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%% Sample TeX file for the HRMS Dijon 2023 abstracts
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\documentclass[11pt]{article}

\usepackage{hrms}  %% Page settings, style ... for the HRMS abstract book.
\usepackage[width=1\textwidth,labelfont={bf,footnotesize},textfont=footnotesize]{caption}
\usepackage{epsfig,graphics,wrapfig}
\usepackage{relsize}
\usepackage{amsmath}

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\title{VARIATIONAL DIRAC--COULOMB APPROACH WITH EXPLICITLY CORRELATED  BASIS FUNCTIONS}

%% Note that \author and \address macros must be paired.
%% The names of authors must also appear IN CAPITALS.
%% The name(s) of author(s) presenting the work is(are) usually underlined.
\author{\underline{\FirstName P. \LastName JESZENSZKI} and \FirstName E. \LastName M{\'A}TYUS}
\address{\\ELTE,~E{\"o}tv{\"o}s~Lor{\'a}nd~University, Institute~of~Chemistry, Budapest, Hungary}

%% The \FirstName and \LastName macros are mandatory for each author
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\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhead[C]{{\footnotesize \textit{HRMS, 28th Colloquium, Dijon, France,
  Aug. 28 - Sept. 1, 2023}}}
\fancyfoot[C]{}
\renewcommand{\headrulewidth}{0.6pt}
\renewcommand{\footrulewidth}{0.6pt}

%% The hyperref package allows to include hyperlinks in a document.
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\usepackage[colorlinks=true,urlcolor=blue,linkcolor=blue,citecolor=blue]{hyperref}
\voffset -.65 cm

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\begin{document}

\maketitle  %% This will also build the list of author(s) and addresse(s).

% Abstract
\noindent
The no-pair Dirac--Coulomb(--Breit) equation is solved with high-accuracy \cite{allorder,DiracCoulomb,Breit,Breit2,LScoupling,twopart} to provide a starting point for a new alternative theoretical method in relation with high-resolution atomic and molecular spectroscopy \cite{QEDcorr}. The sub-parts-per-billion convergence of the energy is achieved by considering the relativistic symmetry with an $LS$ coupling scheme and expanding the relativistic wave function with an explicitly correlated Gaussian (ECG) basis set. The ECG significantly improves the description of the electron correlation compared to {\it e.g.,} a determinant basis set, but the positive-energy projection is more complicated due to the lack of the underlying one-electron picture. Therefore, several positive-energy projectors are examined to achieve and justify the parts-per-billion convergence of the energy. The no-pair Dirac--Coulomb energy is compared with perturbative results for atomic and molecular systems with small nuclear charge numbers and it reproduces the perturbative expressions \cite{SucherPHD} up to $\alpha^3 E_\text{h}$ order.
\vspace{6pt}

\vspace{12pt}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=8cm]{CCRtwoe.pdf}
\caption{Visualization of the complex scaling technique to select the positive-energy states of the non-interacting two-electron system: unbound two-particle energies for $\theta=0$ (solid) and for some finite $\theta>0$ (dashed) value. 
    %
    The red, green, and blue colors indicate the electron-electron, electron-positron (or Brown--Ravenhall), and positron-positron states, respectively.}
\end{center}
\end{figure}
%% Index macro(s): see the abstract samples and the instructions
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\enlargethispage{1cm}

%\vspace{-0.5cm}
\begin{thebibliography}{9.}
%\frenchspacing
\setlength{\itemsep}{0em}
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\bibitem{allorder}
P. Jeszenszki, D. Ferenc, and E. Mátyus, \href{https://aip.scitation.org/doi/10.1063/5.0051237}{\textit{J. Chem. Phys.}} (2021), \textbf{154}, 224110. %\href{https://arxiv.org/abs/2103.04923}{arXiv}

\bibitem{DiracCoulomb}
P. Jeszenszki, D. Ferenc, and E. Mátyus, 
\href{https://aip.scitation.org/doi/abs/10.1063/5.0075096}{\textit{J. Chem. Phys.}} (2022), \textbf{156}, 084111.
%\href{https://arxiv.org/abs/2110.06638}{arXiv}

\bibitem{Breit}
D. Ferenc, P. Jeszenszki, and E. Mátyus, \href{https://aip.scitation.org/doi/abs/10.1063/5.0075097}{\textit{J. Chem. Phys.}} (2022), \textbf{156}, 084110. %\href{https://arxiv.org/abs/2110.06647}{arXiv}

\bibitem{Breit2}
D. Ferenc, P. Jeszenszki, and E. M{\'a}tyus, \href{https://doi.org/10.1063/5.0105355
}{\textit{J. Chem. Phys.}} \textbf{157}, 094113 (2022). 

\bibitem{LScoupling}
P. Jeszenszki and E. M{\'a}tyus, \href{https://doi.org/10.1063/5.0136360}{\textit{J. Chem. Phys.}} \textbf{158}, 054104 (2023). 

\bibitem{twopart}
D. Ferenc and E. M{\'a}tyus, \href{https://doi.org/10.1103/PhysRevA.107.052803}{\textit{Phys. Rev. A.}} \textbf{107}, 052803 (2023).

\bibitem{QEDcorr}
E. M{\'a}tyus, D. Ferenc, P. Jeszenszki, {\'A}. Marg{\'o}csy, \href{https://doi.org/10.1021/acsphyschemau.2c00062}{\emph{ACS Phys. Chem. Au}} \textbf{3}, 222 (2023).

\bibitem{SucherPHD}
J. Sucher, \textit{Ph. D. Thesis} (1958), Columbia University.
 
\end{thebibliography}


\end{document}
