# [Octopus-users] using MGGA from libxc

Miguel Marques marques at teor.fis.uc.pt
Mon Jan 24 09:50:52 WET 2011

   Dear Vladimir,

Meta-GGAs are not standard density-functionals. In fact, although by
virtue of the Hohenberg-Kohn theorem tau is a functional of the density
n, it is an implicit density functional and not an explicit one (several
approximations to \tau[n] do exist though). In view of this, there are
two ways of implementing a meta-GGA in a DFT code:

1) the "correct" DFT way, i.e., treat a meta-GGA as a _orbital_
functional and use the machinery of the optimized effective potential
(OEP) to construct the potential.

2) To approximate the xc potential in DFT by 1/psi \delta E_xc / \delta
psi^* (from memory, but it should be something like that). This is the
pragmatic approach used in all quantum-chemistry codes, but it goes away
from "pure" DFT.

So, the answer to your question, libxc can not provide \delta tau /
\delta \rho as this derivative can not be so easily obtained, but that
derivative is not needed to obtain the potential...

hope this helped,
miguel

On 01/22/2011 01:37 PM, Vladimir Nazarov wrote:
> Hello All,
>
> I have a (probably naive)  question about libxc library:
>
> I want to know the xc potential within MGGA.
> For this, I call xc_mgga_vxc. But how to construct v_xc(r)  from the
> output of
> xc_mgga_vxc: We evidently need  \delta tau / \delta \rho, which is not
> among the output parameters of    xc_mgga_vxc ?
> (\tau is the kinetic energy density, and \rho is the density).
>
> Thank you very much in advance.
> _______________________________________________
> Octopus-users mailing list
> Octopus-users at tddft.org
> http://www.tddft.org/mailman/listinfo/octopus-users
>

--
Dr. Miguel A. L. Marques
marques at tddft.org
http://www.tddft.org/bmg

Laboratoire de Physique de la Matière Condensée et Nanostructures
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