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%% Created for Pierre-Francois Loos at 2020-09-07 10:18:57 +0200
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%% Created for Pierre-Francois Loos at 2020-09-07 14:11:13 +0200
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@article{Page_2003,
|
||||
Author = {Page, Christopher S. and Olivucci, Massimo},
|
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Date-Added = {2020-09-07 14:08:10 +0200},
|
||||
Date-Modified = {2020-09-07 14:08:15 +0200},
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||||
Doi = {10.1002/jcc.10145},
|
||||
Issn = {1096-987X},
|
||||
Journal = {J. Comput. Chem.},
|
||||
Keywords = {second-order perturbation-theory, electronically excited state, potential energy surface, geometry optimization, conical intersection},
|
||||
Number = {3},
|
||||
Pages = {298--309},
|
||||
Publisher = {Wiley Subscription Services, Inc., A Wiley Company},
|
||||
Title = {Ground and Excited State CASPT2 Geometry Optimizations of Small Organic Molecules},
|
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Url = {http://dx.doi.org/10.1002/jcc.10145},
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Volume = {24},
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Year = {2003},
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Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.10145}}
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Author = {K{\'a}nn{\'a}r, D{\'a}niel and Szalay, P{\'e}ter G.},
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Date-Added = {2020-09-07 14:07:47 +0200},
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|
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|
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Title = {Benchmarking Coupled Cluster Methods on Valence Singlet Excited States},
|
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|
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@ -145,7 +145,7 @@ A special emphasis is placed on our latest add-on, QUEST\#5, specifically design
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Section \ref{sec:TBE} discusses the generation of the TBEs, while Sec.~\ref{sec:bench} proposes 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.
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Section \ref{sec:website} describe the feature of the website that we have specifically designed to gather the entire data generated during these last few years.
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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.
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Finally, we draw our conclusions in Sec.~\ref{sec:ccl}.
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Finally, we draw our conclusions in Sec.~\ref{sec:ccl} where we discuss, in particular, future projects aiming at expanding and improving the usability of the QUEST database.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Computational tools}
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@ -158,23 +158,20 @@ Finally, we draw our conclusions in Sec.~\ref{sec:ccl}.
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The molecules included in the QUEST dataset have been systematically optimized at the CC3/aug-cc-pVTZ level of theory, except for a very few cases.
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As shown in Refs.~\cite{Hattig_2005c,Budzak_2017}, CC3 provides extremely accurate ground- and excited-state geometries.
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These optimizations have been performed using DALTON 2017 \cite{dalton} and CFOUR 2.1, \cite{cfour} applying default parameters.
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For the open-shell derivatives, the geometries are optimized at the UCCSD(T)/aug-cc-pVTZ level using the GAUSSIAN16 program \cite{Gaussian16} and applying the \textsc{tight}convergence threshold.
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For the open-shell derivatives, the geometries are optimized at the UCCSD(T)/aug-cc-pVTZ level using the GAUSSIAN16 program \cite{Gaussian16} and applying the ``tight'' convergence threshold.
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||||
For the present review article, we have gathered all the geometries in the {\SupInf}.
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\footnote{These geometries can be found at...}
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||||
%=======================
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\subsection{Basis sets}
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%=======================
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In the entire set, we use one Pople basis set [6-31+G(d)], the augmented family of Dunning basis sets aug-cc-pVXZ (where X $=$ D, T, Q, and 5), and sometimes its doubly- and triply-augmented variants, d-aug-cc-pVXZ and t-aug-cc-pVXZ respectively.
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For the entire set, we rely on one Pople basis set [6-31+G(d)], the augmented family of Dunning basis sets aug-cc-pVXZ (where X $=$ D, T, Q, and 5), and sometimes its doubly- and triply-augmented variants, d-aug-cc-pVXZ and t-aug-cc-pVXZ respectively.
|
||||
Doubly- and triply-augmented basis sets are usually employed for Rydberg states where it is not uncommon to observe a strong basis set dependence due to the very diffuse nature of these excited states.
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||||
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||||
%==================================
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||||
\subsection{Computational methods}
|
||||
%==================================
|
||||
|
||||
|
||||
|
||||
|
||||
%------------------------------------------------
|
||||
\subsubsection{Reference computational methods}
|
||||
%------------------------------------------------
|
||||
@ -183,32 +180,46 @@ For small systems (typically 1--3 non-hydrogen atoms), we resort to SCI methods
|
||||
Obviously, the smaller the molecule, the larger the basis we can afford.
|
||||
For larger systems (\ie, 4--6 non-hydrogen atom), one cannot afford SCI calculations anymore expect in a few exceptions, and we then rely on CC theory (CCSDT and CCSDTQ typically) to obtain accurate transition energies.
|
||||
|
||||
The CC calculations are performed with several codes. For closed-shell molecules, CC3 \cite{Christiansen_1995b,Koch_1997} calculations are achieved with DALTON \cite{dalton} and CFOUR; \cite{cfour} CCSDT calculations are performed
|
||||
with CFOUR \cite{cfour} and MRCC 2017;\cite{Rolik_2013,mrcc} the latter code being also used for CCSDTQ and CCSDTQP. Note that all our excited-state CC calculations are performed within the equation-of-motion (EOM)
|
||||
or linear-response (LR) formalism that yield equivalent excited-state energies. The reported oscillator strengths have been computed in the LR-CC3 formalism only. For open-shell molecules, the CCSDT, CCSDTQ, and
|
||||
CCSDTQP calculations performed with MRCC \cite{Rolik_2013,mrcc} do consider an unrestricted Hartree-Fock (UHF) wave function as reference. All excited-state calculations are performed, except when explicitly mentioned, in
|
||||
the FC approximation using large cores for the third-row atoms. All electrons are correlated for the \ce{Be} atom, for which we systematically applied the basis set as included in MRCC. \cite{Prascjer_2010} (We have noted
|
||||
differences in the definition of the Dunning bases for this particular atom depending on the software that one considers.)
|
||||
The CC calculations are performed with several codes.
|
||||
For closed-shell molecules, CC3 \cite{Christiansen_1995b,Koch_1997} calculations are achieved with DALTON \cite{dalton} and CFOUR \cite{cfour}.
|
||||
CCSDT calculations are performed with CFOUR \cite{cfour} and MRCC 2017 \cite{Rolik_2013,mrcc}, the latter code being also used for CCSDTQ and CCSDTQP.
|
||||
Note that all our excited-state CC calculations are performed within the equation-of-motion (EOM) or linear-response (LR) formalism that yield equivalent excited-state energies.
|
||||
The reported oscillator strengths have been computed in the LR-CC3 formalism only.
|
||||
For open-shell molecules, the CCSDT, CCSDTQ, and CCSDTQP calculations performed with MRCC \cite{Rolik_2013,mrcc} do consider an unrestricted Hartree-Fock (UHF) wave function as reference.
|
||||
All excited-state calculations are performed, except when explicitly mentioned, in the frozen-core (FC) approximation using large cores for the third-row atoms.
|
||||
|
||||
All the SCI calculations are performed within the FC approximation using QUANTUM PACKAGE \cite{Garniron_2019} where the CIPSI algorithm \cite{Huron_1973} is implemented. Details regarding this specific CIPSI implementation
|
||||
can be found in Refs.~\citenum{Gar19} and \citenum{Sce19}. We use a state-averaged formalism which means that the ground and excited states are described with the same number and same set of determinants, but
|
||||
different CI coefficients. The SCI energy is defined as the sum of the variational energy (computed via diagonalization of the CI matrix in the reference space) and a second-order perturbative correction which estimates the
|
||||
contribution of the determinants not included in the CI space. \cite{Garniron_2017b} By extrapolating this second-order correction to zero, one can efficiently estimate the FCI limit for the total energies, and hence, compute the
|
||||
corresponding transition energies. We estimate the extrapolation error by the difference between the transition energies obtained with the largest SCI wave function and the FCI extrapolated value. These errors are
|
||||
systematically reported in the Tables below. Although this cannot be viewed as a true error bar, it provides a rough idea of the quality of the FCI extrapolation and estimate.
|
||||
All the SCI calculations are performed within the FC approximation using QUANTUM PACKAGE \cite{Garniron_2019} where the CIPSI algorithm \cite{Huron_1973} is implemented. Details regarding this specific CIPSI implementation can be found in Refs.~\cite{Garniron_2019} and \cite{Scemama_2019}.
|
||||
We use a state-averaged formalism which means that the ground and excited states are described with the same number and same set of determinants, but different CI coefficients. The SCI energy is defined as the sum of the variational energy (computed via diagonalization of the CI matrix in the reference space) and a PT2 correction which estimates the contribution of the determinants not included in the CI space \cite{Garniron_2017b}.
|
||||
By extrapolating this second-order correction to zero, one can efficiently estimate the FCI limit for the total energies, and hence, compute the corresponding transition energies.
|
||||
Depending on the set, we estimated the extrapolation error via different techniques.
|
||||
For example, in Ref.~\cite{Loos_2020b}, we estimated the extrapolation error by the difference between the transition energies obtained with the largest SCI wave function and the FCI extrapolated value.
|
||||
This definitely cannot be viewed as a true error bar, but it provides a rough idea of the quality of the FCI extrapolation and estimate.
|
||||
Below, we provide a much cleaner way of estimating the extrapolation error in SCI methods, and we adopt this scheme throughout this manuscript.
|
||||
The particularity of the current implementation is that the selection step and the PT2 correction are computed \textit{simultaneously} via a hybrid semistochastic algorithm \cite{Garniron_2017,Garniron_2019}.
|
||||
Moreover, a renormalized version of the PT2 correction has been recently implemented for a more efficient extrapolation to the FCI limit \cite{Garniron_2019}.
|
||||
We refer the interested reader to Ref.~\cite{Garniron_2019} where one can find all the details regarding the implementation of the CIPSI algorithm.
|
||||
|
||||
%------------------------------------------------
|
||||
\subsubsection{Benchmarked computational methods}
|
||||
%------------------------------------------------
|
||||
|
||||
Our benchmark effort consists in evaluating the accuracy of vertical transition energies obtained at lower levels of theory.
|
||||
These calculations are performed with a variety of codes. For the exotic set, we rely on: GAUSSIAN \cite{Gaussian16} and TURBOMOLE 7.3 \cite{Turbomole} for CIS(D); \cite{Hea94,Hea95} Q-CHEM 5.2 \cite{Kry13} for EOM-MP2 [CCSD(2)] \cite{Sta95c} and ADC(3); \cite{Tro02,Har14,Dre15}
|
||||
Q-CHEM \cite{Kry13} and TURBOMOLE \cite{Turbomole} for ADC(2); \cite{Tro97,Dre15} DALTON \cite{dalton} and TURBOMOLE \cite{Turbomole} for CC2; \cite{Chr95,Hat00} DALTON \cite{dalton} and GAUSSIAN
|
||||
for CCSD;\cite{Pur82} DALTON \cite{dalton} for CCSDR(3); \cite{Chr96b} CFOUR \cite{cfour} for CCSDT-3; \cite{Wat96,Pro10} and ORCA \cite{Nee12} for similarity-transformed EOM-CCSD (STEOM-CCSD). \cite{Nooijen_1997,Dut18}
|
||||
In addition, we evaluate the spin-opposite scaling (SOS) variants of ADC(2), SOS-ADC(2), as implemented in both Q-CHEM, \cite{Kra13} and TURBOMOLE. \cite{Hellweg_2008} Note that these two codes have distinct SOS implementations, as explained in Ref.~\citenum{Kra13}. We also test the SOS and spin-component scaled (SCS) versions of CC2, as implemented in TURBOMOLE. \cite{Hellweg_2008,Turbomole} Discussion of various spin-scaling
|
||||
schemes can be found elsewhere. \cite{Goerigk_2010a} When available, we take advantage of the resolution-of-the-identity (RI) approximation in TURBOMOLE and Q-CHEM. 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. For the radical set
|
||||
molecules, 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.
|
||||
Using a large variety of codes, our benchmark effort consists in evaluating the accuracy of vertical transition energies obtained at lower levels of theory.
|
||||
For example, we rely on GAUSSIAN \cite{Gaussian16} and TURBOMOLE 7.3 \cite{Turbomole} for CIS(D) \cite{Head-Gordon_1994,Head-Gordon_1995};
|
||||
Q-CHEM 5.2 \cite{Krylov_2013} for EOM-MP2 [CCSD(2)] \cite{Stanton_1995c} and ADC(3) \cite{Trofimov_2002,Harbach_2014,Dreuw_2015};
|
||||
Q-CHEM \cite{Krylov_2013} and TURBOMOLE \cite{Turbomole} for ADC(2) \cite{Trofimov_1997,Dreuw_2015};
|
||||
DALTON \cite{dalton} and TURBOMOLE \cite{Turbomole} for CC2 \cite{Christiansen_1995a,Hattig_2000};
|
||||
DALTON \cite{dalton} and GAUSSIAN \cite{Gaussian16} for CCSD \cite{Purvis_1982};
|
||||
DALTON \cite{dalton} for CCSDR(3) \cite{Christiansen_1996b};
|
||||
CFOUR \cite{cfour} for CCSDT-3 \cite{Watts_1996b,Prochnow_2010};
|
||||
and ORCA \cite{Neese_2012} for similarity-transformed EOM-CCSD (STEOM-CCSD) \cite{Nooijen_1997,Dutta_2018}.
|
||||
In addition, we evaluate the spin-opposite scaling (SOS) variants of ADC(2), SOS-ADC(2), as implemented in both Q-CHEM \cite{Krauter_2013} and TURBOMOLE \cite{Hellweg_2008}.
|
||||
Note that these two codes have distinct SOS implementations, as explained in Ref.~\cite{Krauter_2013}.
|
||||
We also test the SOS and spin-component scaled (SCS) versions of CC2, as implemented in TURBOMOLE \cite{Hellweg_2008,Turbomole}.
|
||||
Discussion of various spin-scaling schemes can be found elsewhere \cite{Goerigk_2010a}.
|
||||
When available, we take advantage of the resolution-of-the-identity (RI) approximation in TURBOMOLE and Q-CHEM.
|
||||
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.
|
||||
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.
|
||||
|
||||
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 systematically tested. \cite{Angeli_2001a, Angeli_2001b, Angeli_2002}
|
||||
@ -233,6 +244,7 @@ The definition of the active space considered for each system as well as the num
|
||||
\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, triplet, doublet, and double excitations) for molecules ranging from diatomics to ...
|
||||
|
||||
%=======================
|
||||
\subsection{QUEST\#1}
|
||||
%=======================
|
||||
@ -499,10 +511,10 @@ Because computing 450 excitation energies can be a costly exercise, we are plann
|
||||
|
||||
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 currently devoted to the obtention of highly-trustable excited-state properties.
|
||||
This includes, first, 0-0 energies 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 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,Loo20a}
|
||||
However, because 0-0 energies are fairly insensitive to the underlying molecular geometries, \cite{Send_2011a,Winter_2013,Loos_2019a} 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{Page_2003,Guareschi_2013,Bousquet_2013,Tuna_2016,Budzak_2017}, some of them being determined using state-of-the-art models \cite{Guareschi_2013,Budzak_2017}.
|
||||
There are also investigations of the accuracy of the nuclear gradients at the Franck-Condon point \cite{Tajti_2018,Tajti_2019}.
|
||||
The interested reader may find useful several investigations reporting sets of reference oscillator strengths \cite{Silva-Junior_2010c,Harbach_2014,Kannar_2014,Loos_2018a,Loos_2020a}.
|
||||
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.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
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