  Motivated by the considerable importance of material properties in modern
condensed matter physics research, and using techniques of the $N_{e}$
-electron systems in terms of the electron density $n_{\sigma e}\left( r\right)
$ needed to obtain the ground-state energy $E_{e}$ in Density Functional Theory
scenarios, we approach the Exchange-Correlation energy $ E_{xc}\left[ n_{\sigma
e}(r)\right] $ by considering the interelectronic position corrections $\Delta
r_{x}^{\uparrow \uparrow ,\uparrow \downarrow }=\lambda _{x}\left\vert \delta
r^{\uparrow \uparrow }-\delta r^{\uparrow \downarrow }\right\vert $ and $\Delta
r_{c}^{e_{i}e_{j\neq i}}=\lambda _{c}\left\vert r-r^{\prime }\right\vert
^{-\left( N_{e}-1\right) ^{-1}}$ corresponding to the spin and the Coulomb
correlation effects, respectively, through the electron-electron potential
energy. Exploiting such corrections, we get approximate expressions for the
exchange $E_{x}\left[ n_{\sigma e} \right] $ and the correlation $E_{c}\left[
n_{\sigma e}\right] $ functional energies which could be interpreted in terms
of magnetic and electric dipole potential energies associated with the charge
density $n_{\sigma e}\left( r\right) $ described by inverse-square potential
behaviors. Based on these arguments, we expect that such obtained
Exchange-Correlation functional energy could be considered in the Local Density
Approximation functional as an extension to frame such interelectronic effects.
