Category:Exchange-correlation functionals: Difference between revisions

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E_{\rm tot}^{\rm KS}[\rho] = -\frac{1}{2}\sum_{i=1}^{N}\int
E_{\rm tot}^{\rm KS}[\rho] = -\frac{1}{2}\sum_{i=1}^{N}\int
\psi_{i}^{*}({\bf r})\nabla^{2}\psi_{i}({\bf r})d^{3}r + \int v_{\rm ext}({\bf r})\rho({\bf r})d^{3}r + E_{\rm xc} + \frac{1}{2}\int\int\frac{\rho({\bf r})\rho({\bf r'})}{\left\vert{\bf r}-{\bf r'}\right\vert}d^{3}rd^{3}r' + \frac{1}{2}\sum_{A\ne B}\frac{Z_{A}Z_{B}}{\left\vert{\bf R}_{A}-{\bf R}_{B}\right\vert}
\psi_{i}^{*}({\bf r})\nabla^{2}\psi_{i}({\bf r})d^{3}r + \int v_{\rm ext}({\bf r})\rho({\bf r})d^{3}r + E_{\rm xc} + \frac{1}{2}\int\int\frac{\rho({\bf r})\rho({\bf r'})}{\left\vert{\bf r}-{\bf r'}\right\vert}d^{3}rd^{3}r' + \frac{1}{2}\sum_{A\ne B}\frac{Z_{A}Z_{B}}{\left\vert{\bf R}_{A}-{\bf R}_{B}\right\vert}
 
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Revision as of 12:19, 18 January 2022

In the Kohn-Sham (KS) formulation of density functional theory (DFT)[1][2], the total energy is given by

where

is the non-interacting kinetic energy of the electrons,

is the Classical Coulomb Hartree term,

is the electrons-nuclei attraction energy and

is the nuclei-nuclei repulsion energy.

Theoretical Background

How to


Subcategories

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Pages in category "Exchange-correlation functionals"

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