From 690be93a944f09d837d43de69e83bedfe2ea3250 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 8 Apr 2020 13:27:18 +0200 Subject: [PATCH] minor corrections --- Manuscript/FarDFT.tex | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex index 06bf0ce..ccccdc1 100644 --- a/Manuscript/FarDFT.tex +++ b/Manuscript/FarDFT.tex @@ -373,16 +373,18 @@ Doing so, we have found that the present weight-dependent exchange functional (d with \begin{equation} \label{eq:Cxw} - \Cx{\ew{}} = \Cx{} \qty{ 1 - \ew{} (1 - \ew{})\qty[ \alpha + \beta (\ew{} - 1/2) + \gamma (w - 1/2)^2 ]} + \frac{\Cx{\ew{}}}{\Cx{}} = 1 - \ew{} (1 - \ew{})\qty[ \alpha + \beta (\ew{} - 1/2) + \gamma (w - 1/2)^2 ] \end{equation} and +\begin{subequations} \begin{align} \alpha & = + 0.575\,178, - & + \\ \beta & = - 0.021\,108, - & + \\ \gamma & = - 0.367\,189, \end{align} +\end{subequations} makes the ensemble almost perfectly linear (see Fig.~\ref{fig:Ew_H2}), and the excitation energy much more stable and closer to the full configuration interaction (FCI) reference of $28.75$ eV \cite{Barca_2018a} (see Fig.~\ref{fig:Om_H2}) As readily seen from Eq.~\eqref{eq:Cxw}, $\Cx{\ew{}}$ reduces to $\Cx{}$ for $\ew{} = 0$. Note that we are not only using data from $\ew{} = 0$ to $\ew{} = 1/2$, but we also consider $1/2 < \ew{} \le 1$. @@ -505,7 +507,7 @@ Combining these, we build a two-state weight-dependent correlation functional: %%% FIG 1 %%% \begin{figure} - \includegraphics[width=\linewidth]{fig/fig1} + \includegraphics[width=0.8\linewidth]{fig/fig1} \caption{ Reduced (i.e., per electron) correlation energy $\e{\co}{(I)}$ [see Eq.~\eqref{eq:ec}] as a function of $R = 1/(\pi^2 \n{}{})^{1/3}$ for the ground state ($I=0$), and the first doubly-excited state ($I=1$) of the (spin-unpolarised) two-electron FUEG. The data gathered in Table \ref{tab:Ref} are also reported.