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last SF-CIS numbers

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Pierre-Francois Loos 2021-01-18 10:05:45 +01:00
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Manuscript/sfBSE.tex
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@ -613,7 +613,7 @@ Beryllium has a $^1S$ ground state with $1s^2 2s^2$ configuration.
The excitation energies corresponding to the first singlet and triplet single excitations $2s \to 2p$ with $P$ spatial symmetry as well as the first singlet and triplet double excitations $2s^2 \to 2p^2$ with $D$ and $P$ spatial symmetries (respectively) are reported in Table \ref{tab:Be} and depicted in Fig.~\ref{fig:Be}.
The left side of Fig.~\ref{fig:Be} (red lines) reports SF-TD-DFT excitation energies obtained with the BLYP, B3LYP, and BH\&HLYP functionals, which correspond to an increase of exact exchange from 0\% to 50\%.
As mentioned in Ref.~\onlinecite{Casanova_2020}, the $^3P(1s^2 2s^1 2p^1)$ and the $^1P(1s^2 2s^1 2p^1)$ states are degenerate at the SF-TD-BLYP level and their excitation energies are given by the $2s$--$2p$ orbital energy difference due to the lack of coupling terms in the spin-flip block of the SD-TD-DFT equations (\textit{vide supra}).
As mentioned in Ref.~\onlinecite{Casanova_2020}, the $^3P(1s^2 2s^1 2p^1)$ and the $^1P(1s^2 2s^1 2p^1)$ states are degenerate at the SF-TD-BLYP level and their excitation energy is given by the energy difference between the $2s$ and $2p$ orbitals due to the lack of coupling terms in the spin-flip block of the SD-TD-DFT equations (see Subsec.~\ref{sec:BSE}).
Including exact exchange, like in SF-TD-B3LYP and SF-TD-BH\&HLYP, lifts this degeneracy.
However, the SF-TD-BH\&HLYP excitation energy of the $^1P(1s^2 2s^1 2p^1)$ state is still off by $1.6$ eV as compared to the FCI reference.
For the other states, the agreement between SF-TD-BH\&HLYP and FCI is significantly improved.
@ -634,7 +634,7 @@ Generally we can observe that all the scheme with SF-BSE used do not increase si
\label{tab:Be}}
\begin{ruledtabular}
\begin{tabular}{lcccccccccc}
& \mc{5}{c}{6-31G} & \mc{5}{c}{aug-cc-pVTQ} \\
& \mc{5}{c}{6-31G} & \mc{5}{c}{aug-cc-pVQZ} \\
\cline{2-6} \cline{7-11}
Method & $^1S(1s^2 2s^2)$ & $^3P(1s^2 2s^1 2p^1)$ & $^1P(1s^2 2s^1 2p^1)$
& $^3P(1s^22 p^2)$ & $^1D(1s^22p^2)$
@ -790,22 +790,22 @@ So here we have an example where the dynamical corrections are necessary to get
All the spin-flip calculations have been performed with a UHF reference and the cc-pVTZ basis set.
\label{tab:CBD_D2h}}
\begin{ruledtabular}
\begin{tabular}{lccc}
\begin{tabular}{lrrr}
& \mc{3}{c}{Excitation energies (eV)} \\
\cline{2-4}
Method & $1\,{}^3B_{1g}$ & $1\,{}^1B_{1g}$ & $2\,{}^1A_{1g}$ \\
\hline
SF-TD-B3LYP\fnm[3] &1.750 &2.260 &4.094 \\
SF-TD-BH\&HLYP\fnm[3] &1.583 &2.813 & 4.528\\
SF-CIS\fnm[1] & & & \\
EOM-SF-CCSD\fnm[1] &1.654 & 3.416&4.360 \\
EOM-SF-CCSD(fT)\fnm[1] & 1.516& 3.260&4.205 \\
EOM-SF-CCSD(dT)\fnm[1] &1.475 &3.215 &4.176 \\
SF-ADC(2)-s\fnm[2] & 1.573& 3.208& 4.247\\
SF-ADC(2)-x\fnm[2] &1.576 &3.141 &3.796 \\
SF-ADC(3)\fnm[2] & 1.456&3.285 &4.334 \\
SF-BSE@{\GOWO}\fnm[3] & 1.438 & 2.704 &4.540 \\
SF-dBSE@{\GOWO}\fnm[3] & 1.403 &2.883 &4.621 \\
SF-TD-B3LYP\fnm[3] & $1.750$ & $2.260$ & $4.094$ \\
SF-TD-BH\&HLYP\fnm[3] & $1.583$ & $2.813$ & $4.528$ \\
SF-CIS\fnm[1] & $1.521$ & $3.836$ & $5.499$ \\
EOM-SF-CCSD\fnm[1] & $1.654$ & $3.416$ & $4.360$ \\
EOM-SF-CCSD(fT)\fnm[1] & $1.516$ & $3.260$ & $4.205$ \\
EOM-SF-CCSD(dT)\fnm[1] & $1.475$ & $3.215$ & $4.176$ \\
SF-ADC(2)-s\fnm[2] & $1.573$ & $3.208$ & $4.247$ \\
SF-ADC(2)-x\fnm[2] & $1.576$ & $3.141$ & $3.796$ \\
SF-ADC(3)\fnm[2] & $1.456$ & $3.285$ & $4.334$ \\
SF-BSE@{\GOWO}\fnm[3] & $1.438$ & $2.704$ & $4.540$ \\
SF-dBSE@{\GOWO}\fnm[3] & $1.403$ & $2.883$ & $4.621$ \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Spin-flip EOM-CC value from Ref.~\onlinecite{Manohar_2008}.}
@ -821,22 +821,22 @@ So here we have an example where the dynamical corrections are necessary to get
All the spin-flip calculations have been performed with a UHF reference and the cc-pVTZ basis set.
\label{tab:CBD_D4h}}
\begin{ruledtabular}
\begin{tabular}{lccc}
\begin{tabular}{lrrr}
& \mc{3}{c}{Excitation energies (eV)} \\
\cline{2-4}
Method & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ \\
\hline
SF-TD-B3LYP \fnm[3] &-0.020 & 0.486& 0.547\\
SF-TD-BH\&HLYP\fnm[3] &0.048 & 1.282&1.465 \\
SF-CIS\fnm[1] &0.317 & 3.125&2.650 \\
EOM-SF-CCSD\fnm[1] &0.369 & 1.824& 2.143\\
EOM-SF-CCSD(fT)\fnm[1] & 0.163&1.530 &1.921 \\
EOM-SF-CCSD(dT)\fnm[1] &0.098 &1.456 &1.853 \\
SF-ADC(2)-s\fnm[2] & 0.266& 1.664& 1.910 \\
SF-ADC(2)-x\fnm[2] & 0.217&1.123 &1.799 \\
SF-ADC(3)\fnm[2] &0.083 &1.621 &1.930 \\
SF-BSE@{\GOWO}\fnm[3] & -0.049 & 1.189 & 1.480 \\
SF-dBSE@{\GOWO}\fnm[3] & 0.012 & 1.507 & 1.841 \\
SF-TD-B3LYP\fnm[3] & $-0.020$ & $0.486$ & $0.547$ \\
SF-TD-BH\&HLYP\fnm[3] & $0.048$ & $1.282$ & $1.465$ \\
SF-CIS\fnm[1] & $0.317$ & $3.125$ & $2.650$ \\
EOM-SF-CCSD\fnm[1] & $0.369$ & $1.824$ & $2.143$ \\
EOM-SF-CCSD(fT)\fnm[1] & $0.163$ & $1.530$ & $1.921$ \\
EOM-SF-CCSD(dT)\fnm[1] & $0.098$ & $1.456$ & $1.853$ \\
SF-ADC(2)-s\fnm[2] & $0.266$ & $1.664$ & $1.910$ \\
SF-ADC(2)-x\fnm[2] & $0.217$ & $1.123$ & $1.799$ \\
SF-ADC(3)\fnm[2] & $0.083$ & $1.621$ & $1.930$ \\
SF-BSE@{\GOWO}\fnm[3] & $-0.049$ & $1.189$ & $1.480$ \\
SF-dBSE@{\GOWO}\fnm[3] & $0.012$ & $1.507$ & $1.841$ \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Spin-flip EOM-CC value from Ref.~\onlinecite{Manohar_2008}.}