1-4.The exch.-corr. functional

08-18

來自專欄 A note on DFT

the Local Density Approximation

$egin{eqnarray} V_{ext}^{LDA}[ ho]equivint dvec{r} ho(vec{r})epsilon_{xc}( ho(vec{r})) end{eqnarray}$

The function (not: functional) $epsilon_{xc}( ho(vec{r}))$ for the homogeneous electron gas has been determined by the related density $ho(vec{r})$ . That means if we have a value of $ho$ then we can get a determined numerical value of $epsilon$ . So the only thing we dont know is how does the value of $ho$ varies along the $vec{r}$ (the function $ho(vec{r})$ ).

Note that $epsilon_{xc}$ is a function of $ho$ , not a functional!