eHF res

Manuscript/eDFT.tex

@@ -244,7 +244,11 @@ where the KS wavefunctions fulfill the ensemble density constraint
 \eeq 
 The (approximate) description of the correlation part is discussed in Sec.~\ref{sec:eDFA}.
 
-In practice, the ensemble energy is not the most interesting quantity, and one is more concerned with excitation energies or individual energy levels (for geometry optimizations, for example). 
+In practice, the ensemble energy is not the most interesting quantity, and one is more concerned with excitation energies 
+\beq
+	\Ex{(I)} = \E{}{(I)} - \E{}{(0)},
+\eeq
+or individual energy levels (for geometry optimizations, for example). 
 The latter can be extracted exactly as follows~\cite{}
 \beq\label{eq:indiv_ener_from_ens}
 	\E{}{(I)} = \E{}{\bw} + \sum_{K>0} \qty(\delta_{IK} - \ew{K} ) \pdv{\E{}{\bw}}{\ew{K}},
@@ -908,7 +912,7 @@ Even for larger boxes, the discrepancy between FCI and eLDA for double excitatio
 \end{figure}
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-\titou{Need further discussion on DD and LZ shift. Linearity of energy wrt weights?}
+\titou{Need further discussion on DD.}
 
 \titou{For small $L$, the single and double excitations are ``pure''. In other words, the excitation is dominated by a single reference Slater determinant.
 However, when the box gets larger, there is a strong mixing between different degree of excitations.