add Hugh references
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%Control: page (0) single
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%Control: year (1) truncated
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\begin{thebibliography}{113}%
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\begin{thebibliography}{116}%
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\makeatletter
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\providecommand \@ifxundefined [1]{%
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\@ifx{#1\undefined}
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@ -587,6 +587,12 @@
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{Kryachko}}}\ (\bibinfo {publisher} {Kluwer Academic},\ \bibinfo {address}
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{Dordrecht},\ \bibinfo {year} {2003})\ p.~\bibinfo {pages} {67}\BibitemShut
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{NoStop}%
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\bibitem [{\citenamefont {Slater}(1951)}]{Slater_1951}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~C.}\ \bibnamefont
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{Slater}},\ }\href {\doibase 10.1103/PhysRev.82.538} {\bibfield {journal}
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{\bibinfo {journal} {Phys. Rev.}\ }\textbf {\bibinfo {volume} {82}},\
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\bibinfo {pages} {538} (\bibinfo {year} {1951})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Coulson}\ and\ \citenamefont
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{Fischer}(1949)}]{Coulson_1949}%
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\BibitemOpen
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@ -610,6 +616,22 @@
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont
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{Fukutome}},\ }\href {\doibase 10.1002/qua.560200502} {\ \textbf {\bibinfo
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{volume} {20}},\ \bibinfo {pages} {955}}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Roothaan}(1951)}]{Roothaan_1951}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {C.~C.~J.}\
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\bibnamefont {Roothaan}},\ }\href {\doibase 10.1103/RevModPhys.23.69}
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{\bibfield {journal} {\bibinfo {journal} {Rev. Mod. Phys.}\ }\textbf
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{\bibinfo {volume} {23}},\ \bibinfo {pages} {69} (\bibinfo {year}
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{1951})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Hall}\ and\ \citenamefont
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{Lennard-Jones}(1951)}]{Hall_1951}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {G.~G.}\ \bibnamefont
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{Hall}}\ and\ \bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
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{Lennard-Jones}},\ }\href {\doibase 10.1098/rspa.1951.0048} {\bibfield
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{journal} {\bibinfo {journal} {Proc. R. Soc. Lond. A}\ }\textbf {\bibinfo
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{volume} {205}},\ \bibinfo {pages} {541} (\bibinfo {year}
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{1951})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Hiscock}\ and\ \citenamefont
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{Thom}(2014)}]{Hiscock_2014}%
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\BibitemOpen
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@ -1,13 +1,53 @@
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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2020-11-23 11:07:33 +0100
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%% Created for Pierre-Francois Loos at 2020-11-24 09:46:03 +0100
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%% Saved with string encoding Unicode (UTF-8)
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@article{Hall_1951,
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abstract = { An analysis of the `linear combination of atomic orbitals' approximation using the accurate molecular orbital equations shows that it does not lead to equations of the form usually assumed in the semi-empirical molecular orbital method. A new semi-empirical method is proposed, therefore, in terms of equivalent orbitals. The equations obtained, which do have the usual form, are applicable to a large class of molecules and do not involve the approximations that were thought necessary. In this method the ionization potentials are calculated by treating certain integrals as semi-empirical parameters. The value of these parameters is discussed in terms of the localization of equivalent orbitals and some approximate rules are suggested. As an illustration the ionization potentials of the paraffin series are considered and good agreement between the observed and calculated values is found. },
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author = {Hall, G. G. and Lennard-Jones, John Edward},
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date-added = {2020-11-24 09:45:15 +0100},
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date-modified = {2020-11-24 09:45:50 +0100},
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doi = {10.1098/rspa.1951.0048},
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journal = {Proc. R. Soc. Lond. A},
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pages = {541-552},
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title = {The molecular orbital theory of chemical valency VIII. A method of calculating ionization potentials},
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volume = {205},
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year = {1951},
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Bdsk-Url-1 = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1951.0048},
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Bdsk-Url-2 = {https://doi.org/10.1098/rspa.1951.0048}}
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@article{Roothaan_1951,
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author = {Roothaan, C. C. J.},
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date-added = {2020-11-24 09:43:57 +0100},
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date-modified = {2020-11-24 09:44:09 +0100},
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doi = {10.1103/RevModPhys.23.69},
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journal = {Rev. Mod. Phys.},
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pages = {69--89},
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title = {New Developments in Molecular Orbital Theory},
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volume = {23},
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year = {1951},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/RevModPhys.23.69},
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Bdsk-Url-2 = {https://doi.org/10.1103/RevModPhys.23.69}}
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@article{Slater_1951,
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author = {Slater, J. C.},
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date-added = {2020-11-24 09:42:40 +0100},
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date-modified = {2020-11-24 09:42:58 +0100},
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doi = {10.1103/PhysRev.82.538},
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journal = {Phys. Rev.},
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pages = {538--541},
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title = {Magnetic Effects and the Hartree-Fock Equation},
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volume = {82},
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year = {1951},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.82.538},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRev.82.538}}
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@article{Loos_2019d,
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author = {P. F. Loos and B. Pradines and A. Scemama and J. Toulouse and E. Giner},
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date-added = {2020-11-23 11:07:32 +0100},
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@ -124,7 +124,7 @@
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\newcommand{\UOX}{Physical and Theoretical Chemical Laboratory, Department of Chemistry, University of Oxford, Oxford, OX1 3QZ, U.K.}
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\begin{document}
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\title{Perturbation theory in the complex plane: Exceptional points and where to find them}
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\title{Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them}
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\author{Antoine \surname{Marie}}
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\affiliation{\LCPQ}
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@ -574,7 +574,7 @@ between the two closed-shell configurations with both electrons localised on one
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% INTRODUCE PARAMETRISED FOCK HAMILTONIAN
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The inherent non-linearity in the Fock eigenvalue problem arises from self-consistency
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in the HF approximation, and is usually solved through an iterative approach.\cite{Roothaan1951,Hall1951}
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in the HF approximation, and is usually solved through an iterative approach.\cite{Roothaan_1951,Hall_1951}
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Alternatively, the non-linear terms arising from the Coulomb and exchange operators can
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be considered as a perturbation from the core Hamiltonian \eqref{eq:Hcore} by introducing the
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transformation $U \rightarrow \lambda\, U$, giving the parametrised Fock operator
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