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Pierre-Francois Loos 2020-06-05 14:43:10 +02:00
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@ -511,6 +511,14 @@ As a result, BSE singlet excitation energies starting from such improved quasipa
For sake of illustration, an average error of $0.2$ eV was found for the well-known Thiel set \cite{Schreiber_2008} gathering more than hundred representative singlet excitations from a large variety of representative molecules. \cite{Jacquemin_2015a,Bruneval_2015,Gui_2018,Krause_2017} For sake of illustration, an average error of $0.2$ eV was found for the well-known Thiel set \cite{Schreiber_2008} gathering more than hundred representative singlet excitations from a large variety of representative molecules. \cite{Jacquemin_2015a,Bruneval_2015,Gui_2018,Krause_2017}
This is equivalent to the best TD-DFT results obtained by scanning a large variety of global hybrid functionals with various amounts of exact exchange. This is equivalent to the best TD-DFT results obtained by scanning a large variety of global hybrid functionals with various amounts of exact exchange.
%%% FIG 3 %%%
\begin{figure}
\includegraphics[width=6cm]{CTfig}
\caption{
Symbolic representation of (Top) extended Wannier exciton with large electron-hole average distance, and (Bottom) Frenkel and charge-transfer (CT) excitations at a donor-acceptor interface. Wannier and CT excitations require long-range electron-hole interaction accounting for the dielectric constant of the host. In the case of Wannier exciton, the binding energy $E_B$ can be well approximated by the standard hydrogenoid model with $\mu$ the effective mass and $\epsilon$ the dielectric constant.
\label{fig:CTfig}}
\end{figure}
%%% %%% %%%
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\section{Successes \& Challenges} \section{Successes \& Challenges}
@ -520,8 +528,8 @@ This is equivalent to the best TD-DFT results obtained by scanning a large varie
%========================================== %==========================================
\subsection{Charge-transfer excited states} \subsection{Charge-transfer excited states}
%========================================== %==========================================
A very remarkable success of the BSE formalism lies in the description of the charge-transfer (CT) excitations, a notoriously difficult problem for TD-DFT calculations adopting standard functionals. \cite{Dreuw_2004} A very remarkable success of the BSE formalism lies in the description of charge-transfer (CT) excitations, a notoriously difficult problem for TD-DFT adopting standard (semi-)local or hybrid functionals. \cite{Dreuw_2004}
Similar difficulties emerge in solid-state physics for semiconductors where extended Wannier excitons, characterized by weakly overlapping electrons and holes, cause a dramatic deficit of spectral weight at low energy. \cite{Botti_2004} Similar difficulties emerge in solid-state physics for semiconductors where extended Wannier excitons, characterized by weakly overlapping electrons and holes (Fig.~\ref{fig:CTfig}), cause a dramatic deficit of spectral weight at low energy. \cite{Botti_2004}
These difficulties can be ascribed to the lack of long-range electron-hole interaction with local xc functionals. These difficulties can be ascribed to the lack of long-range electron-hole interaction with local xc functionals.
It can be cured through an exact exchange contribution, a solution that explains in particular the success of optimally-tuned range-separated hybrids for the description of CT excitations. \cite{Stein_2009,Kronik_2012} It can be cured through an exact exchange contribution, a solution that explains in particular the success of optimally-tuned range-separated hybrids for the description of CT excitations. \cite{Stein_2009,Kronik_2012}
The analysis of the screened Coulomb potential matrix elements in the BSE kernel [see Eq.~\eqref{eq:BSEkernel}] reveals that such long-range (non-local) electron-hole interactions are properly described, including in environments (solvents, molecular solid, etc) where screening reduces the long-range electron-hole interactions. The analysis of the screened Coulomb potential matrix elements in the BSE kernel [see Eq.~\eqref{eq:BSEkernel}] reveals that such long-range (non-local) electron-hole interactions are properly described, including in environments (solvents, molecular solid, etc) where screening reduces the long-range electron-hole interactions.

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