[Wien] Convergence problem for the slab calculation!

[L. D. Marks]

Let me answer this in a little detail, at the same time expanding a little 
about the issues with mixing.

In the SCF calculation, you are trying to solve for a problem of form
 	x_n = x_n+1
where x_n is a big vector with all the charges in the RMT's and the plane 
wave coefficients at the end of cycle n, x_n+1 similarly at the end of 
cycle n+1. The method used is what is called in the mathematics literature 
"Broyden's bad method", since Broyden did not think that much of it and 
the mathematicians have as a consequence not used it too much (I don't 
think it deserves it's bad reputation).

In a problem like this what becomes important is the sensitivity to small 
changes in the variables, for instance the derivative of the total energy 
with respect to a change in the density at a single point in the RMT, or 
one of the plane wave coefficients. If you look at what these values are 
(e.g. look at your case.clmsum) you will see that the values inside the 
RMT's are large, e.g. 10 or so, whereas the values of the plane wave 
coefficients are small, e.g. 0.05. Hence the derivative (sensitivity) with 
respect to changes in the density at a single point in the RMT is small, 
whereas that for one of the plane wave coefficients is large.

The plane wave scaling term used in case.inm does some remedial action for 
this, reducing the sensitivity to changes in the plane wave coefficients 
in a slightly empirical "user control" fashion. Unfortunately, as 
currently constructed in the code this cannot be done on the fly, and in 
fact scaling variables "right" is a very tricky issue. I'm working with 
someone to try and come up with something better, no progress as yet.

On Tue, 20 Dec 2005, Michael Gurnett wrote:

>
> Wouldn't this type of test be possible to incorporate in the scf so that
> these parameters are adjusted "on the fly"
>
> Michael
>

Note: if you have an old email address for me, please note that "nwu" has
been changed to "northwestern".
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Laurence Marks
Department of Materials Science and Engineering
MSE Rm 2036 Cook Hall
2220 N Campus Drive
Northwestern University
Evanston, IL 60201, USA
Tel: (847) 491-3996 Fax: (847) 491-7820
email: L-marks at northwestern dot edu
http://www.numis.northwestern.edu
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