stash or die
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@ -98,7 +98,6 @@ We hope that the present review will provide a useful summary of our work so far
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\section{Introduction}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Nowadays, there exists a very large number of electronic structure computational approaches, more or less expensive depending on their overall accuracy, able to quantitatively predict the absolute and/or relative energies of electronic states in molecular systems \cite{SzaboBook,JensenBook,CramerBook,HelgakerBook}.
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One important aspect of some of these theoretical methods is their ability to access the energies of electronic excited states, i.e., states that have higher total energies than the so-called ground (that is, lowest-energy) state \cite{Roos_1996,Piecuch_2002,Dreuw_2005,Krylov_2006,Sneskov_2012,Gonzales_2012,Laurent_2013,Adamo_2013,Ghosh_2018,Blase_2020,Loos_2020a}.
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The faithful description of excited states is particularly challenging from a theoretical point of view and is key to a deeper understanding of photochemical and photophysical processes like absorption, fluorescence, phosphorescence or even chemoluminescence \cite{Bernardi_1996,Olivucci_2010,Robb_2007,Navizet_2011}.
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@ -436,7 +435,7 @@ An important addition to this second study was the inclusion of various flavors
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Our results demonstrated that the error of CC methods is intimately linked to the amount of double-excitation character in the vertical transition.
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For ``pure'' double excitations (i.e., for transitions which do not mix with single excitations), the error in CC3 and CCSDT can easily reach $1$ and $0.5$ eV, respectively, while it goes down to a few tenths of an eV for more common transitions involving a significant amount of single excitations (such as in butadiene and benzene) .
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The quality of the excitation energies obtained with CASPT2 and NEVPT2 was harder to predict as the overall accuracy of these methods is highly dependent on both the system and the selected active space.
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Nevertheless, these two methods were found to be more accurate for transition with a small percentage of single excitations (error usually below $0.1$ eV) than for excitations dominated by single excitations where the error is closer from $0.1$--$0.2$ eV
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Nevertheless, these two methods were found to be more accurate for transition with a small percentage of single excitations (error usually below $0.1$ eV) than for excitations dominated by single excitations where the error is closer from $0.1$--$0.2$ eV.
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%=======================
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\subsection{QUEST\#3}
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@ -492,7 +491,7 @@ We refer the interested reader to the {\SupInf} for a detailed discussion of eac
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%SCS-CC2 & 46 & 0.46 & -0.03 & 0.19 & 0.12 & 0.22 & 0.19 \\
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%SOS-ADC(2)$^b$ & 46 & 0.69 & -0.02 & 0.24 & 0.13 & 0.27 & 0.24 \\
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%SOS-CC2 & 46 & 0.77 & 0.02 & 0.28 & 0.16 & 0.32 & 0.28 \\
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%CCSD(2) & 55 & 0.80 & -0.13 & 0.33 & 0.22 & 0.40 & 0.34 \\
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%EOM-MP2 & 55 & 0.80 & -0.13 & 0.33 & 0.22 & 0.40 & 0.34 \\
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%CCSD & 55 & 0.80 & -0.25 & 0.17 & 0.17 & 0.24 & 0.19 \\
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%STEOM-CCSD & 30 & 0.13 & -0.36 & -0.07 & 0.14 & 0.16 & 0.12 \\
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%CCSDR(3) & 37 & 0.43 & 0.00 & 0.09 & 0.08 & 0.12 & 0.09 \\
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@ -531,7 +530,7 @@ All these quantities are computed with the same aug-cc-pVTZ basis.
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Importantly, we also report the composite approach considered to compute the TBEs (see column ``Method'').
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Following an ONIOM-like strategy \cite{Svensson_1996a,Svensson_1996b}, the TBEs are computed as ``A/SB + [B/TB - B/SB]'', where A/SB is the excitation energy computed with a method A in a smaller basis (SB), and B/SB and B/TB are excitation energies computed with a method B in the small basis and target basis TB = aug-cc-pVTZ, respectively.
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Talking about numbers, the QUEST database is composed by 488 excitation energies, 434 of them being considered as ``safe'' (\ie, chemically-accurate for the considered basis set and geometry), 291 singlet, 197 triplet, 361 valence, and 125 Rydberg excited states. From these, 135 transitions corresponds to $n \ra \pis$ excitations, 198 to $\pi \ra \pis$, and 13 are doubly-excited states. In terms of molecular sizes, 146 excitations are obtained in molecules having in-between 1 and 3 non-hydrogen atoms, 97 excitations from 4 non-hydrogen atom compounds, 177 from molecules composed by 5 and 6 non-hydrogen atoms, and, finally, 68 excitations are obtained from systems with 7 to 10 non-hydrogen atoms.
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Talking about numbers, the QUEST database is composed by 488 excitation energies, 434 of them being considered as ``safe'' (\ie, chemically-accurate for the considered basis set and geometry), 291 singlet, 197 triplet, 361 valence, and 125 Rydberg excited states. From these, 135 transitions correspond to $n \ra \pis$ excitations, 198 to $\pi \ra \pis$, and 13 are doubly-excited states. In terms of molecular sizes, 146 excitations are obtained in molecules having in-between 1 and 3 non-hydrogen atoms, 97 excitations from 4 non-hydrogen atom compounds, 177 from molecules composed by 5 and 6 non-hydrogen atoms, and, finally, 68 excitations are obtained from systems with 7 to 10 non-hydrogen atoms.
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\begin{ThreePartTable}
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\scriptsize
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@ -1066,7 +1065,7 @@ All quantities are given in eV. ``Count'' refers to the number of transitions co
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\begin{threeparttable}
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\begin{tabular}{llccccccccccccccc}
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\headrow
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& & \thead{CIS(D)} & \thead{CC2} & \thead{CCSD(2)} & \thead{STEOM-CCSD} & \thead{CCSD} & \thead{CCSDR(3)} & \thead{CCCSDT-3} & \thead{CC3}
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& & \thead{CIS(D)} & \thead{CC2} & \thead{EOM-MP2} & \thead{STEOM-CCSD} & \thead{CCSD} & \thead{CCSDR(3)} & \thead{CCCSDT-3} & \thead{CC3}
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& \thead{SOS-ADC(2)$^a$} & \thead{SOS-CC2$^a$} & \thead{SCS-CC2$^a$} & \thead{SOS-ADC(2)$^b$} & \thead{ADC(2)} & \thead{ADC(3)} & \thead{ADC(2.5)} \\
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Count & & 429 & 431 & 427 & 360 & 431 & 259 & 251 & 431 & 430 & 430 & 430 & 430 & 426 & 423 & 423 \\
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Max(+) & & 1.06 & 0.63 & 0.80 & 0.59 & 0.80 & 0.43 & 0.26 & 0.19 & 0.87 & 0.84 & 0.76 & 0.73 & 0.64 & 0.60 & 0.24 \\
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@ -1114,6 +1113,17 @@ MAE & & 0.22 & 0.16 & 0.22 & 0.11 & 0.12 & 0.05 & 0.04 & 0.02 & 0.20 & 0.22
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\label{fig:QUEST_stat}}
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\end{figure}
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The most striking feature from the statistical indicators gathered in Table \ref{tab:stat} is the overall accuracy of CC3 with MAEs and MSEs systematically below the chemical accuracy threshold, irrespectively of the nature of the transition and the size of the molecule.
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CCSDR(3) are CCCSDT-3 can also be regarded as excellent performers with overall MAEs below $0.05$ eV, though one would notice a slight degradation of their performances for the $n \ra \pis$ excitations and the largest subset of molecules.
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The other third-order method, ADC(3), which enjoys a lower computational cost, is significantly less accuracy and does not really improve upon its second-order analog, even for the largest systems considered here, observation in line with a previous analysis by some of the authors \cite{Loos_2020d}.
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Nonetheless, ADC(3)'s accuracy improves in larger compounds.
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The ADC(2.5) composite method introduced in Ref.~\cite{Loos_2020d}, which corresponds to grossly average the ADC(2) and ADC(3) values, yield an appreciable accuracy improvement, as shown in Fig.~\ref{fig:QUEST_stat}.
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Concerning the second-order methods, in terms of MAEs, we have the following ranking: EOM-MP2 $\approx$ CIS(D) $<$ CC2 $\approx$ ADC(2) $<$ CCSD $\approx$ STEOM-CCSD which fits our previous conclusions on the specific subsets. \cite{Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c,Loos_2020d}
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A very similar ranking is obtained when one looks at the MSEs.
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It is noteworthy that the performances of EOM-MP2 and CCSD are getting notably worse when the system size increases, while CIS(D) and STEOM-CCSD have a very stable behavior with respect to system size. Oppositely, the overall accuracy of CC2 and ADC(2) do improve for larger molecules.
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For the scaled methods [SOS-ADC(2), SOS-CC2, and SCS-CC2], the TURBOMOLE scaling factors do not seem to improve things upon the unscaled versions, while the Q-CHEM scaling factors for ADC(2) provide a small, yet significant improvement for this set of molecules.
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Of course, one of the remaining open questions regarding all these methods is their accuracy for even larger systems.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{The QUESTDB website}
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\label{sec:website}
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@ -1212,7 +1222,7 @@ and the value is considered as not safe when one or more value as not safe
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\section{Concluding remarks}
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\label{sec:ccl}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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In the present review article, we have presented and extended the QUEST database of highly-accurate excitation energies for molecules systems \cite{Loos_2020a,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c} that we started building in 2018 and that is now composed by more than \alert{470} vertical excitations.
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In the present review article, we have presented and extended the QUEST database of highly-accurate excitation energies for molecules systems \cite{Loos_2020a,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c} that we started building in 2018 and that is now composed by more than 400 vertical excitations.
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In particular, we have detailed the specificities of our protocol by providing computational details regarding geometries, basis sets, as well as reference and benchmarked computational methods.
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The content of our five QUEST subsets has been presented in details, and for each of the them, we have provided the number of reference excitation energies, the nature and size of the molecules, the list of benchmarked methods, as well as other specificities.
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Importantly, we have proposed a new method to faithfully estimate the extrapolation error in SCI calculations.
|
||||
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|
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Reference in New Issue
Block a user