numerical values
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0551108122
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FarDFT.nb
70
FarDFT.nb
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@ -245,7 +245,8 @@ We adopt the usual decomposition, and write down the weight-dependent xc functio
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\end{equation}
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where $\e{\ex}{\ew{}}(\n{}{})$ and $\e{\co}{\ew{}}(\n{}{})$ are the weight-dependent exchange and correlation functionals, respectively.
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The construction of these two functionals is described below.
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Here, we restrict our study to spin-unpolarized systems, \ie, $\n{\uparrow}{} = \n{\downarrow}{} = \n{}{}/2$.
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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).
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Extension to spin-polarised systems will be reported in future work.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Weight-dependent exchange functional}
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@ -349,22 +350,22 @@ Combining these, we build a two-state weight-dependent correlation functional:
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$-\e{\co}{(I)}$ 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.
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}
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\begin{ruledtabular}
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\begin{tabular}{ldd}
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\begin{tabular}{lcc}
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& \tabc{Ground state} & \tabc{Doubly-excited state} \\
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$R$ & \tabc{$I=0$} & \tabc{$I=1$} \\
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\hline
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$0$ & & \\
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$1/10$ & & \\
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$1/5$ & & \\
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$1/2$ & & \\
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$1$ & & \\
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$2$ & & \\
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$5$ & & \\
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$10$ & & \\
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$20$ & & \\
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$50$ & & \\
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$100$ & & \\
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$150$ & & \\
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$0$ & $0.023818$ & $0.014463$ \\
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$0.1$ & $0.023392$ & $0.014497$ \\
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$0.2$ & $0.022979$ & $0.014523$ \\
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$0.5$ & $0.021817$ & $0.014561$ \\
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$1$ & $0.020109$ & $0.014512$ \\
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$2$ & $0.017371$ & $0.014142$ \\
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$5$ & $0.012359$ & $0.012334$ \\
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$10$ & $0.008436$ & $0.009716$ \\
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$20$ & $0.005257$ & $0.006744$ \\
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$50$ & $0.002546$ & $0.003584$ \\
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$100$ & $0.001399$ & $0.002059$ \\
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$150$ & $0.000972$ & $0.001458$ \\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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@ -380,8 +381,8 @@ Combining these, we build a two-state weight-dependent correlation functional:
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& \tabc{$I=0$} & \tabc{$I=1$} \\
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\hline
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$a_1$ & $-0.0238184$ & $-0.0144633$ \\
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$a_2$ & $+0.00575719$ & $-0.0504501$ \\
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$a_3$ & $+0.0830576$ & $+0.0331287$ \\
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$a_2$ & $+0.00540994$ & $-0.0506019$ \\
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$a_3$ & $+0.0830766$ & $+0.0331417$ \\
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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