On Exchange-correlation Energy in DFT Scenarios

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_σe(r) needed to obtain the ground-state energy E_e0 in Density Functional theory scenarios, we approach the exchange-correlation energy E_xc[n_σe(r)] by considering the interelectronic position corrections Δ$r_x^{{ \uparrow \uparrow , \uparrow \downarrow }}$ = λ_x|δr^↑↑ - δr^↑↓| and Δ$r_c^{{{{e}_i}{{e}_{{j \ne i}}}}}$ = λ_c|r - r'${{|}^{{ - {{{({{N}_e} - 1)}}^{{ - 1}}}}}}$ 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[n_σe] and the correlation E_c[n_σe] functional energies which could be interpreted in terms of magnetic and electric dipole potential energies associated with the charge density n_σe(r) 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.