From 5153f6fdac7bbcc712bc98379d7b18009c908a91 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Sat, 5 Dec 2020 15:08:17 +0100 Subject: [PATCH] OK with III --- Manuscript/EPAWTFT.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index 9c3727b..7b8e1f2 100644 --- a/Manuscript/EPAWTFT.tex +++ b/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.