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Main Authors: Belhaj, A., Ennadifi, S. E.
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2407.09668
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author Belhaj, A.
Ennadifi, S. E.
author_facet Belhaj, A.
Ennadifi, S. E.
contents 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}\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_{σe}(r)\right] $ by considering the interelectronic position corrections $Δr_{x}^{\uparrow \uparrow ,\uparrow \downarrow }=λ_{x}\left\vert δr^{\uparrow \uparrow }-δr^{\uparrow \downarrow }\right\vert $ and $Δr_{c}^{e_{i}e_{j\neq i}}=λ_{c}\left\vert r-r^{\prime }\right\vert ^{-\left( N_{e}-1\right) ^{-1}}$ 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_{σe} \right] $ and the correlation $E_{c}\left[ n_{σe}\right] $ functional energies which could be interpreted in terms of magnetic and electric dipole potential energies associated with the charge density $n_{σe}\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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_09668
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On Exchange-Correlation Energy in DFT Scenarios
Belhaj, A.
Ennadifi, S. E.
Materials Science
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}\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_{σe}(r)\right] $ by considering the interelectronic position corrections $Δr_{x}^{\uparrow \uparrow ,\uparrow \downarrow }=λ_{x}\left\vert δr^{\uparrow \uparrow }-δr^{\uparrow \downarrow }\right\vert $ and $Δr_{c}^{e_{i}e_{j\neq i}}=λ_{c}\left\vert r-r^{\prime }\right\vert ^{-\left( N_{e}-1\right) ^{-1}}$ 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_{σe} \right] $ and the correlation $E_{c}\left[ n_{σe}\right] $ functional energies which could be interpreted in terms of magnetic and electric dipole potential energies associated with the charge density $n_{σe}\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.
title On Exchange-Correlation Energy in DFT Scenarios
topic Materials Science
url https://arxiv.org/abs/2407.09668