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minor corrections in SI

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Pierre-Francois Loos 2019-12-17 13:56:01 +01:00
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JCTC_revision/SI/GW-srDFT-SI.tex
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@ -215,7 +215,7 @@ with
\begin{equation} \begin{equation}
\be{\text{c,md}}{\srLDA}(\n{}{},\rsmu{}{}) = \be{\text{c}}{\srLDA}(\n{}{},\rsmu{}{}) + \Delta^{\text{lr-sr}}(n,\mu), \be{\text{c,md}}{\srLDA}(\n{}{},\rsmu{}{}) = \be{\text{c}}{\srLDA}(\n{}{},\rsmu{}{}) + \Delta^{\text{lr-sr}}(n,\mu),
\end{equation} \end{equation}
with $\be{\text{c,md}}{\srLDA}(\n{}{},\rsmu{}{})$ is the complementary short-range LDA correlation energy functional (with single-determinant reference) and $\Delta^{\text{lr-sr}}(n,\mu)$ is a mixed long-range/short-range contribution, both parametrized in Ref.~\onlinecite{Paziani_2006}. where $\be{\text{c,md}}{\srLDA}(\n{}{},\rsmu{}{})$ is the complementary short-range LDA correlation energy functional (with single-determinant reference) and $\Delta^{\text{lr-sr}}(n,\mu)$ is a mixed long-range/short-range contribution, both parametrized in Ref.~\onlinecite{Paziani_2006}.
The corresponding complementary srLDA potential is The corresponding complementary srLDA potential is
\begin{eqnarray} \begin{eqnarray}
@ -229,7 +229,7 @@ The density derivative of $\be{\text{c,md}}{\srLDA}$ is calculated as
\begin{eqnarray} \begin{eqnarray}
\frac{\partial \be{\text{c,md}}{\srLDA}}{\partial n} = \frac{\partial \be{\text{c}}{\srLDA}}{\partial n} + \frac{\partial \Delta^{\text{lr-sr}}}{\partial n}, \frac{\partial \be{\text{c,md}}{\srLDA}}{\partial n} = \frac{\partial \be{\text{c}}{\srLDA}}{\partial n} + \frac{\partial \Delta^{\text{lr-sr}}}{\partial n},
\end{eqnarray} \end{eqnarray}
where $\partial \be{\text{c}}{\srLDA}/\partial n$ is given as a subroutine on Paola Gori-Giorgi's web site (\url{https://www.quantummatter.eu/source-codes-2}) and we have calculated $\partial \Delta^{\text{lr-sr}}/\partial n$ by taking the derivative of Eq. (42) of Ref.~\onlinecite{Paziani_2006}. where $\partial \be{\text{c}}{\srLDA}/\partial n$ is given as a subroutine on Paola Gori-Giorgi's website (\url{https://www.quantummatter.eu/source-codes-2}) and we have calculated $\partial \Delta^{\text{lr-sr}}/\partial n$ by taking the derivative of Eq. (42) of Ref.~\onlinecite{Paziani_2006}.
\subsection{Complementary short-range PBE correlation potential} \subsection{Complementary short-range PBE correlation potential}
@ -243,7 +243,7 @@ with
\label{eq:def_epsipbeueg} \label{eq:def_epsipbeueg}
\epspbeueg(n,s,\mu) = \frac{\epspbe(n,s)}{1+\beta(n,s)\mu^3}. \epspbeueg(n,s,\mu) = \frac{\epspbe(n,s)}{1+\beta(n,s)\mu^3}.
\end{equation} \end{equation}
Here, $\epspbe(n,s)$ is the usual PBE correlation functional \cite{Perdew_1996}, $s$ is the reduced density gradient, Here, $\epspbe(n,s)$ is the usual PBE correlation functional,\cite{Perdew_1996} $s$ is the reduced density gradient,
\begin{equation} \begin{equation}
\beta(n,s) = \frac{3}{2\sqrt{\pi}(1-\sqrt{2})}\frac{\epspbe(n,s)}{n_2^{\text{UEG}}(n)/n}, \beta(n,s) = \frac{3}{2\sqrt{\pi}(1-\sqrt{2})}\frac{\epspbe(n,s)}{n_2^{\text{UEG}}(n)/n},
\end{equation} \end{equation}
@ -321,7 +321,7 @@ with
\section{Additional graphs of the convergence of the IPs of the GW20 subset} \section{Additional graphs of the convergence of the IPs of the GW20 subset}
Graphs reporting the convergence of the IPs of each molecule of the GW20 subset at the {\GOWO}@{\HF} and {\GOWO}@{\PBEO} levels are given in Figure~\ref{fig:IP_G0W0HF} and~\ref{fig:IP_G0W0PBE0}, respectively. Graphs reporting the convergence of the IPs of each molecule of the GW20 subset at the {\GOWO}@{\HF} and {\GOWO}@{\PBEO} levels are given in Figs.~\ref{fig:IP_G0W0HF} and~\ref{fig:IP_G0W0PBE0}, respectively.
\begin{figure*} \begin{figure*}
\includegraphics[width=\linewidth]{IP_G0W0HF} \includegraphics[width=\linewidth]{IP_G0W0HF}