From 382a6001c257fd19a93e7054abd9d506aea5ec21 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 11 Sep 2019 09:38:41 +0200 Subject: [PATCH] minor modifications in SI --- Manuscript/SI/eDFT-SI.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/Manuscript/SI/eDFT-SI.tex b/Manuscript/SI/eDFT-SI.tex index 34d0b79..52de70c 100644 --- a/Manuscript/SI/eDFT-SI.tex +++ b/Manuscript/SI/eDFT-SI.tex @@ -548,7 +548,7 @@ The numerical values of the correlation energy for various $R$ are reported in T \begin{figure} \includegraphics[width=\linewidth]{Ec} \caption{ - $\e{c}{(I)}$ [see Eq.~\eqref{eq:ec}] as a function of $R = 1/(\pi n)$ for the ground state ($I=0$), the first singly-excited state ($I=1$), and the first doubly-excited state ($I=2$) of the (spin-polarized) two-electron ringium system. + Reduced (i.e., per electron) correlation energy $\e{c}{(I)}$ [see Eq.~\eqref{eq:ec}] as a function of $R = 1/(\pi n)$ for the ground state ($I=0$), the first singly-excited state ($I=1$), and the first doubly-excited state ($I=2$) of the (spin-polarized) two-electron ringium system. The data gathered in Table \ref{tab:Ref} are also reported. } \label{fig:Ec} @@ -581,10 +581,10 @@ The numerical values of the correlation energy for various $R$ are reported in T Based on these highly-accurate calculations, one can write down, for each state, an accurate analytical expression of the reduced correlation energy \cite{Loos_2013a, Loos_2014a} via the following Pad\'e approximant \begin{equation} \label{eq:ec} - \e{c}{(I)}(n) = \frac{a^{(I)}\,n}{n + b^{(I)} \sqrt{n} + c^{(I)}}, + \e{c}{(I)}(n) = \frac{c_1^{(I)}\,n}{n + c_2^{(I)} \sqrt{n} + c_3^{(I)}}, \end{equation} -where $b^{(I)}$ and $c^{(I)}$ are state-specific fitting parameters, which are provided in Table I of the manuscript. -The value of $a^{(I)}$ is obtained via the exact high-density expansion of the correlation energy. \cite{Loos_2013a, Loos_2014a} +where $c_2^{(I)}$ and $c_3^{(I)}$ are state-specific fitting parameters, which are provided in Table I of the manuscript. +The value of $c_1^{(I)}$ is obtained via the exact high-density expansion of the correlation energy. \cite{Loos_2013a, Loos_2014a} Equation \eqref{eq:ec} is depicted in Fig.~\ref{fig:Ec} for each state alongside the data gathered in Table \ref{tab:Ref}.