[Ifeffit] Overlapping scattering paths
van der Veen Renske
Renske.vanderveen at psi.ch
Wed Dec 19 03:43:05 CST 2007
Dear Bruce
Thanks a lot for your reply! I admit that I was a bit naive in expecting
EXAFS to give me the full molecular structure with 0.01 A resolution...
I learn now that there is "no free lunch"! Nevertheless, doing EXAFS is
fun :-)
As a reply to my mail to the mailing list, somebody from the same
institution where I work contacted me and offered to help a bit out.
Your answer and his help made me to fit a very reasonable model to the
data. In case somebody is interested what exactly led to my success,
below I describe what I did. Please correct me if you think I did
something stupid.
First a short introduction to what I'm actually fitting: I measured 2
transmission spectra of a molecule of 38 atoms, containing a weak Pt-Pt
bond and 4 rigid P-O-P bridges, dissolved in ethanol. Each of the Pt
atoms is surrounded by 4 P-atoms in a square-planar way. Beside the
bridging O's, each P atom also binds to 2 terminal oxygens, one
singly-bonded and one doubly bonded. This makes the total molecular
composition: Pt2 P8 O20 H8. The ultimate goal of the project is to
measure the excited state structure of this molecule in a time-resolved
fashion.
This is what I did:
(1) I realized that the molecule in the crystal structure (used as an
input for ATOMS/FEFF) had reduced symmetry. The salt I used was a K-salt
and coulombic forces between K+ ions and the O atoms in the molecule
distort the structure. Because charges are more homogeneously
distributed in solution, I thought that a more symmetric starting
structure would be better. Therefore, I "built" my own molecule in which
especially the symmetrically equivalent P=O and P-O distances are the
same. (of course one should be very careful in building own molecules;
not every structure is thermodynamically stable. In my case the bond
distances and angles are very similar to ones in the crystal structure,
so I assume the structure is physically "possible")
(2) Because I wanted to increase the information content extrinsically,
I determined sigma_sq for the Pt-Pt distance by making use of optical
Raman measurements in solution. Assuming a harmonic oscillator, I
calculated sigma_sq from the wavenumber of the Pt-Pt vibration. In
consequent fits I fixed the value of sigma_sq_Pt to this value (if let
free one of the other sigma_sq values gets negative; this is probably
due to the correlations)
(3) I fitted from "shell-to-shell" (although in a molecule one cannot
speak of "shells", I mean distinct separated regions in the FT
spectrum). An iterative procedure of fit-grab-fix, while looking at the
statistical variables and the values of the fitting parameters, led to
the final good fit.
The present model is extremely simple: 4 SS paths (Pt-P(near),Pt-P(far),
Pt-O(bridge), Pt-Pt) and one important (nearly) colinear MS path
(4-legged P-Pt-P scattering, this path was expressed in terms of SS
paths: delr_MS=2*delr_SS and ss_MS=2*ss_MS). All the SS paths to the
terminal O atoms could be left out due to the large Debye-Waller
factors, i.e. on the order of 0.02-0.06 A^2. Including them and/or the
Pt-O-P MS paths lead to a small decrease of the R-factor, but an
increase or no change in the reduced chi-square! (HOW CAN THIS BE?)
Leaving them out has the advantage that the other fitting parameters
have smaller error bars. I am actually not sure whether I should include
them or not...they do "clean-up" the fit...but including them also
changes the values of the other parameters...
As a final result I got an R-factor of 0.01. The error bars on the
fitted values are still pretty large (up to 50%) and the correlations
between variables are still present, but at least I am confident now
that the model makes sense. From Bruce's email I understand that large
error bars and correlations are unavoidable for overlapping scattering
contributions without further (extrinsic) information. For the future I
consider measuring at different temperature in order to break the
correlations between the DW factors, although I am not sure whether this
makes sense in solution (do the DW factors change enough in solution?).
This was my fitting story. Comments/suggestions are welcome!
Regards,
Renske
> Message: 2
> Date: Tue, 18 Dec 2007 08:56:22 -0500
> From: Bruce Ravel <bravel at bnl.gov>
> Subject: Re: [Ifeffit] Overlapping scattering paths
> To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
> Message-ID: <200712180856.22803.bravel at bnl.gov>
> Content-Type: text/plain; charset="utf-8"
>
> 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/
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> End of Ifeffit Digest, Vol 58, Issue 15
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