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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.
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:
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.
@ -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.
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.)
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.
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 $B_{1g}$.
So here we have an example where the dynamical corrections are necessary to get the right state ordering.
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 the dynamical correction in SF-dBSE@{\GOWO} not only improves the agreement with SF-ADC(3) but also retrieves 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 %%%
\begin{figure*}