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numerical values

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Pierre-Francois Loos 2019-11-18 16:55:09 +01:00
parent 0551108122
commit c348e8170d
2 changed files with 70 additions and 33 deletions
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70
FarDFT.nb
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@ -10,10 +10,10 @@
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33
Manuscript/FarDFT.tex
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@ -245,7 +245,8 @@ We adopt the usual decomposition, and write down the weight-dependent xc functio
\end{equation} \end{equation}
where $\e{\ex}{\ew{}}(\n{}{})$ and $\e{\co}{\ew{}}(\n{}{})$ are the weight-dependent exchange and correlation functionals, respectively. where $\e{\ex}{\ew{}}(\n{}{})$ and $\e{\co}{\ew{}}(\n{}{})$ are the weight-dependent exchange and correlation functionals, respectively.
The construction of these two functionals is described below. The construction of these two functionals is described below.
Here, we restrict our study to spin-unpolarized systems, \ie, $\n{\uparrow}{} = \n{\downarrow}{} = \n{}{}/2$. Here, we restrict our study to spin-unpolarised systems, \ie, $\n{\uparrow}{} = \n{\downarrow}{} = \n{}{}/2$ (where $\n{\uparrow}{}$ and $\n{\downarrow}{}$ are the spin-up and spin-down electron densities).
Extension to spin-polarised systems will be reported in future work.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Weight-dependent exchange functional} \subsection{Weight-dependent exchange functional}
@ -349,22 +350,22 @@ Combining these, we build a two-state weight-dependent correlation functional:
$-\e{\co}{(I)}$ as a function of the radius of the glome $R = 1/(\pi \n{}{})^{1/3}$ for the ground state ($I=0$), and the first doubly-excited state ($I=1$) of the (spin-unpolarized) two-electron glomium system. $-\e{\co}{(I)}$ as a function of the radius of the glome $R = 1/(\pi \n{}{})^{1/3}$ for the ground state ($I=0$), and the first doubly-excited state ($I=1$) of the (spin-unpolarized) two-electron glomium system.
} }
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{ldd} \begin{tabular}{lcc}
& \tabc{Ground state} & \tabc{Doubly-excited state} \\ & \tabc{Ground state} & \tabc{Doubly-excited state} \\
$R$ & \tabc{$I=0$} & \tabc{$I=1$} \\ $R$ & \tabc{$I=0$} & \tabc{$I=1$} \\
\hline \hline
$0$ & & \\ $0$ & $0.023818$ & $0.014463$ \\
$1/10$ & & \\ $0.1$ & $0.023392$ & $0.014497$ \\
$1/5$ & & \\ $0.2$ & $0.022979$ & $0.014523$ \\
$1/2$ & & \\ $0.5$ & $0.021817$ & $0.014561$ \\
$1$ & & \\ $1$ & $0.020109$ & $0.014512$ \\
$2$ & & \\ $2$ & $0.017371$ & $0.014142$ \\
$5$ & & \\ $5$ & $0.012359$ & $0.012334$ \\
$10$ & & \\ $10$ & $0.008436$ & $0.009716$ \\
$20$ & & \\ $20$ & $0.005257$ & $0.006744$ \\
$50$ & & \\ $50$ & $0.002546$ & $0.003584$ \\
$100$ & & \\ $100$ & $0.001399$ & $0.002059$ \\
$150$ & & \\ $150$ & $0.000972$ & $0.001458$ \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table} \end{table}
@ -380,8 +381,8 @@ Combining these, we build a two-state weight-dependent correlation functional:
& \tabc{$I=0$} & \tabc{$I=1$} \\ & \tabc{$I=0$} & \tabc{$I=1$} \\
\hline \hline
$a_1$ & $-0.0238184$ & $-0.0144633$ \\ $a_1$ & $-0.0238184$ & $-0.0144633$ \\
$a_2$ & $+0.00575719$ & $-0.0504501$ \\ $a_2$ & $+0.00540994$ & $-0.0506019$ \\
$a_3$ & $+0.0830576$ & $+0.0331287$ \\ $a_3$ & $+0.0830766$ & $+0.0331417$ \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table} \end{table}