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@ -639,14 +639,6 @@ via a stationary path of HF solutions.
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This novel approach to identifying excited-state wave functions demonstrates the fundamental
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This novel approach to identifying excited-state wave functions demonstrates the fundamental
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role of \textit{quasi}-EPs in determining the behaviour of the HF approximation.
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role of \textit{quasi}-EPs in determining the behaviour of the HF approximation.
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%\titou{In a recent paper, \cite{Burton_2019} using holomorphic Hartree--Fock (h-HF) \cite{Hiscock_2014,Burton_2018,Burton_2016} as an analytic continuation of conventional HF theory, we have demonstrated, on a simple model, that one can interconvert states of different symmetries and natures by following well-defined contours in the complex $\lambda$-plane, where $\lambda$ is the strength of the electron-electron interaction (see Fig.~\ref{fig:iAC}).
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%In particular, by slowly varying $\lambda$ in a similar (yet different) manner to an adiabatic connection in density-functional theory, \cite{Langreth_1975,Gunnarsson_1976,Zhang_2004} one can ``morph'' a ground-state wave function into an excited-state wave function via a stationary path of HF solutions. \cite{Seidl_2018}
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%In such a way, we could obtain a doubly-excited state wave function starting from the ground state wave function, a process which is not as easy as one might think. \cite{Gilbert_2008,Thom_2008,Shea_2018}
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%One of the fundamental discovery we made was that Coulson-Fischer points (where multiple symmetry-broken solutions coalesce) play a central role and can be classified as \textit{quasi}-exceptional points, as the wave functions do not become self-orthogonal.
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%The findings reported in Ref.~\onlinecite{Burton_2019} represent the very first study of non-Hermitian quantum mechanics for the exploration of multiple solutions at the HF level.
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%It perfectly illustrates the deeper topology of electronic states revealed using a complex-scaled electron-electron interaction.
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%Through the introduction of non-Hermiticity, we have provided a more general framework in which the complex and diverse characteristics of multiple solutions can be explored and understood.}
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\section{M{\o}ller--Plesset Perturbation Theory in the Complex Plane}
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\section{M{\o}ller--Plesset Perturbation Theory in the Complex Plane}
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\label{sec:MP}
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\label{sec:MP}
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