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C..18 EXERF: Short-range LDA correlation functional

Local-density approximation of exchange energy
for short-range interelectronic interaction ${\rm erf}(\mu r_{12})/r_{12}$,
A. Savin, in Recent Developments and Applications of Modern Density Functional Theory, edited by J.M. Seminario (Elsevier, Amsterdam, 1996).


\begin{displaymath}
\epsilon_x^{\rm SR}(r_s,\zeta,\mu) = \frac{3}{4\pi}\frac{\ph...
...a)^{4/3}
f_x\left(r_s,\mu(1\!-\!\zeta)^{-1/3}\right) \nonumber
\end{displaymath}  

with
\begin{displaymath}
\phi_n(\zeta)=\frac{1}{2}\left[ (1\!+\!\zeta)^{n/3}+(1\!-\!\zeta)^{n/3} \right],
\end{displaymath} (82)


\begin{displaymath}
f_x(r_s,\mu) = -\frac{\mu}{\pi}\biggl[(2y-4y^3)\,e^{-1/4y^2}...
...rac{1}{2y}\right)\biggr],
\qquad y=\frac{\mu\,\alpha\,r_s}{2},
\end{displaymath} (83)

and $\alpha=(4/9\pi)^{1/3}$.

molpro@molpro.net 2018-04-21