minor corrections of XB stuff

BSEdyn.tex

@@ -207,10 +207,8 @@
 \begin{abstract}
 Similar to the ubiquitous adiabatic approximation in time-dependent density-functional theory, the static approximation, which substitutes a dynamical (\ie, frequency-dependent) kernel by its static limit, is usually enforced in most implementations of the Bethe-Salpeter equation (BSE) formalism.
 Here, going beyond the static approximation, we compute the dynamical correction in the electron-hole screening for molecular excitation energies thanks to a renormalized first-order perturbative correction to the static BSE excitation energies.
-The present dynamical correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly within the random phase approximation. \xavier{
-\sout{Moreover, we investigate quantitatively the effect of the Tamm-Dancoff approximation by computing both the resonant and anti-resonant dynamical corrections to the BSE excitation energies.}
-Our calculations are benchmarked against high-level (coupled-cluster) calculations, allowing to assess the clear improvements induced by dynamical corrections. }
-%\\
+The present dynamical correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly within the random phase approximation.
+Our calculations are benchmarked against high-level (coupled-cluster) calculations, allowing to assess the clear improvements brought by dynamical corrections.
 %\bigskip
 %\begin{center}
 %	\boxed{\includegraphics[width=0.5\linewidth]{TOC}}
@@ -461,8 +459,8 @@ is an effective dynamically-screened Coulomb potential, \cite{Romaniello_2009b}
 	 = \iint d\br d\br' \, \MO{i}(\br) \MO{j}^*(\br) W(\br ,\br'; \omega) \MO{a}^*(\br') \MO{b}(\br').
 \end{equation}
 
-\xavier{\sout{ A second coupled equation for the $(X_{ia}^{s}, Y_{ia}^{s} )$ vector can be obtained by projecting $\mel{N}{T [ \hpsi(\bx_1) \hpsi^{\dagger}(\bx_{1}') ] } {N,s}$ and $L_0(\bx_1,4;\bx_{1'},3; \Om{s}{})$ onto $\MO{i}^*(\bx_1) \MO{a}(\bx_{1'})$ instead of
-$\MO{a}^*(\bx_1) \MO{i}(\bx_{1'})$. } }
+%\xavier{\sout{ A second coupled equation for the $(X_{ia}^{s}, Y_{ia}^{s} )$ vector can be obtained by projecting $\mel{N}{T [ \hpsi(\bx_1) \hpsi^{\dagger}(\bx_{1}') ] } {N,s}$ and $L_0(\bx_1,4;\bx_{1'},3; \Om{s}{})$ onto $\MO{i}^*(\bx_1) \MO{a}(\bx_{1'})$ instead of
+%$\MO{a}^*(\bx_1) \MO{i}(\bx_{1'})$. } }
 
 
 %================================
@@ -1151,10 +1149,8 @@ We now act on the N-electron ground-state with
       e^{ -i{\hat H} \tau_{65} } {\hat a}_q | N \rangle &=
     e^{-i ( E^N_0 - \varepsilon_q ) \tau_{65} } | N \rangle
   \end{align*}
-  where $\lbrace \varepsilon_{p/q} \rbrace$ are quasiparticle energies, such as the $GW$ ones, namely proper addition/removal energies. Taking the associated  bras that we plug into the MOs product basis expansion of $\langle N | T [\hpsi(6) & \hpsi^{\dagger}(5)] | N,s \rangle $  one obtains Eq.~\ref{eq:spectral65}. \\
-  
-  \center{ \rule{3cm}{1} }
-  
+  where $\lbrace \varepsilon_{p/q} \rbrace$ are quasiparticle energies, such as the $GW$ ones, namely proper addition/removal energies. Taking the associated  bras that we plug into the MOs product basis expansion of $\langle N | T [\hpsi(6) \hpsi^{\dagger}(5)] | N,s \rangle $  one obtains Eq.~\ref{eq:spectral65}. \\
+   
 \bibliography{BSEdyn}
 
 \end{document}