[Ifeffit] Chi^2-Map question

[Norbert Weiher]

Dear Friends,

maybe some of you remember that I was implementing a chi^2 mapping algorithm 
using the IFEFFIT library. This is working now, and for the data analysis of 
the maps I would like to ask your opinion on the following problem:

I want to check with chi^2 maps if I can separate 2 shells, e.g. if a peak is 
comprising two O shells or only one. For this I take the one-shell fit, half 
the coordination number and then vary the distance of the shells against each 
other (all other values taking from the best single shell fit). If I find two 
contributions, I should see 2 mirror-symmetric minima centered at the 
corresponding DR values, e.g. (0,-0.1) and (-0.1,0) if I work with the same 
reference. 

These minima are separated by a saddle point which is more or less pronounced. 
In the case of some Fe complexes I simulated, it is clearly visible, while 
for my gold oxides, it is hardly seen but still there. If I take a system 
where I know there IS only one shell (e.g. Au metal) and do the map, I find 
no saddle point and correspondingly no 2 minima.

Does anyone know a relation between the height of a saddle point and the 
physical significance of the map? I would be glad to learn more about, but 
the statistic books I know don't deal with such a problem (and I am chemist 
and not a mathematician)... 

If you need an example, I can send you two slides of a recent talk which 
explain this problem more in detail - just drop me a mail.

Cheers,

Norbert

-- 
Dr. rer. nat. Norbert Weiher (weiher at chem.ethz.ch)
Institute for Chemical and Bioengineering - ETH Hönggerberg
HCI E 117 - 8093 Zürich - Phone: +41 1 63 3 48 32