diff --git a/Manuscript/sfBSE.tex b/Manuscript/sfBSE.tex index 243ed36..3bf1459 100644 --- a/Manuscript/sfBSE.tex +++ b/Manuscript/sfBSE.tex @@ -713,10 +713,12 @@ A similar graph comparing (SF-)dBSE and EOM-CCSD excitation energies can be foun \includegraphics[width=0.4\linewidth]{H2_CIS} \hspace{0.05\linewidth} \includegraphics[width=0.4\linewidth]{H2_CIS_S2} + \vspace{0.025\linewidth} \\ \includegraphics[width=0.4\linewidth]{H2_BHHLYP} \hspace{0.05\linewidth} \includegraphics[width=0.4\linewidth]{H2_BHHLYP_S2} + \vspace{0.025\linewidth} \\ \includegraphics[width=0.4\linewidth]{H2_BSE} \hspace{0.05\linewidth} @@ -842,7 +844,12 @@ Then, CBD stands as an excellent example for which dynamical corrections are nec \section{Conclusion} \label{sec:ccl} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\alert{Here comes the conclusion.} +In this article, we have presented the extension of the BSE approach of many-body perturbation theory to the spin-flip formalism in order to access double excitations in realistic molecular systems. +The present spin-flip calculations rely on a spin-unrestricted version of the $GW$ approximation and the BSE formalism with, on top of this, a dynamical correction to the static BSE optical excitations via an unrestricted generalization of our recently developed renormalized perturbative treatment. +Taking the beryllium atom, the dissociation of the hydrogen molecule, and cyclobutadiene in two different geometries as examples, we have shown that the spin-flip BSE formalism can accurately model double excitations and seems to surpass systematically its spin-flip TD-DFT parent. +Further improvements could be obtained thanks to a better choice of the starting orbitals and their energies and we hope to investigate this in a forthcoming paper. +Techniques to alleviate the spin contamination in spin-flip calculations will also be explored in the near future. +We hope to these new encouraging results will stimulate new developments around the BSE formalism to further establish it as a valuable \text{ab inito} alternative to TD-DFT for the study of molecular excited states. %%%%%%%%%%%%%%%%%%%%%%%% \acknowledgements{