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 Nₑ -electron systems in terms of the electron density nσ e( r) needed to obtain the ground-state energy Eₑ in Density Functional Theory scenarios, we approach the Exchange-Correlation energy Exc[ nσ e(r)] by considering the interelectronic position corrections Δ rₓ↑ ↑ ,↑ ↓=λ ₓ δ r↑ ↑-δ r↑ ↓ and Δ rc^eᵢej≠ i=λ c r-r ^-( Nₑ-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 Eₓ[ nσ e ] and the correlation Ec[ nσ e] functional energies which could be interpreted in terms of magnetic and electric dipole potential energies associated with the charge density nσ e( 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.