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Pierre-Francois Loos 2019-04-12 09:47:09 +02:00
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Manuscript/G2-srDFT.tex
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@ -293,9 +293,9 @@ such that the long-range interaction
\end{equation} \end{equation}
\PFL{This expression looks like a cheap spherical average. \PFL{This expression looks like a cheap spherical average.
What about $\rsmu{\Bas}{}(\br{1},\br{2}) = \sqrt{\rsmu{\Bas}{}(\br{1}) \rsmu{\Bas}{}(\br{2})}$ and a proper spherical average to get $\rsmu{\Bas}{}(r_{12})$?} What about $\rsmu{\Bas}{}(\br{1},\br{2}) = \sqrt{\rsmu{\Bas}{}(\br{1}) \rsmu{\Bas}{}(\br{2})}$ and a proper spherical average to get $\rsmu{\Bas}{}(r_{12})$?}
coincides with the effective interaction $\W{\Bas}{}(\br{})$ at coalescence, i.e.~$\w{}{\lr,\rsmu{\Bas}{}}(\br{},\br{}) = \W{\Bas}{}(\br{})$. coincides with the effective interaction at coalescence, i.e.~$\w{}{\lr,\rsmu{\Bas}{}}(\br{},\br{}) = \W{\Bas}{}(\br{})$.
Once defined, $\rsmu{\Bas}{}(\br{})$ can be used in RS-DFT functionals defined to approximate $\bE{}{\Bas}[\n{}{}]$. Once defined, $\rsmu{\Bas}{}(\br{})$ can be used in RS-DFT functionals to approximate $\bE{}{\Bas}[\n{}{}]$.
As in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, we approximate $\bE{}{\Bas}[\n{}{}]$ using a specific class of short-range correlation functionals known as ECMD whose general definition reads \cite{TouGorSav-TCA-05} As in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, we approximate $\bE{}{\Bas}[\n{}{}]$ using a specific class of short-range correlation functionals known as ECMD whose general definition reads \cite{TouGorSav-TCA-05}
\begin{multline} \begin{multline}
\label{eq:ec_md_mu} \label{eq:ec_md_mu}