diff --git a/BSE-PES.tex b/BSE-PES.tex
index d5a55c5..9e55b4d 100644
--- a/BSE-PES.tex
+++ b/BSE-PES.tex
@@ -219,11 +219,10 @@ Such a modified BSE polarization propagator was inspired by a previous study on
 With such an approximation, amounting to neglect excitonic effects in the electron-hole propagator, the question of using either KS-DFT or {\GW} eigenvalues in the construction of the propagator becomes further relevant, increasing accordingly the number of possible definitions for the ground-state correlation energy. 
 Finally, renormalizing or not the Coulomb interaction by the coupling parameter $\lambda$ in the Dyson equation for the interacting polarizability leads to two different versions of the BSE correlation energy. 
 
-\alert{Here, in analogy to the random-phase approximation (RPA) formalism,  \cite{Furche_2008} the ground-state BSE energy is calculated via the ``trace'' formula (see below). The excited-state BSE energy is then computed by adding the BSE excitation energy of the selected state to the ground-state BSE energy.
-This definition of the energy has the advantage of treating at the same level of theory the ground state and the excited states.
-Embracing this definition, the purpose of the present study is to investigate the quality of ground- and excited-state PES near equilibrium obtained within the BSE approach.
-The location of the minima on the ground- and (singlet and triplet) excited-state PES is of particular interest.
-This study is a first preliminary step towards the development of analytical nuclear gradients within the BSE@{\GW} formalism.}
+Here, in analogy to the random-phase approximation (RPA)-type formalismes, \cite{Furche_2008, Angyan_2011, Holzer_2018} the ground-state BSE energy is calculated in the adiabatic-connection fluctuation-dissipation theorem framework. 
+Embracing this definition, the purpose of the present study is to investigate the quality of ground--state PES near equilibrium obtained within the BSE approach.
+The location of the minima on the ground-state PES is of particular interest.
+This study is a first preliminary step towards the development of analytical nuclear gradients within the BSE@{\GW} formalism.
 
 %The paper is organized as follows. 
 %In Sec.~\ref{sec:theo}, we introduce the equations behind the BSE formalism.