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Pierre-Francois Loos 2019-11-14 22:00:25 +01:00
parent a7a81f8b81
commit 1433148942
1 changed files with 5 additions and 5 deletions
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10
Manuscript/FarDFT.tex
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@ -224,13 +224,13 @@ with
Knowing that the exchange functional has the following form
\begin{equation}
\e{x}{(I)}(\n{}{}) = \Cx{(I)} \n{}{1/3}
\e{x}{(I)}(\n{}{}) = \Cx{(I)} \n{}{1/3},
\end{equation}
we obtain
\begin{align}
\Cx{(0)} & = - \frac{4}{3} \qty( \frac{2}{\pi} )^{1/3},
\Cx{(0)} & = - \frac{4}{3} \qty( \frac{1}{\pi} )^{1/3},
&
\Cx{(1)} & = - \frac{176}{105} \qty( \frac{2}{\pi} )^{1/3}
\Cx{(1)} & = - \frac{176}{105} \qty( \frac{1}{\pi} )^{1/3}
\end{align}
We can now combine these two exchange functionals to create a weight-dependent exchange functional
\begin{equation}
@ -245,7 +245,7 @@ with
\begin{equation}
\Cx{\ew{}} = (1-\ew{}) \Cx{(0)} + \ew{} \Cx{(1)}
\end{equation}
Amazingly, the weight dependence of the exchange functional can be transfered to the Subscript[C, x] coefficient.
Amazingly, the weight dependence of the exchange functional can be transfered to the $\Cx{}$ coefficient.
This is obvious but kind of nice.
@ -357,7 +357,7 @@ where we use here the Dirac exchange functional and the VWN5 correlation functio
\e{c}{\LDA}(\n{}{}) & \equiv \e{c}{\text{VWN5}}(\n{}{}).
\end{align}
\end{subequations}
with $\Cx{\LDA} = -\frac{3}{2} \qty(\frac{3}{4\pi})^{1/3}$.
with $\Cx{\LDA} = -\frac{3}{4} \qty(\frac{3}{\pi})^{1/3}$.
Equation \eqref{eq:becw} can be recast
\begin{equation}