On Exchange-Correlation Energy in DFT Scenarios

Abstract

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 $n_{\ddot{I}ƒe}\left(r\right)$ needed to obtain the ground-state energy $E_e$ in Density Functional Theory scenarios, we approach the Exchange-Correlation energy $E_{xc}\left[n_{\ddot{I}ƒe}(r)\right]$ by considering the interelectronic position corrections $\hat{I}”r_x^{\uparrow \uparrow ,\uparrow \downarrow }=\hat{I}{»}_x\left|\hat{I}´r^{\uparrow \uparrow }-\hat{I}´r^{\uparrow \downarrow }\right|$ and $\hat{I}”r_c^{e_i{e}_{j\ne i}}=\hat{I}{»}_c{\left|r-r^{\prime }\right|}^{-{\left(N_e-1\right)}^{-1}}$ 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 $E_x\left[n_{\ddot{I}ƒe}\right]$ and the correlation $E_c\left[n_{\ddot{I}ƒe}\right]$ functional energies which could be interpreted in terms of magnetic and electric dipole potential energies associated with the charge density $n_{\ddot{I}ƒe}\left(r\right)$ 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.

11 Pages, 0 Figures, 0 Tables, Hand-conducted work, Authors in alphabetical order