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 Ne-electron systems in terms of the electron density nσe (r) needed to obtain the ground-state energy Ee0 in Density Functional theory scenarios, we approach the exchange-correlation energy Exc [nσe(r)] by considering the interelectronic position corrections Δr↑↑,↑↓ x = |δr↑↑ − δr↑↓| and Δr eiej6≠i c = λc |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 [nσe] and the correlation Ec [nσe] functional energies which could be interpreted in terms of magnetic and electric dipole potential energies associated with the charge density nσe (r) described by inversesquare 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.