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Pierre-Francois Loos 2020-07-23 09:58:52 +02:00
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BSEdyn.tex
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@ -1108,11 +1108,11 @@ These will be our reference as they are known to be extremely accurate ($0.03$--
Errors associated with these excitation energies (with respect to CC3) are represented in Fig.~\ref{fig:SiTr-BigMol}. Errors associated with these excitation energies (with respect to CC3) are represented in Fig.~\ref{fig:SiTr-BigMol}.
As expected the static BSE excitation energies are much more accurate for these larger molecules with a MAE of $0.32$ eV, a MSE of $0.30$ eV, and a RMSE of $0.38$ eV. As expected the static BSE excitation energies are much more accurate for these larger molecules with a MAE of $0.32$ eV, a MSE of $0.30$ eV, and a RMSE of $0.38$ eV.
Here again, the dynamical correction improves the accuracy of BSE by lowering the MAE, MSE, and RMSE to $0.23$, $0.00$, and $0.29$ eV, respectively. Here again, the dynamical correction improves the accuracy of BSE by lowering the MAE, MSE, and RMSE to $0.23$, $0.00$, and $0.29$ eV, respectively.
For these larger systems, Rydberg states are again very slightly affected by dynamical effects, while the dynamical corrections associated with the $n \ra \pis$ and $\pi \ra \pis$ transitions are much larger and of the same magnitude ($0.3$--$0.6$ eV) for both types of transitions. Rydberg states are again very slightly affected by dynamical effects, while the dynamical corrections associated with the $n \ra \pis$ and $\pi \ra \pis$ transitions are much larger and of the same magnitude ($0.3$--$0.6$ eV) for both types of transitions.
This latter observation is quite different from the outcomes reached by Rohlfing and coworkers in previous works \cite{Ma_2009a,Ma_2009b} (see Sec.~\ref{sec:intro}) where they observed i) smaller corrections (maybe due to the plasmon-pole approximation), and ii) that $n \ra \pis$ transitions are more affected by the dynamical screening than $\pi \ra \pis$ transitions. This latter observation is quite different from the outcomes reached by Rohlfing and coworkers in previous works \cite{Ma_2009a,Ma_2009b} (see Sec.~\ref{sec:intro}) where they observed i) smaller corrections (maybe due to the plasmon-pole approximation), and ii) that $n \ra \pis$ transitions are more affected by the dynamical screening than $\pi \ra \pis$ transitions.
As a final comment, let us discuss the two singlet states of butadiene reported in Table \ref{tab:BigMol}.\cite{Maitra_2004,Cave_2004,Saha_2006,Watson_2012,Shu_2017,Barca_2018a,Barca_2018b,Loos_2019} As a final comment, let us discuss the two singlet states of butadiene reported in Table \ref{tab:BigMol}.\cite{Maitra_2004,Cave_2004,Saha_2006,Watson_2012,Shu_2017,Barca_2018a,Barca_2018b,Loos_2019}
As discussed in Sec.~\ref{sec:intro}, these corresponds to a bright $^1B_u$ state with a clear single-excitation character, and a dark $^1A_g$ state including a substantial fraction of double excitation character (roughly $30\%$). As discussed in Sec.~\ref{sec:intro}, these corresponds to a bright state of $^1B_u$ symmetry with a clear single-excitation character, and a dark $^1A_g$ state including a substantial fraction of double excitation character (roughly $30\%$).
Although they are both of $\pi \ra \pis$ nature, they are very slightly altered by dynamical screening with corrections of $-0.12$ and $-0.03$ eV for the $^1B_u$ and $^1A_g$ states, respectively. Although they are both of $\pi \ra \pis$ nature, they are very slightly altered by dynamical screening with corrections of $-0.12$ and $-0.03$ eV for the $^1B_u$ and $^1A_g$ states, respectively.
The small correction on the $^1A_g$ state might be explained by its rather diffuse nature (similar to a Rydberg states). \cite{Boggio-Pasqua_2004} The small correction on the $^1A_g$ state might be explained by its rather diffuse nature (similar to a Rydberg states). \cite{Boggio-Pasqua_2004}