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Pierre-Francois Loos 2019-12-06 14:11:36 +01:00
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JCTC_revision/GW-srDFT.tex
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@ -497,7 +497,7 @@ The frequency-independent local self-energy $\bSig{}{\Bas}[\n{}{}](\br{},\br{}')
Here, we employ two types of complementary, short-range correlation functionals $\bE{}{\Bas}[\n{}{}]$: a short-range local-density approximation ($\srLDA$) functional with multideterminant reference \cite{Toulouse_2005, Paziani_2006} and a short-range Perdew-Burke-Ernzerhof ($\srPBE$) correlation functional \cite{Ferte_2019, Loos_2019} which interpolates between the usual PBE functional \cite{Perdew_1996} at $\mu = 0$ and the exact large-$\mu$ behavior \cite{Toulouse_2004, Gori-Giorgi_2006, Paziani_2006} using the on-top pair density from the uniform-electron gas. \cite{Loos_2019} Here, we employ two types of complementary, short-range correlation functionals $\bE{}{\Bas}[\n{}{}]$: a short-range local-density approximation ($\srLDA$) functional with multideterminant reference \cite{Toulouse_2005, Paziani_2006} and a short-range Perdew-Burke-Ernzerhof ($\srPBE$) correlation functional \cite{Ferte_2019, Loos_2019} which interpolates between the usual PBE functional \cite{Perdew_1996} at $\mu = 0$ and the exact large-$\mu$ behavior \cite{Toulouse_2004, Gori-Giorgi_2006, Paziani_2006} using the on-top pair density from the uniform-electron gas. \cite{Loos_2019}
Additionally to the one-electron density calculated from the HF or KS orbitals, these RS-DFT functionals require a range-separation function $\rsmu{}{\Bas}(\br{})$ which automatically adapts to the spatial inhomogeneity of the basis-set incompleteness error and is computed using the HF or KS opposite-spin pair-density matrix in the basis set $\Bas$. Additionally to the one-electron density calculated from the HF or KS orbitals, these RS-DFT functionals require a range-separation function $\rsmu{}{\Bas}(\br{})$ which automatically adapts to the spatial inhomogeneity of the basis-set incompleteness error and is computed using the HF or KS opposite-spin pair-density matrix in the basis set $\Bas$.
We refer the interested reader to Refs.~\onlinecite{Giner_2018, Loos_2019, Giner_2019} where our procedure is thoroughly detailed. We refer the interested reader to Refs.~\onlinecite{Giner_2018, Loos_2019, Giner_2019} where our procedure is thoroughly detailed.
\titou{The explicit expressions of these two short-range correlation functionals, as well as their functional derivative, are provided in the {\SI}.} \titou{The explicit expressions of these two short-range correlation functionals, as well as their corresponding potentials, are provided in the {\SI}.}
The basis set corrected {\GOWO} quasiparticle energies are thus given by The basis set corrected {\GOWO} quasiparticle energies are thus given by