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first draft of theory

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Pierre-Francois Loos 2020-01-25 22:03:32 +01:00
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BSE-PES.tex
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@ -219,11 +219,10 @@ Such a modified BSE polarization propagator was inspired by a previous study on
With such an approximation, amounting to neglect excitonic effects in the electron-hole propagator, the question of using either KS-DFT or {\GW} eigenvalues in the construction of the propagator becomes further relevant, increasing accordingly the number of possible definitions for the ground-state correlation energy.
Finally, renormalizing or not the Coulomb interaction by the coupling parameter $\lambda$ in the Dyson equation for the interacting polarizability leads to two different versions of the BSE correlation energy.
\alert{Here, in analogy to the random-phase approximation (RPA) formalism, \cite{Furche_2008} the ground-state BSE energy is calculated via the ``trace'' formula (see below). The excited-state BSE energy is then computed by adding the BSE excitation energy of the selected state to the ground-state BSE energy.
This definition of the energy has the advantage of treating at the same level of theory the ground state and the excited states.
Embracing this definition, the purpose of the present study is to investigate the quality of ground- and excited-state PES near equilibrium obtained within the BSE approach.
The location of the minima on the ground- and (singlet and triplet) excited-state PES is of particular interest.
This study is a first preliminary step towards the development of analytical nuclear gradients within the BSE@{\GW} formalism.}
Here, in analogy to the random-phase approximation (RPA)-type formalismes, \cite{Furche_2008, Angyan_2011, Holzer_2018} the ground-state BSE energy is calculated in the adiabatic-connection fluctuation-dissipation theorem framework.
Embracing this definition, the purpose of the present study is to investigate the quality of ground--state PES near equilibrium obtained within the BSE approach.
The location of the minima on the ground-state PES is of particular interest.
This study is a first preliminary step towards the development of analytical nuclear gradients within the BSE@{\GW} formalism.
%The paper is organized as follows.
%In Sec.~\ref{sec:theo}, we introduce the equations behind the BSE formalism.