Re: [Ifeffit] Overlapping scattering paths

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 Subject: Re: [Ifeffit] Overlapping scattering paths To: XAFS Analysis using Ifeffit Message-ID: <200712180856.22803.bravel@bnl.gov> Content-Type: text/plain; charset="utf-8"

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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

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parameters that belong to these overlapping scattering

On Sunday 16 December 2007 04:08:00 van der Veen Renske wrote: the fitting paths? Or is it

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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@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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