diff --git a/JCTC_revision/SI/GW-srDFT-SI.tex b/JCTC_revision/SI/GW-srDFT-SI.tex index 92ccbd9..133609a 100644 --- a/JCTC_revision/SI/GW-srDFT-SI.tex +++ b/JCTC_revision/SI/GW-srDFT-SI.tex @@ -215,7 +215,7 @@ with \begin{equation} \be{\text{c,md}}{\srLDA}(\n{}{},\rsmu{}{}) = \be{\text{c}}{\srLDA}(\n{}{},\rsmu{}{}) + \Delta^{\text{lr-sr}}(n,\mu), \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 \begin{eqnarray} @@ -229,7 +229,7 @@ The density derivative of $\be{\text{c,md}}{\srLDA}$ is calculated as \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}, \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} @@ -243,7 +243,7 @@ with \label{eq:def_epsipbeueg} \epspbeueg(n,s,\mu) = \frac{\epspbe(n,s)}{1+\beta(n,s)\mu^3}. \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} \beta(n,s) = \frac{3}{2\sqrt{\pi}(1-\sqrt{2})}\frac{\epspbe(n,s)}{n_2^{\text{UEG}}(n)/n}, \end{equation} @@ -321,7 +321,7 @@ with \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*} \includegraphics[width=\linewidth]{IP_G0W0HF}