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Pierre-Francois Loos 2020-12-01 17:22:20 +01:00
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@ -1175,7 +1175,7 @@ where we consider one of the sites as a ``ghost atom'' that acts as a
destination for ionised electrons being originally localised on the other site. destination for ionised electrons being originally localised on the other site.
To mathematically model this scenario in this asymmetric Hubbard dimer, we introduce a one-electron potential $-\epsilon$ on the left site to To mathematically model this scenario in this asymmetric Hubbard dimer, we introduce a one-electron potential $-\epsilon$ on the left site to
represent the attraction between the electrons and the model ``atomic'' nucleus [see Eq.~\eqref{eq:H_FCI}], where we define $\epsilon > 0$. represent the attraction between the electrons and the model ``atomic'' nucleus [see Eq.~\eqref{eq:H_FCI}], where we define $\epsilon > 0$.
The reference Slater determinant for a doubly-occupied atom can be represented using the RHF The reference Slater determinant for a doubly-occupied atom can be represented using RHF
orbitals [see Eq.~\eqref{eq:RHF_orbs}] with $\theta_{\alpha}^{\text{RHF}} = \theta_{\beta}^{\text{RHF}} = 0$, orbitals [see Eq.~\eqref{eq:RHF_orbs}] with $\theta_{\alpha}^{\text{RHF}} = \theta_{\beta}^{\text{RHF}} = 0$,
which corresponds to strictly localising the two electrons on the left site. which corresponds to strictly localising the two electrons on the left site.
%and energy %and energy