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