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Done with CBD for now

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Pierre-Francois Loos 2021-01-18 18:23:34 +01:00
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Manuscript/sfBSE.tex
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@ -737,7 +737,8 @@ EOM-CCSD and SF-ADC calculations have been taken from Refs.~\onlinecite{Manohar_
All of them have been obtained with a UHF reference like the SF-BSE calculations performed here. All of them have been obtained with a UHF reference like the SF-BSE calculations performed here.
Tables~\ref{tab:CBD_D2h} and \ref{tab:CBD_D4h} report excitation energies (with respect to the singlet ground state) obtained at the $D_{2h}$ and $D_{4h}$ geometries, respectively, for several methods using the spin-flip \textit{ansatz}. Tables~\ref{tab:CBD_D2h} and \ref{tab:CBD_D4h} report excitation energies (with respect to the singlet ground state) obtained at the $D_{2h}$ and $D_{4h}$ geometries, respectively, for several methods using the spin-flip \textit{ansatz}.
These are also represented in Fig.~\ref{fig:CBD}. For comparison purposes, we also report SF-ADC and EOM-SF-CCSD excitation energies from Ref.~\onlinecite{Lefrancois_2015} and Ref.~\onlinecite{Manohar_2008}, respectively.
All these results are represented in Fig.~\ref{fig:CBD}.
For each geometry, three excited states are under investigation: For each geometry, three excited states are under investigation:
i) the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$ and $2\,{}^1A_{g}$ states of the $D_{2h}$ geometry; i) the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$ and $2\,{}^1A_{g}$ states of the $D_{2h}$ geometry;
ii) the $1\,{}^3 A_{2g}$, $2\,{}^1 A_{1g}$ and $1\,{}^1 B_{2g}$ states of the $D_{4h}$ geometry. ii) the $1\,{}^3 A_{2g}$, $2\,{}^1 A_{1g}$ and $1\,{}^1 B_{2g}$ states of the $D_{4h}$ geometry.
@ -747,11 +748,11 @@ Comparing the present SF-BSE@{\GOWO} results for the rectangular geometry (see T
This difference grows to $0.572$ eV for the $1\,^1B_{1g}$ state and then shrinks to $0.212$ eV for the $2\,^1A_{g}$ state. This difference grows to $0.572$ eV for the $1\,^1B_{1g}$ state and then shrinks to $0.212$ eV for the $2\,^1A_{g}$ state.
Overall, adding dynamical corrections via the SF-dBSE@{\GOWO} scheme does not improve the accuracy of the excitation energies [as compared to SF-ADC(3)] with errors of $0.052$, $0.393$, and $0.293$ eV for the $1\,^3B_{1g}$, $1\,^1B_{1g}$, and $2\,^1 A_{g}$ states, respectively. Overall, adding dynamical corrections via the SF-dBSE@{\GOWO} scheme does not improve the accuracy of the excitation energies [as compared to SF-ADC(3)] with errors of $0.052$, $0.393$, and $0.293$ eV for the $1\,^3B_{1g}$, $1\,^1B_{1g}$, and $2\,^1 A_{g}$ states, respectively.
Now, looking at Table \ref{tab:CBD_D4h} which gathers the results for the square-planar geometry, we see that, at the SF-BSE@{\GOWO} level, the two first states are wrongly ordered with the triplet $1\,^3B_{1g}$ state lower than the singlet $1\,^1A_g$ state. Now, looking at Table \ref{tab:CBD_D4h} which gathers the results for the square-planar geometry, we see that, at the SF-BSE@{\GOWO} level, the first two states are wrongly ordered with the triplet $1\,^3B_{1g}$ state lower than the singlet $1\,^1A_g$ state.
(The same observation can be made at the SF-TD-B3LYP level.) (The same observation can be made at the SF-TD-B3LYP level.)
This is certainly due to the poor Hartree-Fock reference and it could be potentially alleviated by using a better starting point of the $GW$ calculation. This is certainly due to the poor Hartree-Fock reference which lacks opposite-spin correlation and it could be potentially alleviated by using a better starting point for the $GW$ calculation, as discussed in Sec.~\ref{sec:compdet}.
Nonetheless, it is pleasing to see that adding dynamical corrections in SF-dBSE@{\GOWO} not only improve the agreement in excitation energies with SF-ADC(3) but also gives the right ordering for the first excited state, meaning that we retrieve the triplet state $1\,^3A_{2g}$ above the singlet state $B_{1g}$. Nonetheless, it is pleasing to see that adding the dynamical correction in SF-dBSE@{\GOWO} not only improves the agreement with SF-ADC(3) but also retrieves the right state ordering.
So here we have an example where the dynamical corrections are necessary to get the right state ordering. Then, CBD stands as an excellent example for which dynamical corrections are necessary to get the right chemistry at the SF-BSE level.
%%% FIG 3 %%% %%% FIG 3 %%%
\begin{figure*} \begin{figure*}