On Exchange-Correlation Energy in DFT Scenarios

TL;DR

This paper proposes a new approach to approximate exchange-correlation energies in density functional theory by incorporating interelectronic position corrections related to spin and Coulomb effects, aiming to improve local density approximations.

Contribution

It introduces a novel method to include interelectronic position corrections into exchange-correlation functionals within DFT, extending the local density approximation.

Findings

Derived approximate expressions for exchange and correlation energies.

Interpreted these energies in terms of magnetic and electric dipole potentials.

Suggested potential integration into LDA functionals.

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_{\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.