Clean up Sec. IV and new fig 1

Manuscript/eDFT.tex

@@ -1080,27 +1080,23 @@ We use as basis functions the (orthonormal) orbitals of the one-electron system,
 	\end{cases}
 \end{equation} 
 with $ \mu = 1,\ldots,\nBas$ and $\nBas = 30$ for all calculations.
-\manu{The convergence threshold $\tau = \max{ \abs{ \bF{\bw} \bGam{\bw}
+The convergence threshold $\tau = \max{ \abs{ \bF{\bw} \bGam{\bw}
 \bS - \bS \bGam{\bw} \bF{\bw}}}$ [see Eq.~(\ref{eq:commut_F_AO})] is set
 to $10^{-5}$. For comparison, regular HF and KS-DFT calculations 
 are performed with the same threshold.
 In order to compute the various density-functional
 integrals that cannot be performed in closed form, 
-a 51-point Gauss-Legendre quadrature is employed.}
+a 51-point Gauss-Legendre quadrature is employed.
 
 In order to test the present eLDA functional we perform various sets of calculations.
 To get reference excitation energies for both the single and double excitations, we compute full configuration interaction (FCI) energies with the Knowles-Handy FCI program described in Ref.~\onlinecite{Knowles_1989}.
 For the single excitations, we also perform time-dependent LDA (TDLDA)
-calculations [\ie, TDDFT with the LDA functional defined in
-Eq.~\eqref{eq:LDA}], and the effect of the Tamm-Dancoff approximation
-(TDA) has been also investigated. \cite{Dreuw_2005}\manu{Manu: has been
-studied previously (if so why do you mention this?) or will be discussed
-in the present work?}
-Concerning the \manu{ensemble}
-%KS-eDFT and eHF
-calculations, two sets of weight are tested: the zero-weight
-\manu{(ground-state)} limit where $\bw = (0,0)$ and the
-equi\manu{-tri}-ensemble (or \manu{equal-weight} state-averaged) limit where $\bw = (1/3,1/3)$.
+calculations [\ie, TDDFT with the LDA functional defined in Eq.~\eqref{eq:LDA}]. 
+\titou{Its Tamm-Dancoff approximation (TDA) version is also considered.} \cite{Dreuw_2005}
+
+Concerning the ensemble calculations, two sets of weight are tested: the zero-weight
+(ground-state) limit where $\bw = (0,0)$ and the
+equi-tri-ensemble (or equal-weight state-averaged) limit where $\bw = (1/3,1/3)$.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Results and discussion}