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Pierre-Francois Loos 2020-07-20 22:04:50 +02:00
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dynker.tex
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@ -639,17 +639,17 @@ In the case of BSE2, the perturbative partitioning is simply
}
\begin{ruledtabular}
\begin{tabular}{|c|ccccccc|c|}
Singlets & BSE2 & pBSE2 & pBSE2(dTDA) & dBSE2 & BSE2(TDA) & pBSE2(TDA) & dBSE2(TDA) & Exact \\
Singlets & BSE2 & pBSE2 & pBSE2(dTDA) & dBSE2 & BSE2(TDA) & pBSE2(TDA) & dBSE2(TDA) & Exact \\
\hline
$\omega_1$ & 1.84903 & 1.90940 & 1.90950 & 1.90362 & 1.86299 & 1.92356 & 1.92359 & 1.92145 \\
$\omega_2$ & & & & & & & & \\
$\omega_3$ & & & & 4.47124 & & & 4.47097 & 3.47880 \\
$\omega_1^{\updw}$ & 1.84903 & 1.90940 & 1.90950 & 1.90362 & 1.86299 & 1.92356 & 1.92359 & 1.92145 \\
$\omega_2^{\updw}$ & & & & & & & & \\
$\omega_3^{\updw}$ & & & & 4.47124 & & & 4.47097 & 3.47880 \\
\hline
Triplets & BSE2 & pBSE2 & pBSE2(dTDA) & dBSE2 & BSE2(TDA) & pBSE2(TDA) & dBSE2(TDA) & Exact \\
Triplets & BSE2 & pBSE2 & pBSE2(dTDA) & dBSE2 & BSE2(TDA) & pBSE2(TDA) & dBSE2(TDA) & Exact \\
\hline
$\omega_1$ & 1.38912 & 1.44285 & 1.44304 & 1.42564 & 1.40765 & 1.46154 & 1.46155 & 1.47085 \\
$\omega_2$ & & & & & & & & \\
$\omega_3$ & & & & 4.47797 & & & 4.47767 & \\
$\omega_1^{\upup}$ & 1.38912 & 1.44285 & 1.44304 & 1.42564 & 1.40765 & 1.46154 & 1.46155 & 1.47085 \\
$\omega_2^{\upup}$ & & & & & & & & \\
$\omega_3^{\upup}$ & & & & 4.47797 & & & 4.47767 & \\
\end{tabular}
\end{ruledtabular}
\end{table*}
@ -720,9 +720,13 @@ For the double excitation, dBSE2 yields a slightly better energy, yet still in q
%\end{gather}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Take-home messages}
\section{Take-home message}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
What have we learned here?
The take-home message of the present paper is that dynamical kernels have much more to give that one would think.
In more scientific terms, dynamical kernels can provide, thanks to their frequency-dependent nature, additional excitations that can be associated to higher-order excitations (such as the infamous double excitations).
However, they sometimes give too much, and generate spurious excitations, \ie, excitation which does not corresponds to any physical excited state.
The appearance of these factitious excitations is due to the approximate nature of the dynamical kernel.
Moreover, because of the non-linear character of the linear response problem when one employs a dynamical kernel, it is computationally more involved to access these extra excitations.
%%%%%%%%%%%%%%%%%%%%%%%%
\acknowledgements{