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eginer 2019-06-17 17:04:58 +02:00
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Manuscript/Ex-srDFT.tex
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@ -354,7 +354,7 @@ with
\end{equation} \end{equation}
where the UEG on-top pair-distribution function $g_0(n)$ given in Eq.~(46) of Ref.~\citenum{GorSav-PRA-06}. where the UEG on-top pair-distribution function $g_0(n)$ given in Eq.~(46) of Ref.~\citenum{GorSav-PRA-06}.
As shown in Ref~\cite{LooPraSceTouGin-JPCL-19}, the link with the usual PBE functional has shown to improve the results over LDA for weakly correlated systems, but the remaining on-top pair density obtained from the UEG might not be suited for the treatment of excited states and/or strongly-correlated systems. Therefore, we propose here a variant inspired by the work of ~Ref\cite{FerGinTou-JCP-18} where we obtain an approximation of the exact on-top pair density based on an extrapolation proposed by Gori-Giorgi in Ref.~\onlinecite{GorSav-PRA-06}. Introducing the extrapolation function $\extrfunc(\n{2}{},\mu)$ As shown in Ref~\cite{LooPraSceTouGin-JPCL-19}, the link with the usual PBE functional has shown to improve the results over LDA for weakly correlated systems, but the remaining on-top pair density obtained from the UEG might not be suited for the treatment of excited states and/or strongly-correlated systems. Therefore, we propose here a variant inspired by the work of ~Ref\cite{FerGinTou-JCP-18} where we obtain an approximation of the exact on-top pair density based on an extrapolation proposed by Gori-Giorgi \textit{et. al} in Ref.~\onlinecite{GorSav-PRA-06}. Introducing the extrapolation function $\extrfunc(\n{2}{},\mu)$
\begin{equation} \begin{equation}
\extrfunc(\n{2}{},\mu) = \n{2}{} \qty(1+ \frac{2}{\sqrt{\pi}\mu})^{-1}, \extrfunc(\n{2}{},\mu) = \n{2}{} \qty(1+ \frac{2}{\sqrt{\pi}\mu})^{-1},
\end{equation} \end{equation}