diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index 444451f..604c3f6 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -142,7 +142,7 @@ In this review, we explore the extension of quantum chemistry in the complex plane and its link with perturbation theory. We observe that the physics of a quantum system is intimately connected to the position of energy singularities in the complex plane, known as exceptionnal points. After a presentation of the fundamental notions of quantum chemistry in the complex plane, such as the mean-field Hartree-Fock approximation and Rayleigh-Schr\"odinger perturbation theory, and their illustration with the ubiquitous (symmetric) Hubbard dimer at half filling, we provide a historical overview of the various research activities that have been performed on the physics of singularities. -In particular, we highlight the seminal work of several research groups on the convergence behaviour of perturbative series obtained within M{\o}ller-Plesset perturbation theory and its apparent link with quantum phase transitions. +In particular, we highlight the seminal work of several research groups on the convergence behaviour of perturbative series obtained within M{\o}ller--Plesset perturbation theory and its apparent link with quantum phase transitions. \end{abstract} \maketitle @@ -629,7 +629,7 @@ role of \textit{quasi}-EPs in determining the behaviour of the HF approximation. %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.} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{M{\o}ller-Plesset Perturbation Theory in the Complex Plane} +\section{M{\o}ller--Plesset Perturbation Theory in the Complex Plane} \label{sec:MP} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -706,7 +706,7 @@ their relative strengths and weaknesses for various situations, we will restrict to the convergence properties of the MP expansion. %=====================================================% -\subsection{Early Investigations into M{\o}ller-Plesset Convergence} % in Molecular Systems} +\subsection{Early Investigations into M{\o}ller--Plesset Convergence} % in Molecular Systems} %=====================================================% % GENERAL DESIRE FOR WELL-BEHAVED CONVERGENCE AND LOW-ORDER TERMS