Done 2nd iteration for T2

Manuscript/ExPerspective.tex

@@ -92,9 +92,8 @@ First of all (and maybe surprisingly), it is, in most cases, tricky to obtain re
 do not usually match 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}
 
-\titou{Second, developing theories suited for excited states is more complex than ground-state theories because some fundamental safety nets, \eg, bounding from below, are not available in contrast to the ground electronic states, which additionally makes the results often less accurate for excited states
-than for ground states.
-For a given accuracy, excited-state methods are usually more expensive than their ground-state counterpart.}
+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.
+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, 
 triplet, etc). Therefore, it would be highly desirable to possess a computational method (or protocol) that provides a balanced treatment of the entire ``spectrum'' of excited states. 
@@ -108,7 +107,7 @@ respect to system size and small memory footprint cannot be disregarded. Althoug
 %%% TABLE I %%%
 %\begin{squeezetable}
 \begin{table}
-\caption{Formal computational scaling of various excited-state methods with respect to the number of one-electron basis functions $N$ and the accessibility of various key properties in \titou{widely available} computational software packages.
+\caption{Formal computational scaling of various excited-state methods with respect to the number of one-electron basis functions $N$ and the accessibility of various key properties in popular computational software packages.
 The typical error range of estimate for single excitations is also provided as a very rough indicator of the method accuracy.}
 \label{tab:method}
 \begin{ruledtabular}
@@ -193,7 +192,7 @@ For the sake of brevity, we drop the EOM acronym in the rest of this \textit{Per
 The CC family of methods was quickly followed by an approximated and computationally lighter family with, in front line, the second-order CC2 model \cite{Chr95} and its third-order extension, CC3. \cite{Chr95b}
 As a $N^7$ method (where $N$ is the number of basis functions), CC3 has a particularly interesting accuracy/cost ratio with errors usually below the chemical accuracy threshold. \cite{Hat05c,Loo18a,Loo18b,Loo19a}
 The series CC2, CCSD, CC3, CCSDT defines a hierarchy of models with $N^5$, $N^6$, $N^7$ and $N^8$ scaling, respectively.
-It is also noteworthy that CCSDT and CC3 are also able to \titou{pinpoint} the presence of double excitations, a feature that is absent from both CCSD and CC2. \cite{Loo19c} 
+It is also noteworthy that CCSDT and CC3 are also able to detect the presence of double excitations, a feature that is absent from both CCSD and CC2. \cite{Loo19c} 
 
 %%%%%%%%%%%%%%%%%%%
 %%% ADC METHODS %%%
@@ -224,7 +223,25 @@ One of the strength of one of the implementation, based on the CIPSI (configurat
 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}
 However, although the \textit{``exponential wall''} is pushed back, this type of method is only applicable to molecules with a small number of heavy atoms and/or relatively compact basis sets.
 
-%DJ to T2: \hl{ordonner tjrs les methodes pareil + ajouter ADC(3).  J'ai les valeurs dispos, je te renverrais cela}
+%%%%%%%%%%%%%%%%%
+%%% COMPUTERS %%%
+%%%%%%%%%%%%%%%%%
+For someone who has never worked with SCI methods, it might be surprising to see that one is able to compute near-FCI excitation energies for molecules as big as benzene. \cite{Chi18,Loo19c,Loo20}
+This is mainly due to some specific choices in terms of implementation as explained below.
+Indeed, to keep up with Moore's ``Law'' in the early 2000's, the processor designers had no other choice than to propose multi-core chips to avoid an explosion of the energy requirements.
+Increasing the number of floating-point operations per second by doubling the number of CPU cores only requires to double the required energy, while doubling the frequency multiplies the required energy by a factor of $\sim$ 8.
+This bifurcation in hardware design implied a \emph{change of paradigm} \cite{Sut05} in the implementation and design of computational algorithms. A large degree of parallelism is now required to benefit from a significant acceleration.
+Fifteen years later, the community has made a significant effort to redesign the methods with parallel-friendly algorithms. \cite{Val10,Cle10,Gar17b,Pen16,Kri13,Sce13}
+In particular, the change of paradigm to reach FCI accuracy with SCI methods came
+from the use of determinant-driven algorithms which were considered for long as inefficient
+with respect to integral-driven algorithms.
+The first important element making these algorithms efficient is the introduction of new bit manipulation instructions (BMI) in the hardware that enable an extremely fast evaluation of Slater-Condon rules \cite{Sce13b} for the direct calculation of
+the Hamiltonian matrix elements over arbitrary determinants.
+Then massive parallelism can be harnessed to compute the second-order perturbative correction with semi-stochatic algorithms, \cite{Gar17b,Sha17} and perform the sparse matrix multiplications required in Davidson's algorithm to find the eigenvectors associated with the lowest eigenvalues.
+Block-Davidson methods can require a large amount of memory, and the recent introduction of byte-addressable non-volatile memory as a new tier in the memory hierarchy \cite{Pen19} will enable SCI calculations on larger molecules.
+The next generation of supercomputers is going to generalize the presence of accelerators (graphical processing units, GPUs), leading to a new software crisis.
+Fortunately, some authors have already prepared this transition. \cite{Dep11,Kim18,Sny15,Ufi08,Kal17}
+
 
 %%%%%%%%%%%%%%%
 %%% SUMMARY %%% 
@@ -290,7 +307,7 @@ Recently, we made, what we think, is a significant contribution to this quest fo
 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 accurate 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 accounting for double and triple excitations (see Fig.~\ref{fig:Set1}): CIS(D), ADC(2), ADC(3), CC2, STEOM-CCSD, \cite{Noo97} CCSD, CCSDR(3), \cite{Chr77}  CCSDT-3, \cite{Wat96} CC3, CCSDT, and CCSDTQ.
+Importantly, it allowed us to benchmark a series of popular excited-state wave function methods 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 less accurate than CC3, CCSDT-3 could be used as a reliable reference for benchmark studies. 
 Quite surprisingly, ADC(3) was found to have a clear tendency to overcorrect its second-order version ADC(2).
 
@@ -302,25 +319,6 @@ For ``pure'' double excitations (\ie, for transitions which do not mix with sing
 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 more around $0.1$--$0.2$ eV (see Fig.~\ref{fig:Set2}).
 
-%%%%%%%%%%%%%%%%%
-%%% COMPUTERS %%%
-%%%%%%%%%%%%%%%%%
-For someone who has never worked with SCI methods, it might be surprising to see that one is able to compute near-FCI excitation energies for molecules as big as benzene. \cite{Chi18,Loo19c,Loo20}
-This is mainly due to some specific choices in terms of implementation as explained below.
-Indeed, to keep up with Moore's ``Law'' in the early 2000's, the processor designers had no other choice than to propose multi-core chips to avoid an explosion of the energy requirements.
-Increasing the number of floating-point operations per second by doubling the number of CPU cores only requires to double the required energy, while doubling the frequency multiplies the required energy by a factor of $\sim$ 8.
-This bifurcation in hardware design implied a \emph{change of paradigm} \cite{Sut05} in the implementation and design of computational algorithms. A large degree of parallelism is now required to benefit from a significant acceleration.
-Fifteen years later, the community has made a significant effort to redesign the methods with parallel-friendly algorithms. \cite{Val10,Cle10,Gar17b,Pen16,Kri13,Sce13}
-In particular, the change of paradigm to reach FCI accuracy with SCI methods came
-from the use of determinant-driven algorithms which were considered for long as inefficient
-with respect to integral-driven algorithms.
-The first important element making these algorithms efficient is the introduction of new bit manipulation instructions (BMI) in the hardware that enable an extremely fast evaluation of Slater-Condon rules \cite{Sce13b} for the direct calculation of
-the Hamiltonian matrix elements over arbitrary determinants.
-Then massive parallelism can be harnessed to compute the second-order perturbative correction with semi-stochatic algorithms, \cite{Gar17b,Sha17} and perform the sparse matrix multiplications required in Davidson's algorithm to find the eigenvectors associated with the lowest eigenvalues.
-Block-Davidson methods can require a large amount of memory, and the recent introduction of byte-addressable non-volatile memory as a new tier in the memory hierarchy \cite{Pen19} will enable SCI calculations on larger molecules.
-The next generation of supercomputers is going to generalize the presence of accelerators (graphical processing units, GPUs), leading to a new software crisis.
-Fortunately, some authors have already prepared this transition. \cite{Dep11,Kim18,Sny15,Ufi08,Kal17}
-
 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.
 To obtain this new, larger set of TBEs, we employed CC methods up to the highest possible order (CC3, CCSDT, and CCSDTQ), very large SCI calculations (with up to hundred million determinants), as well as the most robust multiconfigurational method, NEVPT2. 
@@ -339,11 +337,13 @@ It would likely stimulate further theoretical developments in excited-state meth
 %%%%%%%%%%%%%%%%%%
 %%% Properties
 %%%%%%%%%%%%%%%%%%
-\titou{Besides all previously described works aiming at reaching chemically accurate vertical transition energies, it should be pointed out that an increasing effort is now set to determine highly-trustable excited-state properties as well. 
-This includes first the 0-0 energies, \cite{Die04b,Hat05c,Goe10a,Sen11b,Win13,Fan14b,Loo18b,Loo19a,Loo19b} that, as mentioned above, as they offer well-grounded comparisons with experiment.  
-However, as these 0-0 energies are not very sensitive to the used geometry, \cite{Sen11b,Win13,Loo19a} they are not very indicative of the quality of the underlying structures.  
-This is why, one can find several sets of excited-state geometries determined with various wavefunction approaches, \cite{Pag03,Gua13,Bou13,Tun16,Bud17} a few using very refined models, \cite{Gua13,Bud17} as well as evaluations of the accuracy of the gradients at the FC point. \cite{Taj18,Taj19}  
-The interested researchers can also find several investigations proposing sets of reference oscillator strengths, \cite{Sil10c,Har14,Kan14,Loo18a,Loo20b} but other more complex properties, such as two-photon cross-sections and vibrations, have been mostly determined at lower levels of theory hinting that the story is far from its end.}
+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 now 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} and also investigate the accuracy of the nuclear gradients at the Franck-Condon point. \cite{Taj18,Taj19}  
+The interested researcher may also 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.
 
 %%%%%%%%%%%%%%%%%%
 %%% CONCLUSION %%%