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Pierre-Francois Loos 2020-12-05 15:08:17 +01:00
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@ -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, In contrast, smaller $\epsilon$ gives a weaker attraction to the atomic site,
representing strong screening of the nuclear attraction by core and valence electrons, representing strong screening of the nuclear attraction by core and valence electrons,
and again a less negative $\lambda$ is required for ionisation to occur. 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}. \ce{O}, \ce{Ne}.
Molecules containing these atoms are therefore often class $\beta$ systems with 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} 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 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 Hamiltonian displayed in Eq.~\eqref{eq:HamiltonianStillinger}, while the explicit electron-electron interaction
becomes increasingly repulsive. 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 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. 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. 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.