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H2 res

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Pierre-Francois Loos 2020-04-08 14:05:37 +02:00
parent 301161158e
commit 6cef03e9f3
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Manuscript/FarDFT.tex
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@ -71,7 +71,7 @@
\newcommand{\VWN}{\text{VWN5}}
\newcommand{\SVWN}{\text{SVWN5}}
\newcommand{\LIM}{\text{LIM}}
\newcommand{\CID}{\text{CID}}
\newcommand{\MOM}{\text{MOM}}
\newcommand{\Hxc}{\text{Hxc}}
\newcommand{\Ha}{\text{H}}
\newcommand{\ex}{\text{x}}
@ -584,9 +584,9 @@ Equation \eqref{eq:becw} can be recast
\label{eq:eLDA}
\begin{split}
\be{\co}{\ew{}}(\n{}{})
& = \e{\co}{\LDA}(\n{}{}) + \ew{} \qty[\e{\co}{(1)}(\n{}{}) - \e{\co}{(0)}(\n{}{})]
& = \e{\co}{\VWN}(\n{}{}) + \ew{} \qty[\e{\co}{(1)}(\n{}{}) - \e{\co}{(0)}(\n{}{})]
\\
& = \e{\co}{\LDA}(\n{}{}) + \ew{} \pdv{\e{\co}{\ew{}}(\n{}{})}{\ew{}},
& = \e{\co}{\VWN}(\n{}{}) + \ew{} \pdv{\e{\co}{\ew{}}(\n{}{})}{\ew{}},
\end{split}
\end{equation}
which nicely highlights the centrality of the LDA in the present weight-dependent density-functional approximation for ensembles.
@ -620,9 +620,14 @@ For comparison purposes, we also report the linear interpolation method (LIM) ex
\begin{equation}
\Ex{\LIM}{(1)} = 2 (\E{}{\ew{}=1/2} - \E{}{\ew{}=0}),
\end{equation}
as well as the MOM excitation energies.
We point out that the MOM excitation energy is obtained by the difference in energy between the doubly-excited state at $\ew{} = 1$ and the ground-state at $\ew{} = 0$.
MOM excitation energies can then be obtained via GOK-DFT ensemble calculations by performing a linear interpolation between $\ew{} = 0$ and $\ew{} = 1$.
as well as the MOM excitation energies. \cite{Gilbert_2008,Barca_2018a,Barca_2018b}
We point out that the MOM excitation energy is obtained by the difference in energy between the doubly-excited state at $\ew{} = 1$ and the ground state at $\ew{} = 0$.
MOM excitation energies can then be obtained via GOK-DFT ensemble calculations by performing a linear interpolation between $\ew{} = 0$ and $\ew{} = 1$, \ie,
\begin{equation}
\Ex{\MOM}{(1)} = \E{}{\ew{}=1} - \E{}{\ew{}=0}.
\end{equation}
The results gathered in Table \ref{tab:BigTab_H2} show that the GOK-DFT excitation energies obtained with the GIC-SeVWN5 functional at zero weight are the most accurate with an improvment of $0.25$ eV as compared to GIC-SVWN5
%%% TABLE I %%%
\begin{table*}