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Manuscript/QUESTDB.bib
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@ -1,13 +1,31 @@
%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/ %% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2020-09-07 22:47:51 +0200 %% Created for Pierre-Francois Loos at 2020-09-08 20:46:59 +0200
%% Saved with string encoding Unicode (UTF-8) %% Saved with string encoding Unicode (UTF-8)
@article{Pitonak_2009,
Abstract = {Abstract Scaled MP3 interaction energies calculated as a sum of MP2/CBS (complete basis set limit) interaction energies and scaled third-order energy contributions obtained in small or medium size basis sets agree very closely with the estimated CCSD(T)/CBS interaction energies for the 22 H-bonded, dispersion-controlled and mixed non-covalent complexes from the S22 data set. Performance of this so-called MP2.5 (third-order scaling factor of 0.5) method has also been tested for 33 nucleic acid base pairs and two stacked conformers of porphine dimer. In all the test cases, performance of the MP2.5 method was shown to be superior to the scaled spin-component MP2 based methods, e.g. SCS--MP2, SCSN--MP2 and SCS(MI)--MP2. In particular, a very balanced treatment of hydrogen-bonded compared to stacked complexes is achieved with MP2.5. The main advantage of the approach is that it employs only a single empirical parameter and is thus biased by two rigorously defined, asymptotically correct ab-initio methods, MP2 and MP3. The method is proposed as an accurate but computationally feasible alternative to CCSD(T) for the computation of the properties of various kinds of non-covalently bound systems.},
Author = {Pito{\v n}{\'a}k, Michal and Neogr{\'a}dy, Pavel and {\v C}ern{\'y}, Ji{\v r}{\'\i} and Grimme, Stefan and Hobza, Pavel},
Date-Added = {2020-09-08 20:46:45 +0200},
Date-Modified = {2020-09-08 20:46:53 +0200},
Doi = {10.1002/cphc.200800718},
Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cphc.200800718},
Journal = {ChemPhysChem},
Keywords = {benchmark calculations, complete basis set limit, DNA nucleic acid, molecular interactions, porphine},
Number = {1},
Pages = {282--289},
Title = {Scaled MP3 Non-Covalent Interaction Energies Agree Closely with Accurate CCSD(T) Benchmark Data},
Url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cphc.200800718},
Volume = {10},
Year = {2009},
Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cphc.200800718},
Bdsk-Url-2 = {https://doi.org/10.1002/cphc.200800718}}
@misc{Applencourt_2018, @misc{Applencourt_2018,
Archiveprefix = {arXiv}, Archiveprefix = {arXiv},
Author = {Thomas Applencourt and Kevin Gasperich and Anthony Scemama}, Author = {Thomas Applencourt and Kevin Gasperich and Anthony Scemama},

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Manuscript/QUEST_WIREs.tex
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@ -120,12 +120,21 @@ Let us also mention the new benchmark set of charge-transfer excited states rece
Following a similar philosophy and striving for chemical accuracy, we have recently reported in several studies highly-accurate vertical excitations for small- and medium-sized molecules \cite{Loos_2020a,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c}. Following a similar philosophy and striving for chemical accuracy, we have recently reported in several studies highly-accurate vertical excitations for small- and medium-sized molecules \cite{Loos_2020a,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c}.
One of the key aspect of the so-called QUEST dataset of vertical excitations which we will describe in details in the present review article is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating in the process theoretical comparisons. The so-called QUEST dataset of vertical excitations which we will describe in details in the present review article is composed by 5 subsets (see Fig.~\ref{fig:scheme}): i) a subset of excitations in small molecules containing from 1 to 3 non-hydrogen atoms known as QUEST\#1, ii) a subset of double excitations for molecules of small and medium sizes known as QUEST\#2, iii) a subset of excitation energies for medium-sized molecules containing from 4 to 6 non-hydrogen atoms known as QUEST\#3, iv) a subset composed by more ``exotic'' molecules and radicals labeled as QUEST\#4, and v) a subset known as QUEST\#5, specifically designed for the present article, gathering excitation energies in larger molecules as well as additional smaller molecules.
One of the key aspect of the QUEST dataset is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating in the process theoretical comparisons.
Moreover, our protocol has been designed to be as uniform as possible, which means that we have designed a very systematic procedure for all excited states in order to make cross-comparison as straightforward as possible. Moreover, our protocol has been designed to be as uniform as possible, which means that we have designed a very systematic procedure for all excited states in order to make cross-comparison as straightforward as possible.
Importantly, it allowed us to benchmark, in a very systematic and fair way, a series of popular excited-state wave function methods partially or fully accounting for double and triple excitations as well as multiconfigurational methods (see below). Importantly, it allowed us to benchmark, in a very systematic and fair way, a series of popular excited-state wave function methods partially or fully accounting for double and triple excitations as well as multiconfigurational methods (see below).
In the same vein, we have also produced chemically-accurate theoretical 0-0 energies \cite{Loos_2018,Loos_2019a,Loos_2019b} which can be more straightforwardly compare to experimental data \cite{Kohn_2003,Dierksen_2004,Goerigk_2010a,Send_2011a,Winter_2013,Fang_2014}. In the same vein, we have also produced chemically-accurate theoretical 0-0 energies \cite{Loos_2018,Loos_2019a,Loos_2019b} which can be more straightforwardly compare to experimental data \cite{Kohn_2003,Dierksen_2004,Goerigk_2010a,Send_2011a,Winter_2013,Fang_2014}.
We refer the interested reader to Ref.~\cite{Loos_2019b} where we review the generic benchmark studies devoted to adiabatic and 0-0 energies performed in the past two decades. We refer the interested reader to Ref.~\cite{Loos_2019b} where we review the generic benchmark studies devoted to adiabatic and 0-0 energies performed in the past two decades.
%%% FIGURE 1 %%%
\begin{figure}[ht]
\centering
\includegraphics[width=0.5\linewidth]{fig1/fig1}
\caption{Composition of each of the five subsets making up the present QUEST dataset of highly-accurate vertical excitation energies.}
\label{fig:scheme}
\end{figure}
The QUEST dataset has the particularity to be based in a large proportion on selected configuration interaction (SCI) reference excitation energies as well as high-order CC methods such as CCSDT and CCSDTQ \cite{Oliphant_1991,Kucharski_1992}. The QUEST dataset has the particularity to be based in a large proportion on selected configuration interaction (SCI) reference excitation energies as well as high-order CC methods such as CCSDT and CCSDTQ \cite{Oliphant_1991,Kucharski_1992}.
Recently, SCI methods have been a force to reckon with for the computation of highly-accurate energies in small- and medium-sized molecules as they yield near full configuration interaction (FCI) quality energies for only a fraction of the computational cost of a genuine FCI calculation \cite{Holmes_2017,Chien_2018,Loos_2018a,Li_2018,Loos_2019,Loos_2020b,Loos_2020c,Loos_2020a,Li_2020,Eriksen_2020,Loos_2020e,Yao_2020}. Recently, SCI methods have been a force to reckon with for the computation of highly-accurate energies in small- and medium-sized molecules as they yield near full configuration interaction (FCI) quality energies for only a fraction of the computational cost of a genuine FCI calculation \cite{Holmes_2017,Chien_2018,Loos_2018a,Li_2018,Loos_2019,Loos_2020b,Loos_2020c,Loos_2020a,Li_2020,Eriksen_2020,Loos_2020e,Yao_2020}.
Due to the fairly natural idea underlying these methods, the SCI family is composed by numerous members \cite{Bender_1969,Whitten_1969,Huron_1973,Abrams_2005,Bunge_2006,Bytautas_2009,Giner_2013,Caffarel_2014,Giner_2015,Garniron_2017b,Caffarel_2016a,Caffarel_2016b,Holmes_2016,Sharma_2017,Holmes_2017,Chien_2018,Scemama_2018,Scemama_2018b,Garniron_2018,Evangelista_2014,Schriber_2016,Schriber_2017,Liu_2016,Per_2017,Ohtsuka_2017,Zimmerman_2017,Li_2018,Ohtsuka_2017,Coe_2018,Loos_2019}. Due to the fairly natural idea underlying these methods, the SCI family is composed by numerous members \cite{Bender_1969,Whitten_1969,Huron_1973,Abrams_2005,Bunge_2006,Bytautas_2009,Giner_2013,Caffarel_2014,Giner_2015,Garniron_2017b,Caffarel_2016a,Caffarel_2016b,Holmes_2016,Sharma_2017,Holmes_2017,Chien_2018,Scemama_2018,Scemama_2018b,Garniron_2018,Evangelista_2014,Schriber_2016,Schriber_2017,Liu_2016,Per_2017,Ohtsuka_2017,Zimmerman_2017,Li_2018,Ohtsuka_2017,Coe_2018,Loos_2019}.
@ -228,6 +237,7 @@ When available, we take advantage of the resolution-of-the-identity (RI) approxi
For the STEOM-CCSD calculations, it was checked that the active character percentage was, at least, $98\%$. For the STEOM-CCSD calculations, it was checked that the active character percentage was, at least, $98\%$.
When comparisons between various codes/implementations were possible, we could not detect variations in the transition energies larger than $0.01$ eV. When comparisons between various codes/implementations were possible, we could not detect variations in the transition energies larger than $0.01$ eV.
For radicals, we applied both the U (unrestricted) and RO (restricted open-shell) versions of CCSD and CC3 as implemented in the PSI4 code \cite{Psi4} to perform our benchmarks. For radicals, we applied both the U (unrestricted) and RO (restricted open-shell) versions of CCSD and CC3 as implemented in the PSI4 code \cite{Psi4} to perform our benchmarks.
Finally, the composite approach, ADC(2.5), which follows the spirit of Grimme's and Hobza's MP2.5 approach \cite{Pitonak_2009} by averaging the ADC(2) and ADC(3) excitation energies, is also tested in the following \cite{Loos_2020d}.
State-averaged (SA) CASSCF and CASPT2 \cite{Roos,Andersson_1990} have been performed with MOLPRO (RS2 contraction level) \cite{molpro}. State-averaged (SA) CASSCF and CASPT2 \cite{Roos,Andersson_1990} have been performed with MOLPRO (RS2 contraction level) \cite{molpro}.
Concerning the NEVPT2 calculations, the partially-contracted (PC) and strongly-contracted (SC) variants have been tested \cite{Angeli_2001a,Angeli_2001b,Angeli_2002}. Concerning the NEVPT2 calculations, the partially-contracted (PC) and strongly-contracted (SC) variants have been tested \cite{Angeli_2001a,Angeli_2001b,Angeli_2002}.
@ -239,6 +249,7 @@ The definition of the active space considered for each system as well as the num
%------------------------------------------------ %------------------------------------------------
\subsubsection{Estimating the extrapolation error} \subsubsection{Estimating the extrapolation error}
\label{sec:error}
%------------------------------------------------ %------------------------------------------------
For the $m$th excited state (where $m = 0$ corresponds to the ground state), we usually estimate its FCI energy $E_{\text{FCI}}^{(m)}$ by performing a linear extrapolation of its variational energy $E_\text{var}^{(m)}$ as a function of its rPT2 correction $E_{\text{rPT2}}^{(m)}$ as follows For the $m$th excited state (where $m = 0$ corresponds to the ground state), we usually estimate its FCI energy $E_{\text{FCI}}^{(m)}$ by performing a linear extrapolation of its variational energy $E_\text{var}^{(m)}$ as a function of its rPT2 correction $E_{\text{rPT2}}^{(m)}$ as follows
@ -302,23 +313,17 @@ A Python code associated with this procedure is provided in the {\SupInf}.
%======================= %=======================
\subsection{Overview} \subsection{Overview}
%======================= %=======================
The QUEST database gathers more than \alert{470} highly-accurate excitation energies of various natures (valence, Rydberg, $n \ra \pis$, $\pi \ra \pis$, singlet, doublet, triplet, and double excitations) for molecules ranging from diatomics to molecules as large as naphthalene. The QUEST database gathers more than \alert{470} highly-accurate excitation energies of various natures (valence, Rydberg, $n \ra \pis$, $\pi \ra \pis$, singlet, doublet, triplet, and double excitations) for molecules ranging from diatomics to molecules as large as naphthalene (see Fig.~\ref{fig:molecules}).
Each of the five subsets making up the QUEST dataset is detailed below. Each of the five subsets making up the QUEST dataset is detailed below.
Throughout the present article, we report several statistical indicators: the mean signed error (MSE), mean absolute error (MAE), root-mean square error (RMSE), and standard deviation of the errors (SDE). Throughout the present article, we report several statistical indicators: the mean signed error (MSE), mean absolute error (MAE), root-mean square error (RMSE), and standard deviation of the errors (SDE).
%%% FIGURE 1 %%%
\begin{figure}[ht]
\centering
\includegraphics[width=0.5\linewidth]{fig1/fig1}
\caption{Composition of each of the five subsets making up the present QUEST dataset of highly-accurate vertical excitation energies.}
\end{figure}
%%% FIGURE 2 %%% %%% FIGURE 2 %%%
\begin{figure}[ht] \begin{figure}[ht]
\centering \centering
\includegraphics[width=0.8\linewidth]{fig2} \includegraphics[width=0.8\linewidth]{fig2}
\caption{Molecules each of the five subsets making up the present QUEST dataset of highly-accurate vertical excitation energies: \caption{Molecules each of the five subsets making up the present QUEST dataset of highly-accurate vertical excitation energies:
QUEST\#1 (red), QUEST\#2 (magenta and/or underlined), QUEST\#3 (black), QUEST\#4 (green), and QUEST\#5 (blue).} QUEST\#1 (red), QUEST\#2 (magenta and/or underlined), QUEST\#3 (black), QUEST\#4 (green), and QUEST\#5 (blue).}
\label{fig:molecules}
\end{figure} \end{figure}
%======================= %=======================
@ -373,8 +378,9 @@ Likewise, the excitation energies obtained with CCSD are much less satisfying fo
The QUEST\#5 subset is composed by additional accurate excitation energies that we have produced for the present article. The QUEST\#5 subset is composed by additional accurate excitation energies that we have produced for the present article.
This new set gathers small molecules as well as larger molecules (aza-naphthalene, benzoquinone, cyclopentadienone, cyclopentadienethione, hexatriene, maleimide, naphthalene, nitroxyl, streptocyanine-C3, streptocyanine-C5, and thioacrolein). This new set gathers small molecules as well as larger molecules (aza-naphthalene, benzoquinone, cyclopentadienone, cyclopentadienethione, hexatriene, maleimide, naphthalene, nitroxyl, streptocyanine-C3, streptocyanine-C5, and thioacrolein).
QUEST\#5 does also provide additional FCI/6-31+G* estimates for the five- and six-membered rings considered in QUEST\#3.
Each of these molecules are discussed below and comparisons are made with literature data. Each of these molecules are discussed below and comparisons are made with literature data.
QUEST\#5 does also provide additional FCI/6-31+G* estimates of the lowest singlet and triplet transitions for the five- and six-membered rings considered in QUEST\#3.
The extrapolation errors for these quite challenging calculations are computed with the scheme presented in Sec.~\ref{sec:error}.
%-------------------------------------- %--------------------------------------
\subsubsection{Toward larger molecules} \subsubsection{Toward larger molecules}
@ -512,10 +518,12 @@ Thioacrolein
%----------------------------------------------------------------------- %-----------------------------------------------------------------------
\alert{Here comes Anthony's new CIPSI numbers for the five- and six-membered rings.} \alert{Here comes Anthony's new CIPSI numbers for the five- and six-membered rings.}
The singlet and triplet excitation energies obtained at the FCI/6-31+G(d) level are reported in Table \ref{tab:cycles} alongside the CC3 and CCSDT values in the same basis from Ref.~\cite{Loos_2020b}.
\begin{table}[bt] \begin{table}[bt]
\centering \centering
\caption{Singlet and triplet excitation energies obtained at the CC3, CCSDT, and FCI levels of theory with the 6-31+G* basis set for various five- and six-membered rings.} \caption{Singlet and triplet excitation energies obtained at the CC3, CCSDT, and FCI levels of theory with the 6-31+G* basis set for various five- and six-membered rings.}
\label{tab:cycles}
\begin{threeparttable} \begin{threeparttable}
\begin{tabular}{lccrr} \begin{tabular}{lccrr}
\headrow \headrow
@ -538,10 +546,14 @@ Cyclopentadienone & $^1A_2(n \ra \pis)$ & 3.03 & 3.03 & 3.084(17) \\
& $^3B_2(\pi \ra \pis)$ & 2.30 & 2.32 & 2.369(47) \\ & $^3B_2(\pi \ra \pis)$ & 2.30 & 2.32 & 2.369(47) \\
Pyrazine & $^1B_{3u}(n \ra \pis)$ & 4.28 & 4.28 & 4.259(91) \\ Pyrazine & $^1B_{3u}(n \ra \pis)$ & 4.28 & 4.28 & 4.259(91) \\
& $^3B_{3u}(n \ra \pis)$ & 3.68 & 3.68 & 3.697(30) \\ & $^3B_{3u}(n \ra \pis)$ & 3.68 & 3.68 & 3.697(30) \\
Pyridine & $^1B_1(n \ra \pis)$ & 5.12 & 5.10 & 5.153(118) \\
& $^3A_1(\pi \ra \pis)$ & 4.33 & 4.31 & 4.263(278) \\
Tetrazine & $^1B_{3u}(n \ra \pis)$ & 2.53 & 2.54 & 2.563(50) \\ Tetrazine & $^1B_{3u}(n \ra \pis)$ & 2.53 & 2.54 & 2.563(50) \\
& $^3B_{3u}(n \ra \pis)$ & 1.87 & 1.88 & 1.914(32) \\ & $^3B_{3u}(n \ra \pis)$ & 1.87 & 1.88 & 1.914(32) \\
Pyridazine & $^1B_1(n \ra \pis)$ & 3.95 & 3.95 & \\
& $^3B_1(n \ra \pis)$ & 3.27 & 3.26 & \\
Pyridine & $^1B_1(n \ra \pis)$ & 5.12 & 5.10 & 5.153(118) \\
& $^3A_1(\pi \ra \pis)$ & 4.33 & 4.31 & 4.263(278) \\
Pyrimidine & $^1B_1(n \ra \pis)$ & 4.58 & 4.57 & \\
& $^3B_1(n \ra \pis)$ & 4.20 & 4.20 & \\
Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.769(132) \\ Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.769(132) \\
& $^3A_2''(n \ra \pis)$ & 4.40 & 4.40 & 4.448(389) \\ & $^3A_2''(n \ra \pis)$ & 4.40 & 4.40 & 4.448(389) \\
%\hiderowcolors %\hiderowcolors
@ -558,12 +570,13 @@ Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.769(132) \\
\section{Theoretical best estimates} \section{Theoretical best estimates}
\label{sec:TBE} \label{sec:TBE}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
We discuss in this section the generation of the TBEs obtained with the aug-cc-pVTZ basis as well as oscillator strengths for most transitions.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Benchmarks} \section{Benchmarks}
\label{sec:bench} \label{sec:bench}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
In this section, we report a comprehensive benchmark of various methods on the entire QUEST set which is composed by more than \alert{470} excitations with, in addition, a specific analysis for each type of excited states.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The QUESTDB website} \section{The QUESTDB website}
@ -571,6 +584,8 @@ Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.769(132) \\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\alert{Here comes the description of Mika's website.} \alert{Here comes the description of Mika's website.}
Here we describe the feature of the website that we have specifically designed to gather the entire data generated during these last few years.
Thanks to this website, one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the size of the basis set, etc.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Concluding remarks} \section{Concluding remarks}