forked from PTEROSOR/QUESTDB
saving work
This commit is contained in:
parent
5941a5ee40
commit
0f1a2632fd
@ -1,13 +1,23 @@
|
||||
%% This BibTeX bibliography file was created using BibDesk.
|
||||
%% http://bibdesk.sourceforge.net/
|
||||
|
||||
%% Created for Pierre-Francois Loos at 2020-09-07 14:11:13 +0200
|
||||
%% Created for Pierre-Francois Loos at 2020-09-07 22:47:51 +0200
|
||||
|
||||
|
||||
%% Saved with string encoding Unicode (UTF-8)
|
||||
|
||||
|
||||
|
||||
@misc{Applencourt_2018,
|
||||
Archiveprefix = {arXiv},
|
||||
Author = {Thomas Applencourt and Kevin Gasperich and Anthony Scemama},
|
||||
Date-Added = {2020-09-07 22:30:24 +0200},
|
||||
Date-Modified = {2020-09-07 22:30:24 +0200},
|
||||
Eprint = {1812.06902},
|
||||
Primaryclass = {physics.chem-ph},
|
||||
Title = {Spin adaptation with determinant-based selected configuration interaction},
|
||||
Year = {2018}}
|
||||
|
||||
@article{Page_2003,
|
||||
Author = {Page, Christopher S. and Olivucci, Massimo},
|
||||
Date-Added = {2020-09-07 14:08:10 +0200},
|
||||
@ -343,7 +353,7 @@
|
||||
Author = {Goerigk, L. and Grimme, S.},
|
||||
Date-Added = {2020-09-07 09:29:41 +0200},
|
||||
Date-Modified = {2020-09-07 09:29:50 +0200},
|
||||
Journal = JCP,
|
||||
Journal = {J. Chem. Phys.},
|
||||
Pages = {184103},
|
||||
Title = {Assessment of TD-DFT Methods and of Various Spin Scaled CIS$_n$D and CC2 Versions for the Treatment of Low-Lying Valence Excitations of Large Organic Dyes},
|
||||
Volume = {132},
|
||||
|
||||
@ -95,12 +95,14 @@ One important aspect of some of these theoretical methods is their ability to ac
|
||||
The faithful description of excited states is particularly challenging from a theoretical point of view \cite{Gonzales_2012,Ghosh_2018,Loos_2020a} and is key to a deeper understanding of photochemical and photophysical processes like absorption, fluorescence, or even chemoluminescence \cite{Bernardi_1996,Olivucci_2010,Robb_2007,Navizet_2011}.
|
||||
For a given level of theory, ground-state methods are usually more accurate than their excited-state analogs.
|
||||
The reasons behind this are (at least) twofold: i) one might lack a proper variational principle for excited-state energies, and ii) excited states are often very close in energy from each other but they can have very different natures ($\pi \to \pis$, $n \to \pis$, charge transfer, double excitation, valence, Rydberg, singlet, doublet, triplet, etc).
|
||||
Designing excited-state methods which can tackle on the same footing all these types of excited states at an affordable cost remain an open challenge in theoretical computational chemistry \cite{Gonzales_2012,Ghosh_2018,Loos_2020a}.
|
||||
Designing excited-state methods able to tackle on the same footing all these types of excited states at an affordable cost remain an open challenge in theoretical computational chemistry \cite{Gonzales_2012,Ghosh_2018,Loos_2020a}.
|
||||
|
||||
When one designs a new theoretical model, the first feature that one might want to test is its overall accuracy, i.e., its ability to reproduce reference (or benchmark) values for a given system with well-defined setup (same geometry, basis set, etc).
|
||||
These values can be absolute or relative energies, geometrical parameters, physical or chemical properties, extracted from experiments, high-level theoretical calculations, or a combination of both.
|
||||
To do so, the electronic structure community has designed along the years benchmark sets, i.e., sets of molecules for which one could (very) accurately compute theoretical estimates and/or access solid experimental data for given properties.
|
||||
Regarding ground-states properties, two of the oldest and most employed sets are probably the Gaussian-1 and Gaussian-2 benchmark sets \cite{Pople_1989,Curtiss_1991,Curtiss_1997} developed by the group of Pople in the 1990's which gathers atomization energies, ionization energies, electron affinities, proton affinities, bond dissociation energies, and reaction barriers.
|
||||
Regarding ground-states properties, two of the oldest and most employed sets are probably the Gaussian-1 and Gaussian-2 benchmark sets \cite{Pople_1989,Curtiss_1991,Curtiss_1997} developed by the group of Pople in the 1990's.
|
||||
For example, the Gaussian-2 set gathers atomization energies, ionization energies, electron affinities, proton affinities, bond dissociation energies, and reaction barriers.
|
||||
This set was subsequently extended and refined \cite{Curtiss_1998,Curtiss_2007}.
|
||||
Another very useful set for the design of methods able to catch dispersion effects is the S22 benchmark set \cite{Jureka_2006} (and its extended S66 version \cite{Rezac_2011}) of Hobza and collaborators which provides benchmark interaction energies for weakly-interacting (non covalent) systems.
|
||||
One could also mentioned the $GW$100 set \cite{vanSetten_2015,Krause_2015,Maggio_2016} (and its $GW$5000 extension \cite{Stuke_2020}) of ionization energies which has helped enormously the community to settle on the implementation of $GW$-type methods for molecular systems \cite{vanSetten_2013,Bruneval_2016,Caruso_2016,Govoni_2018}.
|
||||
The extrapolated ab initio thermochemistry (HEAT) set designed to achieve high accuracy for enthalpies of formation of atoms and small molecules (without experimental data) is yet another successful example of benchmark set \cite{Tajti_2004,Bomble_2006,Harding_2008}.
|
||||
@ -109,43 +111,43 @@ Let us also mention the set of Zhao and Truhlar for small transition metal compl
|
||||
|
||||
The examples presented above are all designed for ground-state properties, and there exists now specific protocols designed to accurately model excited-state energies and properties.
|
||||
Benchmark datasets of excited-state energies and/or properties are less numerous than their ground-state counterparts but their number have been growing at a consistent pace in the past few years.
|
||||
Below, we provide a short description of some of these.
|
||||
One the most characteristic example is the benchmark set of vertical excitations proposed by Thiel and coworkers \cite{Schreiber_2008,Silva-Junior_2008,Silva-Junior_2010,Silva-Junior_2010b,Silva-Junior_2010c}.
|
||||
Below, we provide a short description for some of them.
|
||||
One of the most characteristic example is the benchmark set of vertical excitations proposed by Thiel and coworkers \cite{Schreiber_2008,Silva-Junior_2008,Silva-Junior_2010,Silva-Junior_2010b,Silva-Junior_2010c}.
|
||||
The so-called Thiel (or M\"ulheim) set of excitation energies gathers a large number of excitation energies determined in 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 \cite{Christiansen_1995a,Hattig_2000}, CCSD \cite{Purvis_1982}, CC3 \cite{Christiansen_1995b,Koch_1997}, and CASPT2 \cite{Andersson_1990,Andersson_1992,Roos,Roos_1996} calculations (with the TZVP basis) on MP2/6-31G(d) geometries in order to provide (based on additional high-quality literature data) TBEs for these transitions \cite{Silva-Junior_2010b}.
|
||||
These TBEs were quickly refined with the larger aug-cc-pVTZ basis set, highlighting the importance of diffuse functions in the faithful description of excited states (especially for Rydberg states).
|
||||
In the same spirit, it is also worth mentioning Gordon's set of vertical transitions (based on experimental values) used to benchmark the performance of time-dependent density-functional theory (TD-DFT) \cite{Leang_2012}, as well as its extended version by Goerigk and coworkers \cite{Schwabe_2017,Casanova-Paez_2019,Casanova_Paes_2020} who decided to replace the experimental reference values by CC3 excitation energies instead.
|
||||
Let us also mention the new benchmark set of charge-transfer excited states recently introduced by Szalay and coworkers [based on coupled cluster (CC) methods] \cite{Kozma_2020} as well as the Gagliardi-Truhlar set \cite{Hoyer_2016} employed to compare the accuracy of multiconfiguration pair-density functional theory \cite{Ghosh_2018} against the well-established CASPT2 method.
|
||||
In the same spirit, it is also worth mentioning Gordon's set of vertical transitions (based on experimental values) used to benchmark the performance of time-dependent density-functional theory (TD-DFT) \cite{Leang_2012}, as well as its extended version by Goerigk and coworkers who decided to replace the experimental reference values by CC3 excitation energies instead \cite{Schwabe_2017,Casanova-Paez_2019,Casanova_Paes_2020}.
|
||||
Let us also mention the new benchmark set of charge-transfer excited states recently introduced by Szalay and coworkers [based on coupled cluster (CC) methods] \cite{Kozma_2020} as well as the Gagliardi-Truhlar set employed to compare the accuracy of multiconfiguration pair-density functional theory \cite{Ghosh_2018} against the well-established CASPT2 method \cite{Hoyer_2016}.
|
||||
|
||||
|
||||
Following a similar philosophy, 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.
|
||||
Moreover, our protocol has been designed to be as uniform as possible, which means that we use 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 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).
|
||||
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).
|
||||
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 last 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.
|
||||
|
||||
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}.
|
||||
Due to the fairly natural idea underlying SCI 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}.
|
||||
Their fundamental philosophy consists, roughly speaking, in retaining only the most energetically relevant determinants of the FCI space following a given criterion to avoid the exponential increase of the size of the CI expansion.
|
||||
Originally developed in the late 1960's by Bender and Davidson \cite{Bender_1969} as well as Whitten and Hackmeyer, \cite{Whitten_1969} new efficient SCI algorithms have resurfaced recently.
|
||||
Originally developed in the late 1960's by Bender and Davidson \cite{Bender_1969} as well as Whitten and Hackmeyer \cite{Whitten_1969}, new efficient SCI algorithms have resurfaced recently.
|
||||
Four examples are adaptive sampling CI (ASCI) \cite{Tubman_2016,Tubman_2018,Tubman_2020}, iCI \cite{Liu_2016}, semistochastic heat-bath CI (SHCI) \cite{Holmes_2016,Holmes_2017,Sharma_2017,Li_2018}), and \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2019}.
|
||||
These four flavors of SCI include a second-order perturbative (PT2) correction which is key to estimate the ``distance'' to the FCI solution (see below).
|
||||
The QUEST set of excitation energies relies on the CIPSI algorithm, which is, from a historical point of view, one of the oldest SCI algorithm.
|
||||
It was developed in 1973 by Huron, Rancurel, and Malrieu \cite{Huron_1973} (see also Refs.~\cite{Evangelisti_1983,Cimiraglia_1985,Cimiraglia_1987,Illas_1988,Povill_1992}).
|
||||
Recently, the determinant-driven CIPSI algorithm has been efficiently implemented \cite{Garniron_2019} in the open-source programming environment {\QP} by our group enabling to perform massively parallel computations \cite{Garniron_2017,Garniron_2018,Garniron_2019,Loos_2020e}.
|
||||
CIPSI is also frequently used to provide accurate trial wave functions for QMC calculations in molecules \cite{Caffarel_2014,Caffarel_2016a,Caffarel_2016b,Giner_2013,Giner_2015,Scemama_2015,Scemama_2016,Scemama_2018,Scemama_2018b,Scemama_2019,Dash_2018,Dash_2019,Scemama_2020} and more recently for periodic solids \cite{Benali_2020}.
|
||||
We refer the interested reader to Ref.~\cite{Garniron_2019} where one can find all the details regarding the implementation of the CIPSI algorithm.
|
||||
Recently, the determinant-driven CIPSI algorithm has been efficiently implemented \cite{Garniron_2019} in the open-source programming environment QUANTUM PACKAGE by our group enabling to perform massively parallel computations \cite{Garniron_2017,Garniron_2018,Garniron_2019,Loos_2020e}.
|
||||
CIPSI is also frequently employed to provide accurate trial wave functions for quantum Monte Carlo calculations in molecules \cite{Caffarel_2014,Caffarel_2016a,Caffarel_2016b,Giner_2013,Giner_2015,Scemama_2015,Scemama_2016,Scemama_2018,Scemama_2018b,Scemama_2019,Dash_2018,Dash_2019,Scemama_2020} and more recently for periodic solids \cite{Benali_2020}.
|
||||
We refer the interested reader to Ref.~\cite{Garniron_2019} where one can find additional details regarding the implementation of the CIPSI algorithm.
|
||||
|
||||
The present article is organized as follows.
|
||||
In Sec.~\ref{sec:tools}, we detail the specificities of our protocol by providing the computational details regarding geometries, basis sets, (reference and benchmarked) computational methods, and a new way of estimating rigorously the extrapolation error in SCI calculations.
|
||||
We then describe in Sec.~\ref{sec:QUEST} the content of our five QUEST sub-sets providing for each of them the number of reference excitation energies, the nature and size of the molecules, the list of benchmarked methods, as well as other specificities.
|
||||
In Sec.~\ref{sec:tools}, we detail the specificities of our protocol by providing computational details regarding geometries, basis sets, (reference and benchmarked) computational methods, and a new way of estimating rigorously the extrapolation error in SCI calculations.
|
||||
We then describe in Sec.~\ref{sec:QUEST} the content of our five QUEST subsets providing for each of them the number of reference excitation energies, the nature and size of the molecules, the list of benchmarked methods, as well as other specificities.
|
||||
A special emphasis is placed on our latest add-on, QUEST\#5, specifically designed for the present manuscript where we have considered, in particular but not only, larger molecules as well as additional FCI values for five- and six-membered rings.
|
||||
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.
|
||||
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.
|
||||
Section \ref{sec:website} describes 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.
|
||||
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.
|
||||
Finally, we draw our conclusions in Sec.~\ref{sec:ccl} where we discuss, in particular, future projects aiming at expanding and improving the usability and accuracy of the QUEST database.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Computational tools}
|
||||
@ -157,9 +159,9 @@ Finally, we draw our conclusions in Sec.~\ref{sec:ccl} where we discuss, in part
|
||||
%=======================
|
||||
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.
|
||||
As shown in Refs.~\cite{Hattig_2005c,Budzak_2017}, CC3 provides extremely accurate ground- and excited-state geometries.
|
||||
These optimizations have been performed using DALTON 2017 \cite{dalton} and CFOUR 2.1, \cite{cfour} applying default parameters.
|
||||
These optimizations have been performed using DALTON 2017 \cite{dalton} and CFOUR 2.1 \cite{cfour} applying default parameters.
|
||||
For the open-shell derivatives \cite{Loos_2020c}, the geometries are optimized at the UCCSD(T)/aug-cc-pVTZ level using the GAUSSIAN16 program \cite{Gaussian16} and applying the ``tight'' convergence threshold.
|
||||
%For the present review article, we have gathered all the geometries in the {\SupInf}.
|
||||
For the purpose of the present review article, we have gathered all the geometries in the {\SupInf}.
|
||||
%\footnote{These geometries can be found at...}
|
||||
|
||||
%=======================
|
||||
@ -176,28 +178,34 @@ Doubly- and triply-augmented basis sets are usually employed for Rydberg states
|
||||
\subsubsection{Reference computational methods}
|
||||
%------------------------------------------------
|
||||
In order to compute reference vertical energies, we have designed different strategies depending on the actual nature of the transition and the size of the system.
|
||||
For small systems (typically 1--3 non-hydrogen atoms), we resort to SCI methods which can provide near-FCI excitation energies for compact basis sets.
|
||||
For small molecules (typically 1--3 non-hydrogen atoms), we resort to SCI methods which can provide near-FCI excitation energies for compact basis sets.
|
||||
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.
|
||||
Note that all our excited-state CC calculations are performed within the equation-of-motion (EOM) or linear-response (LR) formalism that yield the same 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.
|
||||
For open-shell molecules, the CCSDT, CCSDTQ, and CCSDTQP calculations performed with MRCC \cite{Rolik_2013,mrcc} do consider an unrestricted Hartree-Fock 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.~\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.
|
||||
A state-averaged formalism is employed, i.e., the ground and excited states are described with the same set of determinants, but different CI coefficients.
|
||||
Our usual protocol \cite{Scemama_2018,Scemama_2018b,Scemama_2019,Loos_2018a,Loos_2019,Loos_2020a,Loos_2020b,Loos_2020c} consists of performing a preliminary SCI calculation using Hartree-Fock orbitals in order to generate a SCI wave function with at least $10^7$ determinants.
|
||||
Natural orbitals are then computed based on this wave function, and a new, larger SCI calculation is performed with this new set of orbitals.
|
||||
This has the advantage to produce a smoother and faster convergence of the SCI energy toward the FCI limit.
|
||||
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 linearly 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.
|
||||
Below, we provide a much cleaner way of estimating the extrapolation error in SCI methods, and we adopt this scheme for the five- and six-membered rings.
|
||||
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.
|
||||
Note that, all our SCI wave functions are eigenfunctions of the $\Hat{S}^2$ spin operator which is, unlike ground-state calculations, paramount in the case of excited states \cite{Applencourt_2018}.
|
||||
|
||||
|
||||
%------------------------------------------------
|
||||
\subsubsection{Benchmarked computational methods}
|
||||
@ -224,7 +232,7 @@ For radicals, we applied both the U (unrestricted) and RO (restricted open-shell
|
||||
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}.
|
||||
From a strict theoretical point of view, we point out that PC-NEVPT2 is supposed to be more accurate than SC-NEVPT2 given that it has a larger number of perturbers and greater flexibility.
|
||||
In the case of double excitations \cite{Loos_2019}, we have also performed calculations with multi-state (MS) CASPT2 (MS-MR formalism), \cite{Finley_1998} and its extended variant (XMS-CASPT2) \cite{Shiozaki_2011}, when there is a strong mixing between states with same spin and spatial symmetries.
|
||||
In the case of double excitations \cite{Loos_2019}, we have also performed calculations with multi-state (MS) CASPT2 (MS-MR formalism), \cite{Finley_1998} and its extended variant (XMS-CASPT2) \cite{Shiozaki_2011} when there is a strong mixing between states with same spin and spatial symmetries.
|
||||
The CASPT2 calculations have been performed with level shift and IPEA parameters set to the standard values of $0.3$ and $0.25$ a.u., respectively, unless otherwise stated.
|
||||
Large active spaces carefully chosen and tailored for the desired transitions have been selected.
|
||||
The definition of the active space considered for each system as well as the number of states in the state-averaged calculation is provided in their corresponding publication.
|
||||
@ -243,8 +251,9 @@ 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 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, soublet, triplet, and double excitations) for molecules ranging from diatomics to molecules as large as naphthalene.
|
||||
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).
|
||||
|
||||
%%% FIGURE 1 %%%
|
||||
\begin{figure}[bt]
|
||||
@ -290,7 +299,7 @@ This was further demonstrated in a recent study by two of the present authors \c
|
||||
%=======================
|
||||
\subsection{QUEST\#4}
|
||||
%=======================
|
||||
The QUEST\#4 benchmark set \cite{Loos_2020c} consists of two subsets of excitations.
|
||||
The QUEST\#4 benchmark set \cite{Loos_2020c} consists of two subsets of excitations and oscillator strengths.
|
||||
An ``exotic'' subset of 30 excited states for closed-shell molecules containing F, Cl, P, and Si atoms (carbonyl fluoride, \ce{CCl2}, \ce{CClF}, \ce{CF2}, difluorodiazirine, formyl fluoride, \ce{HCCl}, \ce{HCF}, \ce{HCP}, \ce{HPO}, \ce{HPS}, \ce{HSiF}, \ce{SiCl2}, and silylidene) and a ``radical'' subset of 51 doublet-doublet transitions in small radicals (allyl, \ce{BeF}, \ce{BeH}, \ce{BH2}, \ce{CH}, \ce{CH3}, \ce{CN}, \ce{CNO}, \ce{CON}, \ce{CO+}, \ce{F2BO}, \ce{F2BS}, \ce{H2BO}, \ce{HCO}, \ce{HOC}, \ce{H2PO}, \ce{H2PS}, \ce{NCO}, \ce{NH2}, nitromethyl, \ce{NO}, \ce{OH}, \ce{PH2}, and vinyl) characterized by open-shell electronic configurations and an unpaired electron.
|
||||
This represents a total of 81 high-quality TBEs, the vast majority being obtained at the FCI level with at least the aug-cc-pVTZ basis set.
|
||||
We further performed high-order CC calculations to ascertain these estimates.
|
||||
@ -306,6 +315,7 @@ 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.
|
||||
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.
|
||||
|
||||
%--------------------------------------
|
||||
\subsubsection{Toward larger molecules}
|
||||
@ -509,13 +519,13 @@ Triazine & $^1A_1''(n \ra \pis)$ & 4.85 & 4.84 & 4.769(132) \\
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
Because computing 450 excitation energies can be a costly exercise, we are planning on developing a ``diet set'' following the philosophy of the ``diet GMTKN55'' set \cite{Goerigk_2017} proposed recently by Gould \cite{Gould_2018b}.
|
||||
|
||||
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{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.
|
||||
%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{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.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section*{acknowledgements}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user