Day 3

Manuscript/ExPerspective.bib

@@ -1,7 +1,7 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2019-10-30 17:34:05 +0100 
+%% Created for Pierre-Francois Loos at 2019-10-31 16:08:35 +0100 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
@@ -82,6 +82,194 @@
 @string{theo = {J. Mol. Struct. (THEOCHEM)}}
 
 
+@article{Tro99,
+	Author = {A. B. Trofimov and G. Stelter and J. Schirmer},
+	Date-Added = {2019-10-31 15:04:29 +0100},
+	Date-Modified = {2019-10-31 15:05:20 +0100},
+	Journal = {J. Chem. Phys.},
+	Pages = {9982},
+	Title = {A Consistent Third-Order Propagator Method For Electronic Excitation},
+	Volume = {111},
+	Year = {1999}}
+
+@article{Sch82,
+	Author = {J. Schirmer},
+	Date-Added = {2019-10-31 15:02:19 +0100},
+	Date-Modified = {2019-10-31 15:03:19 +0100},
+	Journal = {Phys. Rev. A},
+	Pages = {2395},
+	Title = {Beyond The Random-Phase Approximation: a New Approximation Scheme For The Polarization Propagator},
+	Volume = {26},
+	Year = {1982}}
+
+@article{Sce14,
+	Author = {Scemama, A. and Applencourt, T. and Giner, E. and Caffarel, M.},
+	Date-Added = {2019-10-31 15:00:17 +0100},
+	Date-Modified = {2019-10-31 15:00:17 +0100},
+	Doi = {10.1063/1.4903985},
+	Issn = {1089-7690},
+	Journal = {J. Chem. Phys.},
+	Month = {Dec},
+	Number = {24},
+	Pages = {244110},
+	Publisher = {AIP Publishing},
+	Title = {Accurate nonrelativistic ground-state energies of 3d transition metal atoms},
+	Url = {http://dx.doi.org/10.1063/1.4903985},
+	Volume = {141},
+	Year = {2014},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4903985}}
+
+@article{Sce16,
+	Author = {Scemama, Anthony and Applencourt, Thomas and Giner, Emmanuel and Caffarel, Michel},
+	Date-Added = {2019-10-31 15:00:15 +0100},
+	Date-Modified = {2019-10-31 15:00:15 +0100},
+	Doi = {10.1002/jcc.24382},
+	Issn = {0192-8651},
+	Journal = {J. Comput. Chem.},
+	Month = {Jun},
+	Number = {20},
+	Pages = {1866--1875},
+	Publisher = {Wiley-Blackwell},
+	Title = {Quantum Monte Carlo with Very Large Multideterminant Wavefunctions},
+	Url = {http://dx.doi.org/10.1002/jcc.24382},
+	Volume = {37},
+	Year = {2016},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.24382}}
+
+@article{Gin15,
+	Author = {Emmanuel Giner and Anthony Scemama and Michel Caffarel},
+	Date-Added = {2019-10-31 15:00:09 +0100},
+	Date-Modified = {2019-10-31 15:00:09 +0100},
+	Doi = {10.1063/1.4905528},
+	Issn = {1089-7690},
+	Journal = {J. Chem. Phys.},
+	Month = {Jan},
+	Number = {4},
+	Pages = {044115},
+	Publisher = {AIP Publishing},
+	Title = {Fixed-Node Diffusion Monte Carlo Potential Energy Curve of the Fluorine Molecule F$_2$ Using Selected Configuration Interaction Trial Wavefunctions},
+	Url = {http://dx.doi.org/10.1063/1.4905528},
+	Volume = {142},
+	Year = {2015},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4905528}}
+
+@article{Gin13,
+	Author = {Giner, Emmanuel and Scemama, Anthony and Caffarel, Michel},
+	Date-Added = {2019-10-31 15:00:06 +0100},
+	Date-Modified = {2019-10-31 15:00:06 +0100},
+	Doi = {10.1139/cjc-2013-0017},
+	Issn = {1480-3291},
+	Journal = {Can. J. Chem.},
+	Month = {Sep},
+	Number = {9},
+	Pages = {879--885},
+	Publisher = {Canadian Science Publishing},
+	Title = {Using Perturbatively Selected Configuration Interaction in Quantum Monte Carlo Calculations},
+	Url = {http://dx.doi.org/10.1139/cjc-2013-0017},
+	Volume = {91},
+	Year = {2013},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1139/cjc-2013-0017}}
+
+@inbook{Caf16b,
+	Author = {Michel Caffarel and Thomas Applencourt and Emmanuel Giner and Anthony Scemama},
+	Booktitle = {Recent Progress in Quantum Monte Carlo},
+	Chapter = {2},
+	Date-Added = {2019-10-31 14:59:58 +0100},
+	Date-Modified = {2019-10-31 14:59:58 +0100},
+	Doi = {10.1021/bk-2016-1234.ch002},
+	Eprint = {http://pubs.acs.org/doi/pdf/10.1021/bk-2016-1234.ch002},
+	Pages = {15-46},
+	Title = {Using CIPSI Nodes in Diffusion Monte Carlo},
+	Url = {http://pubs.acs.org/doi/abs/10.1021/bk-2016-1234.ch002},
+	Year = {2016},
+	Bdsk-Url-1 = {http://pubs.acs.org/doi/abs/10.1021/bk-2016-1234.ch002},
+	Bdsk-Url-2 = {http://dx.doi.org/10.1021/bk-2016-1234.ch002}}
+
+@article{Caf14,
+	Author = {Caffarel, Michel and Giner, Emmanuel and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro},
+	Date-Added = {2019-10-31 14:59:55 +0100},
+	Date-Modified = {2019-10-31 14:59:55 +0100},
+	Doi = {10.1021/ct5004252},
+	Issn = {1549-9626},
+	Journal = {J. Chem. Theory Comput.},
+	Month = {Dec},
+	Number = {12},
+	Pages = {5286--5296},
+	Publisher = {American Chemical Society (ACS)},
+	Title = {Spin Density Distribution in Open-Shell Transition Metal Systems: A Comparative Post-Hartree--Fock, Density Functional Theory, and Quantum Monte Carlo Study of the CuCl$_2$ Molecule},
+	Url = {http://dx.doi.org/10.1021/ct5004252},
+	Volume = {10},
+	Year = {2014},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1021/ct5004252}}
+
+@article{Caf16,
+	Author = {Caffarel, Michel and Applencourt, Thomas and Giner, Emmanuel and Scemama, Anthony},
+	Date-Added = {2019-10-31 14:59:52 +0100},
+	Date-Modified = {2019-10-31 14:59:52 +0100},
+	Doi = {10.1063/1.4947093},
+	Issn = {1089-7690},
+	Journal = {J. Chem. Phys.},
+	Month = {Apr},
+	Number = {15},
+	Pages = {151103},
+	Publisher = {AIP Publishing},
+	Title = {Toward an Improved Control of the Fixed-Node Error in Quantum Monte Carlo: The Case of the Water Molecule},
+	Url = {http://dx.doi.org/10.1063/1.4947093},
+	Volume = {144},
+	Year = {2016},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4947093}}
+
+@article{Hur73,
+	Author = {Huron, B. and Malrieu, J. P. and Rancurel, P.},
+	Date-Added = {2019-10-31 14:59:32 +0100},
+	Date-Modified = {2019-10-31 14:59:32 +0100},
+	Doi = {10.1063/1.1679199},
+	Issn = {1089-7690},
+	Journal = {J. Chem. Phys.},
+	Month = {Jun},
+	Number = {12},
+	Pages = {5745--5759},
+	Publisher = {AIP Publishing},
+	Title = {Iterative Perturbation Calculations of Ground and Excited State Energies from Multiconfigurational Zeroth-Order Wavefunctions},
+	Url = {http://dx.doi.org/10.1063/1.1679199},
+	Volume = {58},
+	Year = {1973},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1679199}}
+
+@article{Whi69,
+	Author = {Whitten, J. L. and Hackmeyer, Melvyn},
+	Date-Added = {2019-10-31 14:59:24 +0100},
+	Date-Modified = {2019-10-31 14:59:24 +0100},
+	Doi = {10.1063/1.1671985},
+	Issn = {1089-7690},
+	Journal = {J. Chem. Phys.},
+	Month = {Dec},
+	Number = {12},
+	Pages = {5584--5596},
+	Publisher = {AIP Publishing},
+	Title = {Configuration Interaction Studies of Ground and Excited States of Polyatomic Molecules. I. The CI Formulation and Studies of Formaldehyde},
+	Url = {http://dx.doi.org/10.1063/1.1671985},
+	Volume = {51},
+	Year = {1969},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1671985}}
+
+@article{Ben69,
+	Author = {Bender, Charles F. and Davidson, Ernest R.},
+	Date-Added = {2019-10-31 14:59:14 +0100},
+	Date-Modified = {2019-10-31 14:59:14 +0100},
+	Doi = {10.1103/physrev.183.23},
+	Issn = {0031-899X},
+	Journal = {Phys. Rev.},
+	Month = {Jul},
+	Number = {1},
+	Pages = {23--30},
+	Publisher = {American Physical Society (APS)},
+	Title = {Studies in Configuration Interaction: The First-Row Diatomic Hydrides},
+	Url = {http://dx.doi.org/10.1103/physrev.183.23},
+	Volume = {183},
+	Year = {1969},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1103/physrev.183.23}}
+
 @article{Koc90,
 	Author = {Koch, Henrik and J{\o}rgensen, Poul},
 	Date-Added = {2019-10-30 17:29:21 +0100},
@@ -392,10 +580,10 @@
 @article{Sil10c,
 	Author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
 	Date-Added = {2019-10-30 14:10:21 +0100},
-	Date-Modified = {2019-10-30 14:10:21 +0100},
+	Date-Modified = {2019-10-31 15:57:49 +0100},
 	Journal = JCP,
 	Pages = {174318},
-	Title = {Benchmarks of Electronically Excited States: Basis Set Effecs Benchmarks of Electronically Excited States: Basis Set Effects on CASPT2 Results},
+	Title = {Benchmarks of Electronically Excited States: Basis Set Effecs on {{CASPT2}} Results},
 	Volume = 133,
 	Year = 2010}
 

Manuscript/ExPerspective.tex

@@ -110,7 +110,7 @@ The access to other properties, such as oscillator strength, dipole moment and a
 Let us not forget about minimal user input and chemical intuition requirements (\ie, black box method preferable) in order to minimise the bias brought by the user's appreciation of the problem complexity.
 Finally, low computational scaling with respect to system size and small memory footprint cannot be disregarded.
 Although the simultaneous fulfilment of all these requirements seems elusive, it is always essential to keep these criteria in mind.
-%In summary, each method has its own strengths and weaknesses, and none of them is able to provide accurate and reliable excitation energies in all scenarios. 
+
 
 %%% TABLE I %%%
 %\begin{squeezetable}
@@ -147,11 +147,11 @@ $N$ is the number of basis functions.}
 \end{table}
 %\end{squeezetable}
 
-%%%%%%%%%%%%%%%
+%**************
-%%% HISTORY %%%
+%** HISTORY **%
-%%%%%%%%%%%%%%%
+%**************
 Before detailing some key past and present contributions towards the obtention of highly-accurate excitation energies, we start by giving a historical overview of the various excited-state \textit{ab initio} methods that have emerged in the last fifty years.
-Interestingly, for pretty much every single method, the theory was derived much earlier than their actual implementation in electronic structure software  packages.
+Interestingly, for pretty much every single methods, the theory was derived much earlier than their actual implementation in electronic structure software  packages.
 Here, we only mention methods that, we think, ended up becoming mainstream.
 
 %%%%%%%%%%%%%%%%%%%%%
@@ -173,9 +173,9 @@ The limited applicability of these so-called multiconfigurational methods is mai
 %%%%%%%%%%%%%
 %%% TDDFT %%%
 %%%%%%%%%%%%%
-The advent of time-dependent density-functional theory (TD-DFT) \cite{Run84} was a real shock for the community as TD-DFT was able to provide accurate excitation energies at a much lower cost than its predecessors in a very black-box way.
+The advent of time-dependent density-functional theory (TD-DFT) \cite{Run84,Dre05} was a real shock for the community as TD-DFT was able to provide accurate excitation energies at a much lower cost than its predecessors in a very black-box way.
-However, a large number of shortcomings were quickly discovered.
+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}
+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.
 Despite all of this, TD-DFT is still nowadays the most employed excited-state method in the electronic structure community.
@@ -183,11 +183,16 @@ Despite all of this, TD-DFT is still nowadays the most employed excited-state me
 %%%%%%%%%%%%%%%%%%
 %%% CC METHODS %%%
 %%%%%%%%%%%%%%%%%%
-Thanks to the development of coupled cluster (CC) response theory, \cite{Koc90} and the hugh 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, 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.
 
+%%%%%%%%%%%%%%%%%%%
+%%% ADC METHODS %%%
+%%%%%%%%%%%%%%%%%%%
+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}
 
 %%%%%%%%%%%%%%
 %%% BSE@GW %%%
@@ -199,22 +204,11 @@ Although  and TD-DFT the BSE formalism have emerged as powerful tools for comput
 For example, the simplest and most widespread approximation in state-of-the-art electronic structure programs where TD-DFT and BSE are implemented consists in neglecting memory effects. 
 This has drastic consequences such as, for example, the complete absence of double excitations from the TD-DFT and BSE spectra.
 
-%%%%%%%%%%%%%%%%%%%%%
-%%% THIEL'S GROUP %%%
-%%%%%%%%%%%%%%%%%%%%%
-A major contribution originates from the Thiel's group \cite{Sch08,Sil08,Sau09,Sil10b,Sil10c} with in particular the introduction of the Thiel's set  gathering, for the first time, a large number of excitation energies of different natures. \cite{Sch08}
-
-Although people usually don't really like reading, reviewing or even the idea of benchmark studies, these are definitely essential for the validation of existing theoretical methods and to understand their strengths and, more importantly, their limitations.
-
-%%%%%%%%%%%%%%%%%%%
-%%% ADC METHODS %%%
-%%%%%%%%%%%%%%%%%%%
-ADC(2) \cite{Dre15}, ADC(3) \cite{Dre15},  
 %%%%%%%%%%%%%%%%%%%
 %%% SCI METHODS %%%
 %%%%%%%%%%%%%%%%%%%
 
-Alternatively to CC and multiconfigurational methods, one can also compute transition energies for various types of excited states using selected configuration interaction (sCI) methods \cite{Ben69,Whi69,Hur73} which have recently demonstrated their ability to reach near full CI (FCI) quality energies for small molecules \cite{Gin13,Caf14,Gin15,Caf16,Gar17b,Hol16,Sha17,Hol17,Chi18,Sce18a,Sce18b,Loo18b,Gar18}.
+Alternatively to CC and multiconfigurational methods, one can also compute transition energies for various types of excited states using selected configuration interaction (sCI) methods \cite{Ben69,Whi69,Hur73} which have recently demonstrated their ability to reach near full CI (FCI) quality energies for small molecules \cite{Gin13,Gin15,Caf16,Gar17b,Hol16,Sha17,Hol17,Chi18,Sce18,Sce18b,Loo18a,Gar18}.
 The idea behind such methods is to avoid the exponential increase of the size of the CI expansion by retaining the most energetically relevant determinants only, thanks to the use of a second-order energetic criterion to select perturbatively determinants in the FCI space.
 However, although the \textit{``exponential wall''} is pushed back, this type of methods is only applicable to molecules with a small number of heavy atoms with relatively compact basis sets.
 
@@ -222,21 +216,51 @@ However, although the \textit{``exponential wall''} is pushed back, this type of
 In the past five years, we have witnessed a resurgence of selected CI (sCI) methods thanks to the development and implementation of new and fast algorithm to select cleverly determinants in the FCI space.
 sCI methods rely on the same principle as the usual CI approach, except that determinants are not chosen 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. 
 Indeed, it has been noticed long ago that, even inside a predefined subspace of determinants, only a small number of them significantly contributes.
-Therefore, an on-the-fly selection of determinants is a rather natural idea that has been proposed in the late 1960s by Bender and Davidson19 as well as Whitten and Hackmeyer's
+Therefore, an on-the-fly selection of determinants is a rather natural idea that has been proposed in the late 1960's by Bender and Davidson as well as Whitten and Hackmeyer's sCI methods are still very much under active development. 
-sCI methods are still very much under active development. 
 The main advantage of sCI methods is that no a priori assumption is made on the type of electronic correlation. 
 Therefore, at the price of a brute force calculation, a sCI calculation is less biased by the user's appreciation of the problem's complexity.
 The approach that we have implemented in QUANTUM PACKAGE is based on the CIPSI algorithm developed by Huron, Rancurel, and Malrieu in 1973.
 
+%%%%%%%%%%%%%%%
+%%% SUMMARY %%%
+%%%%%%%%%%%%%%%
+In summary, each method has its own strengths and weaknesses, and none of them is able to provide accurate and reliable excitation energies for all classes of electronic states. 
+This ultimately leads to an unbalanced description of different excited states.
 
-In Ref., we studied 18 small molecules (water, hydrogen sulfide, ammonia, hydrogen chloride, dinitrogen, carbon monoxide, acetylene, ethylene, formaldehyde, methanimine, thioformaldehyde, acetaldehyde, cyclopropene, diazomethane, formamide, ketene, nitrosomethane, and the smallest strepto- cyanine) with sizes ranging from one to three nonhydrogen atoms. 
+%*****************
+%** BENCHMARKS ***
+%*****************
+Although people usually don't really like reading, reviewing or even the idea of benchmark studies, these are definitely essential for the validation of existing theoretical methods and to understand their strengths and, more importantly, their limitations. 
+
+%%%%%%%%%%%%%%%%%%%
+%%% THIEL'S SET %%%
+%%%%%%%%%%%%%%%%%%%
+A major contribution originates from the Thiel's group \cite{Sch08,Sil08,Sau09,Sil10b,Sil10c} with the introduction of the so-called Thiel's set of excitation energies. \cite{Sch08}
+For the first time, this benchmark set gathers a large number of excitation energies consisting of 28 medium-size organic molecules with a total of 223 excited states (152 singlet and 71 triplet states).
+In their first study they performed CC2, EOM-CCSD, CC3 and MS-CASPT2 calculations in order to provide (based on additional high-level literature data) best theoretical estimates (TBE).
+These TBEs were later refined with the larger aug-cc-pVTZ basis set. \cite{Sil10b}
+
+%%%%%%%%%%%%%%%%%%%%%%%
+%%% JACQUEMIN'S SET %%%
+%%%%%%%%%%%%%%%%%%%%%%%
+Very recently, we also made a contribution to this quest for highly-accurate excitation energies. \cite{Loo18a}
+We studied 18 small molecules (water, hydrogen sulfide, ammonia, hydrogen chloride, dinitrogen, carbon monoxide, acetylene, ethylene, formaldehyde, methanimine, thioformaldehyde, acetaldehyde, cyclopropene, diazomethane, formamide, ketene, nitrosomethane, and the smallest streptocyanine) with sizes ranging from one to three nonhydrogen atoms. 
 For such systems, using sCI expansions of several million determinants, we were able to compute more than 100 highly accurate vertical excitation energies with typically augmented triple-$\zeta$ basis sets. 
 It allowed us to benchmark a series of 12 state-of-the-art excited-state wave function methods accounting for double and triple excitations.
-Even more recently, we provided accurate reference excitation energies for transitions involving a substantial amount of double excitation using a series of increasingly large diffuse-containing atomic basis sets. 
+We use this series theoretical best estimates to benchmark a series of popular methods for excited state calculations [CIS(D), ADC(2), CC2, STEOM-CCSD, CCSD, CCSDR(3), and CCSDT-3]. 
+
+Even more recently, we provided accurate reference excitation energies for transitions involving a substantial amount of double excitation using a series of increasingly large diffuse-containing atomic basis sets. \cite{Loo19c}
 Our set gathered 20 vertical transitions from 14 small- and medium-sized molecules (acrolein, benzene, beryllium atom, butadiene, carbon dimer and trimer, ethylene, formaldehyde, glyoxal, hexatriene, nitrosomethane, nitroxyl, pyrazine, and tetrazine). 
 For the smallest molecules, we were able to obtain well converged excitation energies with an augmented quadruple-$\zeta$ basis set, while only augmented double-$\zeta$ bases were manageable for the largest systems (such as acrolein, butadiene, hexatriene, and benzene). 
 Note that the largest sCI expansion considered in this study had more than 200 million determinants.
 
+In order to push further our analysis to larger compounds, we provided highly-accurate vertical transition energies obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms (acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione, diacetylene, furan, glyoxal, imidazole, isobutene, methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine). 
+To obtain these energies, we use CC approaches up to the highest possible order (CC3, CCSDT, and CCSDTQ), sCI approach up to several millions determinants, and NEVPT2. 
+All approaches being combined with diffuse-containing atomic basis sets. 
+For all transitions, we report at least CC3/aug-cc-pVQZ transition energies and as well as CC3/aug-cc-pVTZ oscillator strengths for all dipole-allowed transitions. 
+We show that CC3 almost systematically delivers transition energies in agreement with higher-level of theories ($\pm 0.04$ eV) but for transitions presenting a dominant double excitation character. 
+This contribution encompasses a set of more than 200 highly-accurate transition energies for states of various nature (valence, Rydberg, singlet, triplet, $n \ra \pi^*$, $\pi \ra \pi^*$, etc). 
+
 %%%%%%%%%%%%%%%%%%
 %%% CONCLUSION %%%
 %%%%%%%%%%%%%%%%%%