diff --git a/Manuscript/sfBSE.tex b/Manuscript/sfBSE.tex index 317dbee..a6829cc 100644 --- a/Manuscript/sfBSE.tex +++ b/Manuscript/sfBSE.tex @@ -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*}