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@ -442,7 +442,7 @@ We have also computed total energies at the exFCI/AV5Z level and used these alon
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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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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 exFCI/CBS values are still off by a few tenths of a {\kcal} compared to the DMC results of Zimmerman \textit{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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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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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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@ -749,7 +749,7 @@ In order to have a miscellaneous test set of excitations, in a third time, we pr
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These two valence excitations --- $1\,^{1}\Sigma_g^+ \ra 1\,^{1}\Delta_g$ and $1\,^{1}\Sigma_g^+ \ra 2\,^{1}\Sigma_g^+$ --- are both of $(\pi,\pi) \ra (\si,\si)$ character.
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These two valence excitations --- $1\,^{1}\Sigma_g^+ \ra 1\,^{1}\Delta_g$ and $1\,^{1}\Sigma_g^+ \ra 2\,^{1}\Sigma_g^+$ --- are both of $(\pi,\pi) \ra (\si,\si)$ character.
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They have been recently studied with state-of-the-art methods, and have been shown to be ``pure'' doubly-excited states as they involve an insignificant amount of single excitations. \cite{LooBogSceCafJac-JCTC-19}
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They have been recently studied with state-of-the-art methods, and have been shown to be ``pure'' doubly-excited states as they involve an insignificant amount of single excitations. \cite{LooBogSceCafJac-JCTC-19}
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The vertical excitation energies associated with these transitions are reported in Table \ref{tab:Mol} and represented in Fig.~\ref{fig:C2}.
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The vertical excitation energies associated with these transitions are reported in Table \ref{tab:Mol} and represented in Fig.~\ref{fig:C2}.
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An interesting point here is that one really needs to consider the $\PBEot$ functional to get chemically accurate absorption energies with the AVDZ atomic basis set.
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An interesting point here is that one really needs to consider the $\PBEot$ functional to get chemically accurate excitation energies with the AVDZ atomic basis set.
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We believe that the present result is a direct consequence of the multireference character of the \ce{C2} molecule.
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We believe that the present result is a direct consequence of the multireference character of the \ce{C2} molecule.
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In other words, the UEG on-top pair density used in the $\LDA$ and $\PBEUEG$ functionals (see Sec.~\ref{sec:func}) is a particularly bad approximation of the true on-top pair density for the present system.
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In other words, the UEG on-top pair density used in the $\LDA$ and $\PBEUEG$ functionals (see Sec.~\ref{sec:func}) is a particularly bad approximation of the true on-top pair density for the present system.
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@ -836,7 +836,7 @@ 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 Ob\'elix 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 Jarvis-Alpha 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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@ -372,7 +372,7 @@ Here, we report the absolute energetic corrections for each state of each molecu
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\begin{squeezetable}
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\begin{squeezetable}
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\begin{table*}[h]
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\begin{table*}[h]
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\caption{
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\caption{
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Basis set energetic corrections (in hartree) on absorption energies for excited states of water, ammonia, carbon dimer and ethylene for various methods and basis sets.}
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Basis set energetic corrections (in hartree) on vertical excitation energies for excited states of water, ammonia, carbon dimer, and ethylene for various methods and basis sets.}
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\begin{ruledtabular}{}
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\begin{ruledtabular}{}
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\begin{tabular}{llddddddddd}
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\begin{tabular}{llddddddddd}
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& & \mc{9}{c}{Deviation with respect to TBE}
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& & \mc{9}{c}{Deviation with respect to TBE}
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