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%% This BibTeX bibliography file was created using BibDesk.
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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2019-07-01 12:03:08 +0200
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%% Created for Pierre-Francois Loos at 2019-07-01 14:00:38 +0200
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@article{LooGalJac-JPCL-18,
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Author = {Loos, Pierre-Fran{\c c}ois and Galland, Nicolas and Jacquemin, Denis},
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Date-Added = {2019-07-01 13:58:30 +0200},
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Date-Modified = {2019-07-01 13:59:12 +0200},
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Doi = {10.1021/acs.jpclett.8b02058},
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Journal = {J. Phys. Chem. Lett.},
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Number = {16},
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Pages = {4646--4651},
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Title = {Theoretical 0--0 Energies with Chemical Accuracy},
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Volume = {9},
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Year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.8b02058}}
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@article{LooJac-JCTC-19,
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Author = {P. F. Loos and D. Jacquemin},
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Date-Added = {2019-07-01 13:57:45 +0200},
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Date-Modified = {2019-07-01 14:00:29 +0200},
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Doi = {10.1021/acs.jctc.8b01103},
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Journal = {J. Chem. Theory Comput.},
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Pages = {2481--2491},
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Title = {Chemically accurate 0-0 energies with not-so-accurate excited state geometries},
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Volume = {15},
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Year = {2019}}
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@article{LooGil-MP-10,
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@article{LooGil-MP-10,
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Author = {P. F. Loos and P. M. W. Gill},
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Author = {P. F. Loos and P. M. W. Gill},
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Date-Added = {2019-07-01 09:27:40 +0200},
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Date-Added = {2019-07-01 09:27:40 +0200},
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@ -176,7 +176,7 @@
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\affiliation{\LCPQ}
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\affiliation{\LCPQ}
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\begin{abstract}
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\begin{abstract}
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By combining extrapolated selected configuration interaction (sCI) energies obtained with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm with the recently proposed short-range density-functional correction for basis-set incompleteness [\href{https://doi.org/10.1063/1.5052714}{Giner \textit{et al.}, \textit{J.~Chem.~Phys.}~\textbf{149}, 194301 (2018)}], we show that one can get chemically accurate vertical and adiabatic excitation energies with, typically, augmented double-$\zeta$ basis sets.
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By combining extrapolated selected configuration interaction (sCI) energies obtained with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm with the recently proposed short-range density-functional correction for basis-set incompleteness [\href{https://doi.org/10.1063/1.5052714}{Giner \textit{et al.}, \textit{J.~Chem.~Phys.}~ \textbf{2018}, \textit{149}, 194301}], we show that one can get chemically accurate vertical and adiabatic excitation energies with, typically, augmented double-$\zeta$ basis sets.
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We illustrate the present approach on various types of excited states (valence, Rydberg, and double excitations) in several small organic molecules (methylene, water, ammonia, carbon dimer and ethylene).
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We illustrate the present approach on various types of excited states (valence, Rydberg, and double excitations) in several small organic molecules (methylene, water, ammonia, carbon dimer and ethylene).
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The present study clearly evidences that special care has to be taken with very diffuse excited states where the present correction does not catch the radial incompleteness of the one-electron basis set.
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The present study clearly evidences that special care has to be taken with very diffuse excited states where the present correction does not catch the radial incompleteness of the one-electron basis set.
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\end{abstract}
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\end{abstract}
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@ -443,10 +443,12 @@ We have also computed total energies at the exFCI/AV5Z level and used these alon
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\begin{equation}
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\begin{equation}
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\E{}{\text{AVXZ}}(\tX) = \E{}{\CBS} + \frac{\alpha}{\tX^{3}}.
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\E{}{\text{AVXZ}}(\tX) = \E{}{\CBS} + \frac{\alpha}{\tX^{3}}.
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\end{equation}
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\end{equation}
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These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{tab:CH2} alongside reference values from the literature obtained with various deterministic and stochastic approaches. \cite{ChiHolAdaOttUmrShaZim-JPCA-18, SheLeiVanSch-JCP-98, JenBun-JCP-88, SheLeiVanSch-JCP-98, ZimTouZhaMusUmr-JCP-09}
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These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{tab:CH2} alongside reference values from the literature obtained with various deterministic and stochastic approaches. \cite{ChiHolAdaOttUmrShaZim-JPCA-18, SheLeiVanSch-JCP-98, JenBun-JCP-88, SheLeiVanSch-JCP-98, ZimTouZhaMusUmr-JCP-09}
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Total energies for each state can be found in the {\SI}.
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Total energies for each state can be found in the {\SI}.
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\titou{Comment on the difference between DMC and CBS results.}
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The exFCI/CBS values are still off by a few tenths of a {\kcal} compared to the DMC results of Zimmerman et al. \cite{ZimTouZhaMusUmr-JCP-09} which are extremely close from the experimentally-derived adiabatic energies.
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The reason of this discrepancy is probably due to the frozen-core approximation which has been applied in our case and has shown to significantly affect adiabatic energies. \cite{LooGalJac-JPCL-18, LooJac-JCTC-19}
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However, the exFCI/CBS energies are in perfect agreement with the semistochastic heat-bath CI (SHCI) calculations from Ref.~\onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}, as expected.
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Figure \ref{fig:CH2} clearly shows that, for the double-$\zeta$ basis, the exFCI adiabatic energies are far from being chemically accurate with errors as high as 0.15 eV.
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Figure \ref{fig:CH2} clearly shows that, for the double-$\zeta$ basis, the exFCI adiabatic energies are far from being chemically accurate with errors as high as 0.15 eV.
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From the triple-$\zeta$ basis onward, the exFCI excitation energies are chemically accurate though (i.e. error below 1 {\kcal} or 0.043 eV), and converge steadily to the CBS limit when one increases the size of the basis set.
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From the triple-$\zeta$ basis onward, the exFCI excitation energies are chemically accurate though (i.e. error below 1 {\kcal} or 0.043 eV), and converge steadily to the CBS limit when one increases the size of the basis set.
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Concerning the basis-set correction, already at the double-$\zeta$ level, the $\PBEot$ correction returns chemically accurate excitation energies.
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Concerning the basis-set correction, already at the double-$\zeta$ level, the $\PBEot$ correction returns chemically accurate excitation energies.
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@ -806,9 +808,7 @@ As a final example, we consider the ethylene molecule, yet another system which
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We refer the interested reader to the work of Feller \textit{et al.}\cite{FelPetDav-JCP-14} for an exhaustive investigation dedicated to the excited states of ethylene using state-of-the-art CI calculations.
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We refer the interested reader to the work of Feller \textit{et al.}\cite{FelPetDav-JCP-14} for an exhaustive investigation dedicated to the excited states of ethylene using state-of-the-art CI calculations.
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In the present context, ethylene is a particularly interesting system as it contains a mixture of valence and Rydberg excited states.
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In the present context, ethylene is a particularly interesting system as it contains a mixture of valence and Rydberg excited states.
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Our basis-set corrected vertical excitation energies are gathered in Table \ref{tab:Mol} and depicted in Fig.~\ref{fig:C2H4}.
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Our basis-set corrected vertical excitation energies are gathered in Table \ref{tab:Mol} and depicted in Fig.~\ref{fig:C2H4}.
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%Except for one particular excitation (the lowest singlet-triplet excitation $1\,^{1}A_{1g} \ra 1\,^{3}B_{1u}$),
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The exFCI+$\PBEot$/AVDZ excitation energies are at near chemical accuracy and the errors drop further when one goes to the triple-$\zeta$ basis.
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The exFCI+$\PBEot$/AVDZ excitation energies are at near chemical accuracy and the errors drop further when one goes to the triple-$\zeta$ basis.
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%(Note that one cannot afford exFCI/AVQZ calculations for ethylene.)
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Consistently with the previous examples, the $\LDA$ and $\PBEUEG$ functionals are slightly less accurate, although they still correct the excitation energies in the right direction.
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Consistently with the previous examples, the $\LDA$ and $\PBEUEG$ functionals are slightly less accurate, although they still correct the excitation energies in the right direction.
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%%% FIG 6 %%%
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%%% FIG 6 %%%
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@ -839,7 +839,7 @@ See {\SI} for geometries and additional information (including total energies an
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{acknowledgements}
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\begin{acknowledgements}
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PFL would like to thank Denis Jacquemin for numerous discussions on excited states.
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PFL would like to thank Denis Jacquemin for numerous discussions on excited states.
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This work was performed using HPC resources from GENCI-TGCC (Grant No.~2018-A0040801738), CALMIP (Toulouse) under allocation 2019-18005 and the Obelix cluster from the \textit{Institut Parisien de Chimie Physique et Th\'eorique}.
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This work was performed using HPC resources from GENCI-TGCC (Grant No.~2018-A0040801738), CALMIP (Toulouse) under allocation 2019-18005 and the Ob\'elix cluster from the \textit{Institut Parisien de Chimie Physique et Th\'eorique}.
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\end{acknowledgements}
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\end{acknowledgements}
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%
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