The ABINIT Users Mailing List ( CLOSED )

[Daniel Åberg <aberg2@llnl.gov>]

Dear Matteo,
I had always skipped the xc-parts when reading the PAW-papers, but I was
finally forced to actually read and rederive those equations too ;) 

Yes, you're certainly right that (\tilde n + \hat n) and (\tilde n^1 + \hat n)
can become negative. I wonder, however, why add the (\hat n) at all in this
case? One can add any density (as long as it's zero outside the augmentation
region) to \tilde n_v and \tilde n_v^1 in Eq. 24 of Arnaud and Alouani's 
paper,
but I don't see any apparent reason as to why. 

As long as the basis is complete I think the individual densities \tilde n,
n^1, and \tilde n^1 should all be positive right? \tilde n is as you said
directly composed from the plane-waves and hence positive. Inside the
augmentation spheres, n^1 equals the exact valence density (positive) and
\tilde n^1 equals \tilde n (positive). 

Approximating vxc[n_{val}] as 
vxc[\tilde + \hat n + \tilde n_{core}] - vxc[\tilde n_{core}],
seems to introduce an extra linearization but it may be fine anyway. 

Right now, I have just removed the \hat n:s for calculating v_xc, but haven't
yet tried to converge all the parameters... I'll try it out during my
non-existing spare time ;)

Cheers,
/Daniel