revision minus abstract
This commit is contained in:
parent
a41794b36b
commit
030c387449
500
JPCL.nb
500
JPCL.nb
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@ -191,7 +191,7 @@ assess fairly the performance of computationally lighter theoretical models. We
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%%%%%%%%%%%%%%%%%%%%
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%%% INTRODUCTION %%%
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%%%%%%%%%%%%%%%%%%%%
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The accurate modeling of excited-state properties with \textit{ab initio} quantum chemistry methods is a challenging \hl{ambition} of the electronic structure theory community that will certainly keep us busy for (at the very least) the next few decades to come
|
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The accurate modeling of excited-state properties with \textit{ab initio} quantum chemistry methods is a \hl{clear ambition} of the electronic structure theory community that will certainly keep us busy for (at the very least) the next few decades to come
|
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(see, for example, Refs.~\citenum{Dre05,Gon12,Gho18} and references therein). Of particular interest is the access to precise excitation energies, \ie, the energy difference between ground and excited electronic states, and their intimate link with photophysical and
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photochemical processes. The factors that makes this quest for high accuracy particularly delicate are very diverse.
|
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@ -204,21 +204,23 @@ As a consequence, for a given level of theory, excited-state methods are usually
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Another feature that makes excited states particularly fascinating and challenging is that they can be both \hl{very} close in energy from each other and have very different natures ($\pi \ra \pi^*$, $n \ra \pi^*$, charge transfer, double excitation, valence, Rydberg, singlet,
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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.
|
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And \hl{we think that at this stage,} none of the existing methods does provide such a feat at an affordable cost for chemically-meaningful compounds.
|
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\hl{We think that, at this stage,} none of the existing methods does provide such a feat at an affordable cost for chemically-meaningful compounds.
|
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|
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What are the requirement of the ``perfect'' theoretical model? As mentioned above, a balanced treatment of excited states with different character is highly desirable. Moreover, chemically accurate excitation energies (\ie, with error smaller than $1$~kcal/mol or $0.043$~eV)
|
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would be also beneficial in order to provide a quantitative chemical picture. The access to other properties, such as oscillator strengths, dipole moments, and analytical energy gradients, is also an asset if one wants to compare with experimental data.
|
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Let us not forget about the requirements of minimal user input and minimal chemical intuition (\ie, black box models are preferable) in order to minimize the potential bias brought by the user appreciation of the problem complexity. Finally, low computational scaling with
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respect to system size and small memory footprint cannot be disregarded. Although the simultaneous fulfillment of all these requirements seems elusive, it is useful to keep these criteria in mind. Table \ref{tab:method} is here for fulfill such a purpose. \hl{In that Table,
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we also provide an error bar for the various methods. In Table S1 of the SI, the interested reader will find more details about (some of the) existing benchmarks for BSE and wavefunction approaches, whereas a review of the results of TD-DFT's benchmark
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can be found elsewhere.} \cite{Lau13} \hl{As can be seen in Table S1, the actual error bars obtained for all methods will typically depend ton the selected set of excited states and compounds, so that the values listed in Table} \ref{tab:method} \hl{should be viewed
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as typical errors, but not as a guaranteed result. }
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respect to system size and small memory footprint cannot be disregarded. Although the simultaneous fulfillment of all these requirements seems elusive, it is useful to keep these criteria in mind. Table \ref{tab:method} is here for fulfill such a purpose.
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\hl{In this Table, we also provide the typical error bar associated with each of these methods.
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Table S1 of the} {\SI} \hl{reports additional details about (some of the) existing BSE and wave function theory benchmarks, whereas a review of TD-DFT benchmark studies
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can be found elsewhere.} \cite{Lau13}
|
||||
\hl{As can be seen in Table S1, the actual error bar obtained for a given method strongly depends on the actual type of excited states and compounds.
|
||||
Hence, the values listed in Table} \ref{tab:method} \hl{should be viewed as ``typical'' errors for organic molecules, nothing more.}
|
||||
|
||||
%%% TABLE I %%%
|
||||
\begin{table}
|
||||
\footnotesize
|
||||
\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 for single excitations \hl{of organic derivatives} is also provided as a qualitative indicator of the method accuracy.}
|
||||
\hl{For organic derivatives,} the typical error range for single excitations is also provided as a qualitative indicator of the method accuracy.}
|
||||
\label{tab:method}
|
||||
\begin{tabular}{p{2.1cm}cccc}
|
||||
\hline
|
||||
@ -277,7 +279,7 @@ Nonetheless, it is of common knowledge that CASPT2 has the clear tendency of und
|
||||
Driven by Angeli 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.
|
||||
For example, NEVPT2 is known to be intruder state free and size consistent.
|
||||
The limited applicability of these multiconfigurational methods is mainly due to the need of carefully defining an active space based on the desired transition(s) in order to obtain meaningful results, as well as their factorial computational growth with the number of active electrons and orbitals.
|
||||
With a typical minimal valence active space tailored for the desired transitions, the usual error with CASPT2 or NEVPT2 calculations is $0.1$--$0.2$ eV, \hl{with also the difficult question of the IPEA correction for the former method.} \cite{Zob17}
|
||||
With a typical minimal valence active space tailored for the desired transitions, the usual error with CASPT2 or NEVPT2 calculations is $0.1$--$0.2$ eV, \hl{with the additional complication of the possible IPEA correction for the former method.} \cite{Zob17}
|
||||
We also point out that some emergent approaches, like DMRG (density matrix renormalization group), \cite{Bai19} offer a new path for the development of these multiconfigurational methods.
|
||||
|
||||
%%%%%%%%%%%%%
|
||||
@ -287,7 +289,7 @@ The advent of time-dependent density-functional theory (TD-DFT) \cite{Run84,Cas9
|
||||
For low-lying valence excited states, TD-DFT calculations relying on hybrid exchange-correlation functionals have a typical error of $0.2$--$0.4$ eV.
|
||||
However, a large number of shortcomings were quickly discovered. \cite{Toz98,Toz99,Dre04,Mai04,Dre05,Lev06,Eli11}
|
||||
In the present context, one of the most annoying feature of TD-DFT --- in its most standard (adiabatic) approximation --- is its inability to describe, even qualitatively, charge-transfer states, \cite{Toz99,Dre04} Rydberg states, \cite{Toz98} and double excitations. \cite{Mai04,Lev06,Eli11}
|
||||
\hl{These problems, and other shortcomings of DFT and TD-DFT for other properties, have been related to the so-called delocalization error.} \cite{Aut14a}
|
||||
\hl{These issues, as well as other shortcomings of DFT and TD-DFT, have been related to the so-called delocalization error.} \cite{Aut14a}
|
||||
One closely related issue is the selection of the exchange-correlation functional from an ever-growing zoo of functionals and the variation of the excitation energies that one can observe with different functionals. \cite{Goe19,Sue19}
|
||||
More specifically, despite the development of new, more robust approaches (including the so-called range-separated \cite{Sav96,IIk01,Yan04,Vyd06} and double \cite{Goe10a,Bre16,Sch17} hybrids), it is still difficult (not to say impossible) to select a functional adequate for all families of transitions. \cite{Lau13}
|
||||
Moreover, the difficulty of making TD-DFT systematically improvable obviously hampers its applicability.
|
||||
@ -366,8 +368,8 @@ In summary, each method has its own strengths and weaknesses, and none of them i
|
||||
|
||||
%%% FIG 1 %%%
|
||||
\begin{figure*}
|
||||
\includegraphics[width=\linewidth]{Set1}
|
||||
\caption{Mean absolute error (in eV) with respect to the TBE/\textit{aug}-cc-pVTZ values from the {\SetA} set (as described in Ref.~\citenum{Loo18a}) for various methods and types of excited states.
|
||||
\includegraphics[width=\linewidth]{QUEST1}
|
||||
\caption{\hl{Mean absolute error (MAE, top) and mean signed error (MSE, bottom)} with respect to the TBE/\textit{aug}-cc-pVTZ values from the {\SetA} set (as described in Ref.~\citenum{Loo18a}) for various methods and types of excited states.
|
||||
}
|
||||
\label{fig:Set1}
|
||||
\end{figure*}
|
||||
@ -375,8 +377,8 @@ In summary, each method has its own strengths and weaknesses, and none of them i
|
||||
|
||||
%%% FIG 2 %%%
|
||||
\begin{figure}
|
||||
\includegraphics[width=\linewidth]{Set2}
|
||||
\caption{Mean absolute error (in eV) (with respect to FCI excitation energies) for the doubly excited states reported in Ref.~\citenum{Loo19c} for various methods taking into account at least triple excitations.
|
||||
\includegraphics[width=\linewidth]{QUEST2}
|
||||
\caption{\hl{Mean absolute error (MAE, top) and maximum absolute error (MAX, bottom)} with respect to FCI excitation energies for the doubly excited states reported in Ref.~\citenum{Loo19c} for various methods taking into account at least triple excitations.
|
||||
$\%T_1$ corresponds to single excitation percentage in the transition calculated at the CC3 level.}
|
||||
\label{fig:Set2}
|
||||
\end{figure}
|
||||
@ -384,8 +386,8 @@ In summary, each method has its own strengths and weaknesses, and none of them i
|
||||
|
||||
%%% FIG 3 %%%
|
||||
\begin{figure*}
|
||||
\includegraphics[width=\linewidth]{Set3}
|
||||
\caption{Mean absolute error (in eV) with respect to the TBE/\textit{aug}-cc-pVTZ values from the {\SetC} set (as described in Ref.~\citenum{Loo20a}) for various methods and types of excited states.}
|
||||
\includegraphics[width=\linewidth]{QUEST3}
|
||||
\caption{\hl{Mean absolute error (MAE, top) and mean signed error (MSE, bottom)} with respect to the TBE/\textit{aug}-cc-pVTZ values from the {\SetC} set (as described in Ref.~\citenum{Loo20a}) for various methods and types of excited states.}
|
||||
\label{fig:Set3}
|
||||
\end{figure*}
|
||||
%%% %%% %%%
|
||||
@ -400,7 +402,7 @@ For excited states, things started moving a little later but some major contribu
|
||||
%%%%%%%%%%%%%%%%%%%
|
||||
%%% THIEL'S SET %%%
|
||||
%%%%%%%%%%%%%%%%%%%
|
||||
One of these major contributions was provided by the group of Walter Thiel \cite{Sch08,Sil08,Sau09,Sil10b,Sil10c} with the introduction of the \hl{now called Thiel or M\"ulheium} set of excitation energies. \cite{Sch08}
|
||||
One of these major contributions was provided by the group of Walter Thiel \cite{Sch08,Sil08,Sau09,Sil10b,Sil10c} with the introduction of the \hl{so-called Thiel (or M\"ulheim)} set of excitation energies. \cite{Sch08}
|
||||
For the first time, this set was large, diverse, consistent, and accurate enough to be used as a proper benchmarking set for excited-state methods.
|
||||
More specifically, it gathers a large number of excitation energies consisting of 28 medium-size organic molecules with a total of 223 valence excited states (152 singlet and 71 triplet states) for which theoretical best estimates (TBEs) were defined.
|
||||
In their first study Thiel and collaborators performed CC2, CCSD, CC3 and CASPT2 calculations (with the TZVP basis) in order to provide (based on additional high-quality literature data) TBEs for these transitions.
|
||||
@ -459,10 +461,10 @@ However, because 0-0 energies are fairly insensitive to the underlying molecular
|
||||
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 reader may find useful several investigations reporting sets of reference oscillator strengths. \cite{Sil10c,Har14,Kan14,Loo18a,Loo20b}
|
||||
\hl{Up to now, these investigations of geometries and oscillator strengths have been mostly focussed on theory-to-theory comparisons. Indeed, while for tiny compounds, typically from di to tetra-atomics,
|
||||
one can find very accurate experimental measurements of excited state dipole moments, oscillator strengths, vibrational frequencies, etc., these data are rarely measured in larger compounds. Nevertheless,
|
||||
the emergence of X-ray free electron lasers might soon allow to obtain accurate experimental excited state densities and geometrical structures through diffraction experiments. Such developments will
|
||||
likely offer new opportunities for experiment-theory comparisons going beyond energies.}
|
||||
\hl{Up to now, these investigations focusing on geometries and oscillator strengths have been mostly based on theory-vs-theory comparisons. Indeed, while for small compounds (\ie, typically from di- to tetra-atomic molecules),
|
||||
one can find very accurate experimental measurements (excited state dipole moments, oscillator strengths, vibrational frequencies, etc), these data are usually not accessible in larger compounds.
|
||||
Nevertheless, the emergence of X-ray free electron lasers might soon allow to obtain accurate experimental excited state densities and geometrical structures through diffraction experiments.
|
||||
Such new experimental developments will likely offer new opportunities for experiment-vs-theory comparisons going beyond standard energetics.}
|
||||
Finally, 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.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%
|
||||
@ -489,7 +491,11 @@ DJ acknowledges the \textit{R\'egion des Pays de la Loire} for financial support
|
||||
|
||||
\section*{Biographies}
|
||||
|
||||
\noindent{\bfseries \hl{P.F. Loos}} \hl{xxxx}
|
||||
\noindent{\bfseries \hl{P.F. Loos}} \hl{was born in Nancy, France in 1982. He received his M.S.~in Computational and Theoretical Chemistry from the Universit\'e Henri Poincar\'e (Nancy, France) in 2005 and his Ph.D.~from the same university in 2008. From 2009 to 2013, He was undertaking postdoctoral research with Peter M.W.~Gill at the Australian National University (ANU). From 2013 to 2017, he was a \textit{``Discovery Early Career Researcher Award''} recipient at the ANU. Since 2017, he holds a researcher position from the \textit{``Centre National de la Recherche Scientifique (CNRS)} at the \textit{Laboratoire de Chimie et Physique Quantiques} in Toulouse (France), and was awarded, in 2019, an ERC consolidator grant.}
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[width=3cm]{PFLoos.png}
|
||||
\end{center}
|
||||
|
||||
\noindent{\bfseries \hl{A. Scemama}}\hl{xxxx}
|
||||
|
||||
|
||||
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