new fig

Manuscript/BSE_JPCL.tex

@@ -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} 
 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} 
+%%% %%% %%%
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \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} 
 %==========================================
-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} 
-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} 
+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 (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.
 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.