OK with III

Manuscript/EPAWTFT.tex

@@ -1266,7 +1266,7 @@ Large $U$ can be physically interpreted as strong electron repulsion effects in
 In contrast, smaller $\epsilon$ gives a weaker attraction to the atomic site, 
 representing strong screening of the nuclear attraction by core and valence electrons, 
 and again a less negative $\lambda$ is required for ionisation to occur.
-Both of these factors are common in atoms on the right-hand side of the periodic table, \eg\ \ce{F},
+Both of these factors are common in atoms on the right-hand side of the periodic table, \eg, \ce{F},
 \ce{O}, \ce{Ne}.
 Molecules containing these atoms are therefore often class $\beta$ systems with
 a divergent RMP series due to the MP critical point. \cite{Goodson_2004,Sergeev_2006} 
@@ -1324,9 +1324,9 @@ connection to MP critical points and QPTs (see Sec.~\ref{sec:MP_critical_point})
 For $\lambda>1$, the HF potential becomes an attractive component in Stillinger's 
 Hamiltonian displayed in Eq.~\eqref{eq:HamiltonianStillinger}, while the explicit electron-electron interaction
 becomes increasingly repulsive.
-Closed--shell critical points along the positive real $\lambda$ axis then represent 
+Closed-shell critical points along the positive real $\lambda$ axis then represent 
 points where the two-electron repulsion overcomes the attractive HF potential 
-and a single electron dissociates from the molecule (see Ref.~\onlinecite{Sergeev_2006})
+and a single electron dissociates from the molecule (see Ref.~\onlinecite{Sergeev_2006}).
 
 In contrast, symmetry-breaking in the UMP reference creates different HF potentials for the spin-up and spin-down electrons.
 Consider one of the two reference UHF solutions where the spin-up and spin-down electrons are localised on the left and right sites respectively.