diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex index 825836c..2517150 100644 --- a/Manuscript/G2-srDFT.tex +++ b/Manuscript/G2-srDFT.tex @@ -293,7 +293,7 @@ such that the long-range interaction of RS-DFT, \titou{$\w{}{\lr,\mu}(r_{12}) = %\begin{equation} % \w{}{\lr,\mu}(r_{12}) = \frac{\erf( \mu r_{12})}{r_{12}} %\end{equation} -coincides with the effective interaction at coalescence, i.e.~$\w{}{\lr,\rsmu{}{\Bas}(\br{})}(0) = \W{}{\Bas}(\br{},\br{})$ at any point $\br{}$. +coincides with the effective interaction at coalescence, i.e.~$\w{}{\lr,\rsmu{}{\Bas}(\br{})}(0) = \W{}{\Bas}(\br{},\br{})$ at any \trashPFL{point} $\br{}$. %================================================================= %\subsection{Short-range correlation functionals} @@ -339,7 +339,7 @@ In order to correct such a defect, we propose here a new Perdew-Burke-Ernzerhof \\ \int \n{}{}(\br{}) \be{\text{c,md}}{\sr,\PBE}\qty(\qty{\n{\sigma}{}(\br{})},\qty{\nabla \n{\sigma}{}(\br{})},\rsmu{}{\Bas}(\br{})) \dbr{}, \end{multline} -inspired by the recent functional proposed by some of the authors \cite{FerGinTou-JCP-18} which interpolates between the usual PBE correlation functional~\cite{PerBurErn-PRL-96} $\e{\text{c}}{\PBE}(\qty{\n{\sigma}{}},\qty{\nabla \n{\sigma}{}})$ for $\rsmu{}{}=0$ and the exact large-$\rsmu{}{}$ behavior, \cite{TouColSav-PRA-04, GoriSav-PRA-06, PazMorGorBac-PRB-06} yielding +inspired by the recent functional proposed by some of the authors \cite{FerGinTou-JCP-18} which interpolates between the usual PBE correlation functional, \cite{PerBurErn-PRL-96} $\e{\text{c}}{\PBE}(\qty{\n{\sigma}{}},\qty{\nabla \n{\sigma}{}})$, \titou{at} $\rsmu{}{}=0$ and the exact large-$\rsmu{}{}$ behavior, \cite{TouColSav-PRA-04, GoriSav-PRA-06, PazMorGorBac-PRB-06} yielding \begin{subequations} \begin{gather} \label{eq:epsilon_cmdpbe} @@ -381,7 +381,7 @@ with \end{gather} \end{subequations} and the corresponding FC range-separation function \titou{$\rsmuFC{}{\Bas}(\br{}) = (\sqrt{\pi}/2) \WFC{}{\Bas}(\br{},\br{})$}. -It is \titou{noteworthy} that, within the present definition, $\WFC{}{\Bas}(\br{1},\br{2})$ still tends to the regular Coulomb interaction when $\Bas \to \infty$. +It is \titou{noteworthy} that, within the present definition, $\WFC{}{\Bas}(\br{1},\br{2})$ still tends to the regular Coulomb interaction \titou{as} $\Bas \to \infty$. Defining $\nFC{\modZ}{\Bas}$ as the FC (i.e.~valence-only) one-electron density obtained with a method $\modZ$ \titou{in $\Bas$}, the FC contribution of the complementary functional is then \titou{approximated by} $\bE{\LDA}{\Bas}[\nFC{\modZ}{\Bas},\rsmuFC{}{\Bas}]$ or $\bE{\PBE}{\Bas}[\nFC{\modZ}{\Bas},\rsmuFC{}{\Bas}]$.