex and costly than their ground-state equivalent, as one might lack a proper variational principle for excited-state energies. 
 As a consequence, for a given level of theory, excited-state methods are usually less accurate than their ground-state counterpart.
 
 Another feature that makes excited states particularly fascinating and challenging is that they can be both extremely close in energy from each other and have very different natures ($\pi \ra \pi^*$, $n \ra \pi^*$, charge transfer, double excitation, valence, Rydberg, singlet, 
@@ -198,7 +198,8 @@ It is also noteworthy that CCSDT and CC3 are also able to detect the presence of
 %%% ADC METHODS %%%
 %%%%%%%%%%%%%%%%%%%
 It is also important to mention the recent rejuvenation of the second- and third-order algebraic diagrammatic construction [ADC(2) \cite{Sch82} and ADC(3) \cite{Tro99,Har14}] methods that scale as $N^5$ and $N^6$, respectively.
-This renaissance was certainly initiated by the enormous amount of work invested by Dreuw's group in order to provide a fast and efficient implementation of these methods, \cite{Dre15}  including the analytical gradients, \cite{Reh19} as well as other interesting variants.
+These methods are related to the older second- and third-order polarization propagator approaches (SOPPA and TOPPA). \cite{Odd78,Pac96}
+This renaissance was certainly initiated by the enormous amount of work invested by Dreuw's group in order to provide a fast and efficient implementation of these methods, \cite{Dre15} including the analytical gradients, \cite{Reh19} as well as other interesting variants.
 These Green's function one-electron propagator techniques indeed represent valuable alternatives thanks to their reduced cost compared to their CC equivalents.
 In that regard, ADC(2) is particularly attractive with an error around $0.1$--$0.2$ eV.
 However, we have recently observed that ADC(3) generally overcorrects the ADC(2) excitation energies and is significantly less accurate than CC3. \cite{Tro02,Loo18a,Loo20}
@@ -207,8 +208,8 @@ However, we have recently observed that ADC(3) generally overcorrects the ADC(2)
 %%% BSE@GW %%%
 %%%%%%%%%%%%%%
 Finally, let us mention the many-body Green's function Bethe-Salpeter equation (BSE) formalism \cite{Str88} (which is usually performed on top of a \emph{GW} calculation). \cite{Hed65}
-BSE has gained momentum in the past few years and is a serious candidate as a computationally inexpensive electronic structure theory method that can effectively model  excited states with a typical error of $0.1$--$0.3$ eV, as well as  some related properties. \cite{Jac17b,Bla18}
+BSE has gained momentum in the past few years and is a serious candidate as a computationally inexpensive electronic structure theory method that can effectively model excited states with a typical error of $0.1$--$0.3$ eV, as well as some related properties. \cite{Jac17b,Bla18}
-One of the main advantage of BSE compared to TD-DFT (with a similar computational cost) is that it allows a faithful description of charge-transfer states and, when performed on top of a (partially) self-consistently  \emph{GW}  calculation, BSE@\emph{GW}  has been shown to be weakly dependent on its starting point (\ie, on the functional selected for the underlying DFT calculation). \cite{Jac16,Gui18}
+One of the main advantage of BSE compared to TD-DFT (with a similar computational cost) is that it allows a faithful description of charge-transfer states and, when performed on top of a (partially) self-consistently \emph{GW} calculation, BSE@\emph{GW} has been shown to be weakly dependent on its starting point (\ie, on the functional selected for the underlying DFT calculation). \cite{Jac16,Gui18}
 However, due to the adiabatic (\ie, static) approximation, doubly excited states are completely absent from the BSE spectrum.
 
 %%%%%%%%%%%%%%%%%%%
@@ -217,7 +218,7 @@ However, due to the adiabatic (\ie, static) approximation, doubly excited states
 In the past five years, \cite{Gin13,Gin15} we have witnessed a resurgence of the so-called selected CI (SCI) methods \cite{Ben69,Whi69,Hur73} thanks to the development and implementation of new, fast, and efficient algorithms to select cleverly determinants in the full CI (FCI) space (see Refs.~\onlinecite{Gar18,Gar19} and references therein). 
 SCI methods rely on the same principle as the usual CI approach, except that determinants are not chosen \textit{a priori} based on occupation or excitation criteria but selected among the entire set of determinants based on their estimated contribution to the FCI wave function or energy. 
 Indeed, it has been noticed long ago that, even inside a predefined subspace of determinants, only a small number of them significantly contributes.
-The main advantage of SCI methods is that no  \textit{a priori}  assumption is made on the type of electron correlation. 
+The main advantage of SCI methods is that no \textit{a priori} assumption is made on the type of electron correlation. 
 Therefore, at the price of a brute force calculation, a SCI calculation is not, or at least less, biased by the user appreciation of the problem's complexity.
 One of the strength of one of the implementation, based on the CIPSI (configuration interaction using a perturbative selection made iteratively) algorithm developed by Huron, Rancurel, and Malrieu \cite{Hur73} is its parallel efficiency which makes possible to run on thousands of CPU cores. \cite{Gar19}
 Thanks to these tremendous features, SCI methods deliver near FCI quality excitation energies for both singly and doubly excited states, \cite{Hol17,Chi18,Loo18a,Loo19c} with an error of roughly $0.03$ eV, mostly originating from the extrapolation procedure. \cite{Gar19}
@@ -305,7 +306,7 @@ These two studies clearly demonstrate and motivate the need for higher accuracy
 %%%%%%%%%%%%%%%%%%%%%%%
 Recently, we made, what we think, is a significant contribution to this quest for highly accurate vertical excitation energies. \cite{Loo18a}
 More specifically, we studied 18 small molecules with sizes ranging from one to three non-hydrogen atoms.
-For such systems, using a combination of high-order CC methods, SCI calculations and large diffuse basis sets, we were able to compute a list of 110 highly accurate vertical excitation energies for excited states of various natures (valence, Rydberg, $n \ra \pi^*$, $\pi \ra \pi^*$, singlet, triplet and doubly excited) based on  CC3/\emph{aug}-cc-pVTZ geometries.
+For such systems, using a combination of high-order CC methods, SCI calculations and large diffuse basis sets, we were able to compute a list of 110 highly accurate vertical excitation energies for excited states of various natures (valence, Rydberg, $n \ra \pi^*$, $\pi \ra \pi^*$, singlet, triplet and doubly excited) based on CC3/\emph{aug}-cc-pVTZ geometries.
 In the following, we label this set of TBEs as {\SetA}.
 Importantly, it allowed us to benchmark a series of popular excited-state wave function methods partially or fully accounting for double and triple excitations (see Fig.~\ref{fig:Set1}): CIS(D), CC2, CCSD, STEOM-CCSD, \cite{Noo97} CCSDR(3), \cite{Chr77} CCSDT-3, \cite{Wat96} CC3, ADC(2), and ADC(3).
 Our main conclusion was that CC3 is extremely accurate (with a mean absolute error of only $\sim 0.03$ eV), and that, although slightly less accurate than CC3, CCSDT-3 could be used as a reliable reference for benchmark studies. 
@@ -318,7 +319,7 @@ An important addition to this second study was the evaluation of various flavors
 Our results clearly evidence that the error in CC methods is intimately related to the amount of double-excitation character in the vertical transition. 
 For ``pure'' double excitations (\ie, for transitions which do not mix with single excitations), the error in CC3 and CCSDT can easily reach $1$ and $0.5$ eV, respectively, while it goes down to a few tenths of an electronvolt for more common transitions (such as in \emph{trans}-butadiene and benzene) involving a significant amount of singles.\cite{Shu17,Bar18b,Bar18a}
 The quality of the excitation energies obtained with multiconfigurational methods was harder to predict as the overall accuracy of these methods is highly dependent on both the system and the selected active space.
-Nevertheless, CASPT2 and NEVPT2 were found to be more accurate for transition with a small percentage of single excitations (error usually below $0.1$ eV) than for excitations dominated by single excitations where the error is  closer from $0.1$--$0.2$ eV (see Fig.~\ref{fig:Set2}).
+Nevertheless, CASPT2 and NEVPT2 were found to be more accurate for transition with a small percentage of single excitations (error usually below $0.1$ eV) than for excitations dominated by single excitations where the error is closer from $0.1$--$0.2$ eV (see Fig.~\ref{fig:Set2}).
 
 In our latest study, \cite{Loo20} in order to provide more general conclusions, we generated highly accurate vertical transition energies for larger compounds with a set composed by 27 organic molecules encompassing from four to six non-hydrogen atoms for a total of 223 vertical transition energies of various natures.
 This set, labeled as {\SetC} and still based on CC3/\emph{aug}-cc-pVTZ geometries, is constituted by a reasonably good balance of singlet, triplet, valence, and Rydberg states.
@@ -326,7 +327,7 @@ To obtain this new, larger set of TBEs, we employed CC methods up to the highest
 Each approach was applied in combination with diffuse-containing atomic basis sets.
 For all the transitions of the {\SetC} set, we reported at least CCSDT/\emph{aug}-cc-pVTZ (sometimes with basis set extrapolation) and CC3/\emph{aug}-cc-pVQZ transition energies as well as CC3/\emph{aug}-cc-pVTZ oscillator strengths for each dipole-allowed transition. 
 Pursuing our previous benchmarking efforts, \cite{Loo18a,Loo19c} we confirmed that CC3 almost systematically delivers transition energies in agreement with higher-level theoretical models ($\pm 0.04$ eV) except for transitions presenting a dominant double excitation character (see Fig.~\ref{fig:Set3}).
-This  settles down, at least for now, the debate by demonstrating the superiority of CC3 (in terms of accuracy) compared to methods like CCSDT-3 or ADC(3), see Fig.~\ref{fig:Set3}.
+This settles down, at least for now, the debate by demonstrating the superiority of CC3 (in terms of accuracy) compared to methods like CCSDT-3 or ADC(3), see Fig.~\ref{fig:Set3}.
 Moreover, thanks to the exhaustive and detailed comparisons made in Ref.~\onlinecite{Loo20}, we could safely conclude that CC3 also regularly outperforms CASPT2 (which often underestimates excitation energies) and NEVPT2 (which typically overestimates excitation energies) as long as the corresponding transition does not show any strong multiple excitation character.
 
 Our current efforts are now focussing on expanding and merging these sets to create an complete test set of highly accurate excitations energies.
@@ -341,7 +342,7 @@ It would likely stimulate further theoretical developments in excited-state meth
 Besides all the studies described above aiming at reaching chemically accurate vertical transition energies, it should be pointed out that an increasing amount of effort is currently devoted to the obtention of highly-trustable excited-state properties. 
 This includes, first, 0-0 energies, \cite{Die04b,Hat05c,Goe10a,Sen11b,Win13,Fan14b,Loo18b,Loo19a,Loo19b} which, as mentioned above, offer well-grounded comparisons with experiment. 
 However, because 0-0 energies are fairly insensitive to the underlying molecular geometries, \cite{Sen11b,Win13,Loo19a} they are not a good indicator of their overall quality. 
-Consequently, one can find in the literature several sets of excited-state geometries obtained at various levels of theory, \cite{Pag03,Gua13,Bou13,Tun16,Bud17} some of them are determined using state-of-the-art models. \cite{Gua13,Bud17} 
+Consequently, one can find in the literature several sets of excited-state geometries obtained at various levels of theory, \cite{Pag03,Gua13,Bou13,Tun16,Bud17} some of them being determined using state-of-the-art models. \cite{Gua13,Bud17} 
 There are also investigations of the accuracy of the nuclear gradients at the Franck-Condon point. \cite{Taj18,Taj19} 
 The interested researcher may find useful several investigations reporting sets of reference oscillator strengths. \cite{Sil10c,Har14,Kan14,Loo18a,Loo20b} 
 More complex properties, such as two-photon cross-sections and vibrations, have been mostly determined at lower levels of theory, hinting at future studies on this particular subject.