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@ -256,7 +256,7 @@ A central property of the one-body Green's function is that its spectral represe
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\end{equation}
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\end{equation}
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where $\mu$ is the chemical potential, $\eta$ is a positive infinitesimal, $\varepsilon_s = E_s^{N+1} - E_0^{N}$ for $\varepsilon_s > \mu$, and $\varepsilon_s = E_0^{N} - E_s^{N-1}$ for $\varepsilon_s < \mu$,
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where $\mu$ is the chemical potential, $\eta$ is a positive infinitesimal, $\varepsilon_s = E_s^{N+1} - E_0^{N}$ for $\varepsilon_s > \mu$, and $\varepsilon_s = E_0^{N} - E_s^{N-1}$ for $\varepsilon_s < \mu$,
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Here, $E_s^{N}$ is the total energy of the $s$th excited state of the $N$-electron system, and $E_0^N$ corresponds to its ground-state energy.
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Here, $E_s^{N}$ is the total energy of the $s$th excited state of the $N$-electron system, and $E_0^N$ corresponds to its ground-state energy.
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\titou{The $f_s$'s are the so-called Lehmann amplitudes that reduce to one-body orbitals in the case of single-determinant many-body wave functions [more ??].}
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The $f_s$'s are the so-called Lehmann amplitudes that reduce to one-body orbitals in the case of single-determinant many-body wave functions (see below).
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Unlike Kohn-Sham (KS) eigenvalues, the Green's function poles $\lbrace \varepsilon_s \rbrace$ are thus the proper \titou{charging} energies of the $N$-electron system, leading to well-defined ionization potentials and electronic affinities. Contrary to standard $\Delta$SCF techniques, the knowledge of $G$ provides the full ionization spectrum, as measured by direct and inverse photoemission, not only that associated with frontier orbitals.
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Unlike Kohn-Sham (KS) eigenvalues, the Green's function poles $\lbrace \varepsilon_s \rbrace$ are thus the proper \titou{charging} energies of the $N$-electron system, leading to well-defined ionization potentials and electronic affinities. Contrary to standard $\Delta$SCF techniques, the knowledge of $G$ provides the full ionization spectrum, as measured by direct and inverse photoemission, not only that associated with frontier orbitals.
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Using the equation-of-motion formalism for the creation/destruction operators, it can be shown formally that $G$ verifies
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Using the equation-of-motion formalism for the creation/destruction operators, it can be shown formally that $G$ verifies
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@ -412,10 +412,12 @@ We emphasise that these equations can be solved at exactly the same cost as the
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\subsection{Practical considerations}
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\subsection{Practical considerations}
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From a practical point of view, it is important to understand that, to compute the BSE neutral excitations, it is required to perform, first, several calculations (see Fig.~\ref{fig:pentagon}).
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From a practical point of view, it is important to understand that, to compute the BSE neutral excitations, one must perform, first, several calculations.
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In a first time, a Kohn-Sham DFT calculation has to be performed in order to get orbitals and their corresponding energies .
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First, a KS-DFT (or HF) calculation has to be performed in order to get orbitals and their corresponding energies.
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Then, a $GW$ calculation has to be performed in order to correct these quantities.
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Then, these are used as input variables for the $GW$ calculation, whose main purpose is to correct these quantities.
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In the case of a $G_0W_0$ calculation, a single, perturbative correction is applied to the
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Depending on the level of self-consistency, only the eigenvalues or both the eigenvalues and the orbitals are updated.
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In the case of a $G_0W_0$ calculation, a single, perturbative correction is applied to the orbital energies only.
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The partially self-consistent ev$GW$ scheme update
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\\
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\\
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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@ -493,12 +495,6 @@ The success of the BSE formalism to treat CT excitations has been demonstrated i
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\titou{T2: introduce discussion about coupling between BSE and solvent models.}
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\titou{T2: introduce discussion about coupling between BSE and solvent models.}
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We now leave the description of successes to discuss difficulties and Perspectives.\\
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We now leave the description of successes to discuss difficulties and Perspectives.\\
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%==========================================
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\subsection{Unphysical discontinuities}
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\titou{T2: talking about multiple solution issues.}
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%==========================================
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\subsection{The computational challenge}
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\subsection{The computational challenge}
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@ -535,6 +531,12 @@ An additional issue concerns the formalism taken to calculate the ground-state e
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This points to another direction for the BSE formlism, namely the calculation of GS total energy with the correlation energy calculated at the BSE level. Such a task was performed by several groups using in particular the adiabatic connection fluctuation-dissipation theorem (ACFDT), focusing in particular on small dimers. \cite{Olsen_2014,Holzer_2018b,Li_2020,Loos_2020}\\
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This points to another direction for the BSE formlism, namely the calculation of GS total energy with the correlation energy calculated at the BSE level. Such a task was performed by several groups using in particular the adiabatic connection fluctuation-dissipation theorem (ACFDT), focusing in particular on small dimers. \cite{Olsen_2014,Holzer_2018b,Li_2020,Loos_2020}\\
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%==========================================
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\subsection{Unphysical discontinuities}
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%==========================================
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\titou{T2: talking about multiple solution issues.}
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%==========================================
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%==========================================
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\subsection{The double excitation challenge}
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\subsection{The double excitation challenge}
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@ -631,4 +633,37 @@ DJ acknowledges the \textit{R\'egion des Pays de la Loire} for financial support
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%%%%%%%%%%%%%%%%%%%%
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\bibliography{xbbib}
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\bibliography{xbbib}
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\clearpage
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\section*{Biographies}
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\begin{center}
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\includegraphics[width=3cm]{XBlase}
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\end{center}
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\noindent{\bfseries Xavier Blase} holds his PhD in Physics from the University of California at Berkeley.
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He is presently CNRS Research Director at Institut N\'eel, Grenoble, France.
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His research focuses on the electronic and optical properties of systems relevant to condensed matter physics, materials sciences and physical chemistry, with much emphasis on methodology.
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He is the co-author of the FIESTA code (Bull-Fourier prize 2014) that implements the $GW$ and Bethe-Salpeter formalisms with Gaussian basis sets.
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He received the 2008 CNRS silver medal.
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\begin{center}
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\includegraphics[width=3cm]{IDuchemin}
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\end{center}
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\noindent{\bfseries Ivan Duchemin} holds his PhD from the CEMES in Toulouse, France.
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He stayed as a postdoctoral fellow at the UC Davis Physics department, California, and the Max Plank Institute for Polymer Research in Mainz, Germany, before joining the French Center for Alternative Energies (CEA), Grenoble, France, as a senior scientist.
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His research interests focus on methodological and code developments in ab initio quantum simulations.
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He is presently the main developer of the FIESTA code (Bull-Fourier prize 2014).
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\begin{center}
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\includegraphics[width=4cm]{DJacquemin}
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\end{center}
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\noindent{\bfseries Denis Jacquemin} received his PhD in Chemistry from the University of Namur in 1998, before moving to the University of Florida for his postdoctoral stay. He is currently full Professor at the University of Nantes (France).
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His research is focused on modeling electronically excited-state processes in organic and inorganic dyes as well as photochromes using a large panel of \emph{ab initio} approaches. His group collaborates with many experimental
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and theoretical groups. He is the author of more than 500 scientific papers. He has been ERC grantee (2011--2016), member of Institut Universitaire de France (2012--2017) and received the WATOC's Dirac Medal (2014).
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\begin{center}
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\includegraphics[width=3cm]{PFLoos}
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\end{center}
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\noindent{\bfseries Pierre-Fran\c{c}ois Loos} was born in Nancy, France in 1982. He received his M.S.~in Computational and Theoretical Chemistry from the Universit\'e Henri Poincar\'e (Nancy, France) in 2005 and his Ph.D.~from the same university in 2008. From 2009 to 2013, He was undertaking postdoctoral research with Peter M.W.~Gill at the Australian National University (ANU). From 2013 to 2017, he was a \textit{``Discovery Early Career Researcher Award''} recipient at the ANU. Since 2017, he holds a researcher position from the \textit{``Centre National de la Recherche Scientifique (CNRS)} at the \textit{Laboratoire de Chimie et Physique Quantiques} in Toulouse (France), and was awarded, in 2019, an ERC consolidator grant for the development of new excited-state methodologies.
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\end{document}
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\end{document}
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