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Note about libxc/libnxc unpolarized functional

Submitted by yyamamoto on Fri, 04/15/2022 - 13:16

In a libxc or libnxc correlation functional, the current dftsw implementation always uses the functional in spin polarized form in calculations.

In the case of spin unpolarized systems with GGA, XC_POLARIZED Ec[$\rho_\uparrow$, $\rho_\downarrow$, $\sigma_{\uparrow\uparrow}$, $\sigma_{\uparrow\downarrow}$, $\sigma_{\downarrow\downarrow}$] (where $\rho_\downarrow = \rho_\uparrow$) is equivalent of XC_UNPOLARIZED Ec[$\rho_{tot}$, $\sigma_{tot}$].

$\rho_{tot}$ is twice the $\rho_\uparrow$ and $\sigma_{tot}$ is four times the $\sigma_{\uparrow\uparrow}$.
For meta-GGAs, add $\tau_{tot} = 2 \times \tau_\uparrow$ in Ec[$\rho_{tot}$,$\sigma_{tot}$,$\tau_{tot}$].