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OK up to Sec IIIc

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Pierre-Francois Loos 2020-12-05 14:27:40 +01:00
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@ -299,7 +299,7 @@ unless otherwise stated, atomic units will be used throughout.
\label{fig:FCI}}
\end{figure*}
To illustrate the concepts discussed throughout this article, we consider the symmetric Hubbard dimer at half filling, \ie\ with two opposite-spin fermions.
To illustrate the concepts discussed throughout this article, we consider the symmetric Hubbard dimer at half filling, \ie, with two opposite-spin fermions.
Analytically solvable models are essential in theoretical chemistry and physics as their mathematical simplicity compared to realistic systems (e.g., atoms and molecules) allows new concepts and methods to be
easily tested while retaining the key physical phenomena.
@ -730,7 +730,7 @@ unrestricted reference orbitals.
Although practically convenient for electronic structure calculations, the MP partitioning is not
the only possibility and alternative partitionings have been considered including:
i) the Epstein-Nesbet (EN) partitioning which consists in taking the diagonal elements of $\hH$ as the zeroth-order Hamiltonian. \cite{Nesbet_1955,Epstein_1926}
i) the Epstein-Nesbet (EN) partitioning which consists in taking the diagonal elements of $\hH$ as the zeroth-order Hamiltonian, \cite{Nesbet_1955,Epstein_1926}
ii) the weak correlation partitioning in which the one-electron part is consider as the unperturbed Hamiltonian $\hH^{(0)}$ and the two-electron part is the perturbation operator $\hV$, and
iii) the strong coupling partitioning where the two operators are inverted compared to the weak correlation partitioning. \cite{Seidl_2018}
While an in-depth comparison of these different approaches can offer insight into
@ -770,7 +770,7 @@ The divergence of RMP expansions for stretched bonds can be easily understood fr
Firstly, the exact wave function becomes increasingly multi-configurational as the bond is stretched, and the
RHF wave function no longer provides a qualitatively correct reference for the perturbation expansion.
Secondly, the energy gap between the bonding and antibonding orbitals associated with the stretch becomes
increasingly small at larger bond lengths, leading to a divergence, for example, in the second-order MP correction \eqref{eq:EMP2}.
increasingly small at larger bond lengths, leading to a divergence, for example, in the \trash{second-order MP} \titou{MP2} correction \eqref{eq:EMP2}.
In contrast, the origin of slow UMP convergence is less obvious as the reference UHF energy remains
qualitatively correct at large bond lengths and the orbital degeneracy is avoided.
Furthermore, this slow convergence can also be observed in molecules with a UHF ground state at the equilibrium