ADC

Manuscript/ExPerspective.bib

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-%% Created for Pierre-Francois Loos at 2019-11-01 22:45:06 +0100 
+%% Created for Pierre-Francois Loos at 2019-11-02 15:06:53 +0100 
 
 
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Manuscript/ExPerspective.tex

@@ -166,7 +166,7 @@ Twenty years later, CIS(D) which adds a second-order perturbative correction to
 In the early 90's, the complete-active-space self-consistent field (CASSCF) method \cite{And90} and its second-order perturbation-corrected variant CASPT2 \cite{And92} (both developed in Roos' group) appeared.
 This was a real breakthrough.
 Although it took more than ten years to obtain analytic nuclear gradients, \cite{Cel03} CASPT2 was probably the first method that could provide quantitative results for molecular excited states of genuine photochemical interest. \cite{Roo96}
-Driven by Celestino and Malrieu, the creation of the second-order $n$-electron valence state perturbation theory (NEVPT2) method \cite{Ang01} several years later was able to cure some of the main theoretical deficiencies of CASPT2.
+Driven by Celestino and Malrieu, \cite{Ang01} the creation of the second-order $n$-electron valence state perturbation theory (NEVPT2) method several years later was able to cure some of the main theoretical deficiencies of CASPT2.
 In particular, NEVPT2 is known to be intruder state free.
 The limited applicability of these so-called multiconfigurational methods is mainly due to the necessity of defining an active space, as well as their factorial computational growth with the number of active electrons and orbitals.
 
@@ -177,27 +177,28 @@ The advent of time-dependent density-functional theory (TD-DFT) \cite{Run84,Dre0
 However, a large number of shortcomings were quickly discovered. \cite{Dre05}
 One of the most annoying feature of TD-DFT in the present context is its inability to describe, even qualitatively, charge-transfer states, \cite{Toz99} Rydberg states, \cite{Toz98} and double excitations. \cite{Lev06}
 Moreover, the difficulty of making TD-DFT systematically improvable obviously hampers its applicability.
-One of the main problem is the selection of the exchange-correlation functional and the variation of the results one can obtain with different choices.
+One of the main issue is the selection of the exchange-correlation functional from an ever growing zoo of functionals and the variation of the excitation energies one can obtain with different choices. \cite{Sue19}
 Despite all of this, TD-DFT is still nowadays the most employed excited-state method in the electronic structure community.
  
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-Thanks to the development of coupled cluster (CC) response theory, \cite{Koc90} and the huge growth of computer power, EOM-CCSD \cite{Sta93} became mainstream in the 2000's.
+Thanks to the development of coupled cluster (CC) response theory, \cite{Koc90} and the huge growth of computer power, equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) \cite{Sta93} became mainstream in the 2000's.
 EOM-CCSD gradient were also quickly available. \cite{Sta95}
-Higher orders are possible but extremely expensive. \cite{Nog87, Kuc91}
-This was quickly followed by the CC2 \cite{Chr95} and CC3 \cite{Chr95b} methods.
+Its third-order version EOM-CCSDT was also implemented and provides high accuracy at a significant higher cost. \cite{Nog87} 
+Although extremely expensive and tedious to implement, higher orders are also technically possible for small systems thanks to automatically-generated code. \cite{Kuc91}
+The EOM-CC family of methods was quickly followed by a slightly computationally lighter family with in front line the second-order CC2 method \cite{Chr95} and its third-order extension CC3 \cite{Chr95b} with formal computational scaling of $N^5$ and $N^7$ compared to $N^6$ and $N^8$ for EOM-CCSD and EOM-CCSDT, respectively.
 
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-Second- and third-order algebraic diagrammatic construction, ADC(2) \cite{Sch82} and ADC(3) \cite{Tro99,Har14}, represent interesting alternatives thanks to their reduced scaling compared to their CC equivalents.
-Moreover, fast and efficient implementation are now available. \cite{Dre15}
+The second- and third-order algebraic diagrammatic construction [ADC(2) \cite{Sch82} and ADC(3) \cite{Tro99,Har14}] which scale as $N^5$ and $N^6$ respectively, represent interesting alternatives thanks to their reduced scaling compared to their CC equivalents.
+Moreover, Dreuw's group has put an enormous amount of work to provide a fast and efficient implementation. \cite{Dre15} 
 
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-In that regard, the Bethe-Salpeter equation (BSE) formalism is a real plus.
+More recentky Finally, let us mention the Bethe-Salpeter equation (BSE) formalism (which is usually performed on top of a GW calculation).
 
 There is a clear need for computationally inexpensive electronic structure theory methods which can model accurately excited-state energetics and their corresponding properties. 
 Although  and TD-DFT the BSE formalism have emerged as powerful tools for computing excitation energies, fundamental deficiencies remain to be solved.