[Ifeffit] Overlapping scattering paths

[Bruce Ravel]

On Sunday 16 December 2007 04:08:00 van der Veen Renske wrote:
> Hello EXAFS experts,
>
> I started using Athena and Artemis two weeks ago by applying it to the
> EXAFS analysis of a moderately complicated molecule in solution. The
> final fit is very good (R=0.006) but the errors on the fitting
> parameters are very large and there are many high correlations between
> parameters that shouldn't be correlated (even though I do multiple
> k-weighted fitting). I think the problem is that there are at least 4
> scattering pathways that overlap in the FT (spread in path lengths of
> +-0.4 Angstrom). In addition, these scattering paths involve different
> atoms and bonds, so that I have to define different delta_r and sigma_sq
> parameters for all of them.
>
> My question is now: how could I reduce the error bars of the fitting
> parameters that belong to these overlapping scattering paths? Or is it
> hopeless without further information of the system?

Hi Renske,

You question is at the very heart of the problem of EXAFS analysis.  I
hope you won't be disappointed that I do not have an easy answer for
you.

With Feff and Ifeffit, we treat EXAFS as a signal processing problem
in the sense that we consider a band width defined buy the Foruier
transform range in k and the fitting range in R.  That band width sets
some kind of upper limit on the amount of information we can ever hope
to extract from the signal.  Typically, that is not a very large
number.  Also typically, we have complicated structural problems about
which we are trying to gain insight with that limited information
content. 

The whole trick in using the Fourier transform to help us interpret
our data is to rely on different paths contributing different Fourier
components to the measured signal.  In the case of, say, the first and
second coordination shells of copper metal, that works extremely
well.  In most cases -- not so much because, as you have observed,
paths contributing significant spectral weight may have overlapping
Fourier components.

If all we have is the EXAFS signal itself, we would be stuck where you
are right now -- reasonable fits but huge correlations.  The only way
out of this problem is to rely on other information.  Sometimes that
other information might be intrinisc to the problem, other times
extrinsic.  Let me give a couple of examples.  These examples may be
pretty far away from what you are working on.  Since you gave us a
very scant description of your problem, I cannot speak directly to it.

An example of intrinsic knowledge would be the handling of the short
oxygen bond in a uranyl or plutanyl compound.  In those cases, there
is a dioxo-actinide chain consisting of two double bonded oxygen atoms
on either side of the actinide atom forming a linear chain.  These
bonds are very stiff and contribute a strong multiple scattering
signal that often overlaps with single scattering signals around 3
angstroms.  Those MS paths do not, however, require the use of new
parameters.  The bond length and sigma^2 parameters for the MS paths
can be easily written in terms of the parameters for the SS paths to
those oxygen atoms.  In that way, the contribution of those MS paths
is added correctly to the fit without having to introduce any new
parameters.  That is a good thing.

Examples of extrinsic knowledge are easy to come across.  One example
might be the temperature dependence of a sigma^2 parameter in a
temperature series measurement, which should behave like a single
frequency (or Einstein) oscillator.  Another example might be
knowledge that you bring to the problem from, say, vibrational
spectroscopy emasurements on the same compound.  In that case, you
would expect EXAFS and the other measurement to be consistent, within
the caveat that the time and length scales of the XAS measurement are
very short.

So, I don't think I have answered your specific question, but
hopefully, I have written something useful to you.  If you would like
to ask a more specific question about your problem, feel free to ask
on the list.  As you have no doubt seen even in the last two weeks
since you started using our codes, folks on the list are very
welcoming to newcomers and very generous with useful information.

Regards,
B


-- 
 Bruce Ravel  ------------------------------------ bravel at bnl.gov

 National Institute of Standards and Technology
 Synchrotron Methods Group at NSLS --- Beamlines U7A, X24A, X23A2
 Building 535A
 Upton NY, 11973

 My homepage:    http://xafs.org/BruceRavel
 EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/