[Wien] use of PW scaling factor

[L. D. Marks]

Let me add something, since I think I now have a slightly better 
understanding of when the PW term matters (and when it does not). caveat: 
these generalizations may not always be correct.

A "well posed" calculation has "good" relative sizes for the RMT's of the 
different atoms, most of the valence charge is in the muffin tins and 
enough LM's in case.in2(c). Normally the defaults + setrmt will work fine; 
perhaps add some more LM's for f electrons.

Unfortunately, in some structures two atoms are relatively close so you 
end up with small RMTs. In these cases setrmt can also not find good 
values, so be careful. In this case much of the valence density is in the 
plane waves (PW).

In the code the PWs are stored as fourier coefficients, ranging from about 
0.2 down. The density in the RMTs is (with some other terms) essentially a 
density per voxel with typical values of 100 or so down.

In any optimization or non-linear root finding method (mixing is the 
second) you can think of the relative sensitivity of the results to a 
variation, i.e.

 	d [Results] / d [Variable n]

and a similar second derivative. A well-conditioned problem has the second 
derivatives roughly the same and one often wants to include a scaling to 
try and make them similar. Because the density in the RMT and the PWs are 
very different variables, they are intrinsically badly scaled. For a well 
posed problem this does not matter because the RMTs dominate the valence 
density. For a poorly posed problem adjusting the PW scaling as detailed 
in the link below helps a lot. The code has some built in scalings (e.g. 
with the number of atoms) which help, but it is not perfect; this is an 
ongoing research topic.

For a well posed problem a big mixing (0.3-0.4) is good, the the 
convergence is quick and the PW term matters little. For a poorly posed 
problem smaller mixing (0.1-0.2) and adjusting the PW scaling makes a lot 
of difference. Really badly posed problems may require a mixing of 0.05 
and a small PW term (0.05) -- I've never had to go beyond this. Sometimes 
a problem is very badly posed because the Hamiltonian is incorrect. An 
example of this is trying to solve NiO in a cubic cell without spin 
polarization.

On Sun, 23 Jul 2006, Saeid Jalali wrote:

> Regarding your first question you would see:
>  http://zeus.theochem.tuwien.ac.at/pipermail/wien/2005-May/005277.html

-----------------------------------------------
Laurence Marks
Department of Materials Science and Engineering
MSE Rm 2036 Cook Hall
2220 N Campus Drive
Northwestern University
Evanston, IL 60208, USA
Tel: (847) 491-3996 Fax: (847) 491-7820
email: L-marks at northwestern dot edu
http://www.numis.northwestern.edu
-----------------------------------------------