Category:Exchange-correlation functionals: Difference between revisions

Revision as of 09:55, 18 January 2022

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

{\displaystyle E_{\rm tot}^{\rm KS}[\rho] = T_{\rm s} + J + E_{\rm xc} + \int v_{\rm ext}({\bf r})\rho({\bf r})d^{3}r + V_{\rm nn} }

where $T_{\rm s}[\rho]$

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-In density functional theory (DFT){{cite|hohenberg:pr:1964}}{{cite|kohn:pr:1965}}, the total energy is given by
+In Kohn-Sham density functional theory (DFT){{cite|hohenberg:pr:1964}}{{cite|kohn:pr:1965}}, the total energy is given by
-<math>
+:<math>
-E^{\rm KS}[\rho] = T_{\rm s}[\rho] + J[\rho] + E_{\rm xc}[\rho] +
+E_{\rm tot}^{\rm KS}[\rho] = T_{\rm s} + J + E_{\rm xc} +
 \int v_{\rm ext}({\bf r})\rho({\bf r})d^{3}r + V_{\rm nn}
 </math>
+where <math>T_{\rm s}[\rho]</math>