bond distance resolution and correlation of parameters in MS analyses?
Hi, I would like general opinions of some EXAFS practioners in regards to the most widely accepted methods for bond distance resolution and correlation of parameters in both single scattering (SS) and multiple scattering (MS) EXAFS refinements and if these can be said to differ? 1)Does the equation for bond distance resolution (r = pi/2deltak) only apply to SS? I have held the opinion that this can be applied to MS analysis however I have recently been informed that this equation does not correctly describe distance resolution in MS analyses. The paper in Coord. Chem. Rev. 2005, 249, 141-160 describes this and is this concordant with the views of the wider EXAFS community? 2) What is the actual equation which defines the determinacy of a fitting procedure and does this differ between SS and MS analyses? For MS analyses there has been a recently published equation (Coord. Chem. Rev. 2005, 249, 141-160) which takes into acount the number of dimensions used in the analyses and is this only relevant to MS analyses of data? This has also been expressed in the paper by Binsted (Biochemistry. 1992, 31, 12117-12125) however a different equation has been detailed by Stern (Phys. Rev. B. 1993, 48, 9825-9827) which I have been using as a guide in my MS analyses. Is this acceptable? Any thoughts and opinions would be greatly appreciated as this relates directly to corrections suggested to be made to my PhD thesis! Many thanks, Mark
On Wednesday 06 June 2007, MarkBondin wrote:
1)Does the equation for bond distance resolution (r = pi/2deltak) only apply to SS? I have held the opinion that this can be applied to MS analysis however I have recently been informed that this equation does not correctly describe distance resolution in MS analyses. The paper in Coord. Chem. Rev. 2005, 249, 141-160 describes this and is this concordant with the views of the wider EXAFS community?
Mark, Strictly speaking, that equation doesn't have anything to do with EXAFS. That is the equation that tells you what your Fourier component resolution is in a general Fourier analysis problem. It just so happens that, in the case of single scattering EXAFS analysis, that equation is easily interpreted in terms of photoelectron wavenumber k and SS path length r. The equation is neither different nor incorrect for MS analysis. That's true becuase MS analysis isn't any different from SS analysis. In either case, you do a Fourier transform. In either case, you attempt to model Fourier components using the contributions from some number of scattering geometries as computed by theory. In either case, you are asking yourself if you can actually resolve small differences in phase of the various things that contribute to the fit. The only difference lies in how you *interpret* the physical meaning of the Fourier components. And even then, things aren't so very different. In the case of SS analysis, you assert that the R axis is a measure of "bond length" while for MS analysis the R axis is a measure of "half path length" -- acknowledging, of course, that there is a phase shift in the EXAFS equation such that the R axis actually measures something a bit shorter than the bond or half path length. Off the top of my head, I don't recall the paper you cite and I most certainly cannot speak for the "wider EXAFS community". Speaking for myself, the physical interpretation of the equation for Fourier component resolution may change when you consider MS paths, but to claim that a property of the Fourier transform somehow becomes invalid when you change the details of the fitting model is just silly. B -- Bruce Ravel ---------------------------------------------- bravel@anl.gov Molecular Environmental Science Group, Building 203, Room E-165 MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007 Argonne National Laboratory phone and voice mail: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://cars9.uchicago.edu/~ravel EXAFS software: http://cars9.uchicago.edu/~ravel/software/
On Wednesday 06 June 2007, MarkBondin wrote:
2) What is the actual equation which defines the determinacy of a fitting procedure and does this differ between SS and MS analyses? For MS analyses there has been a recently published equation (Coord. Chem. Rev. 2005, 249, 141-160) which takes into acount the number of dimensions used in the analyses and is this only relevant to MS analyses of data? This has also been expressed in the paper by Binsted (Biochemistry. 1992, 31, 12117-12125) however a different equation has been detailed by Stern (Phys. Rev. B. 1993, 48, 9825-9827) which I have been using as a guide in my MS analyses. Is this acceptable?
1. I don't know what you mean by the word "determinacy". In any case, I thought I made it clear in my last post that, in my opinion, the differences between SS and MS analysis are in the physical interpretation and not in the statistical interpretation. Feff, Ifeffit, and Artemis certainly go to great lengths to downplay the differences between SS and MS paths in the context of the formalism of the theory and analysis, instead emphasizing their differences only in the context of physical interpretation. 2. Argonne's library only has access to the last year of Coord. Chem. Rev. and I don't have time this week to go fetch it from the stacks. So I cannot comment on that paper. 3. The paper by Stern should be read with some care. The argument Ed makes in that paper can only be true in the case of a perfectly packed signal. EXAFS data, although treated as signal processing problem, is never perfectly packed. The Nyquist criterion is an upper bound on the information content, but the actual content of the data is always somewhat less. There are some very fine papers by Rossner and Krappe about using Baysian techniques to find the actual information content of the EXAFS signal. The executive summary is that if think you need Ed's magic "+2", you are probably overusing the information content of your data. Most of us here in this list aren't as careful in practice as all that Baysian stuff. In general, one tries to stay "well below" the Nyquist upper bound. If your fitting parameters make sense physically, if the correlations are not "too high", and if the error bars on your parameters are not "too big", then you are probably not overusing the information content of your data. What is "too high" and "too big"? Well, I am purposefully using squishy language. It is kind of difficult to use Gaussian statistical techniques on EXAFS data, despite the fact that that's exactly what Ifeffit does. The reason is that Gaussin statistics presumes that your measurememt errors are statistical and normally distributed. In practice, exafs analysis is dominated by systematic uncertainties. Things like detector or sample non-linearities and the approximations made by Feff are much bigger sources of error than shot noise for most experiments. Most of those systematic problems are present in your analysis, but I have no idea how you could possibly quantify them. Hence I find myself using squishy language to discuss fit statistics. Read the papers by the frequent contributors to this mailing list. Scott Calvin and Shelly Kelly in particular are careful EXAFS practitioners who work on tough analysis problems and deal well with these issues. Doing what they do may not be as right as possible, but it certainly ain't wrong. HTH, B -- Bruce Ravel ---------------------------------------------- bravel@anl.gov Molecular Environmental Science Group, Building 203, Room E-165 MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007 Argonne National Laboratory phone and voice mail: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://cars9.uchicago.edu/~ravel EXAFS software: http://cars9.uchicago.edu/~ravel/software/
HI Mark,
Any thoughts and opinions would be greatly appreciated as this relates directly to corrections suggested to be made to my PhD thesis!
This is going to re-iterate most of what Bruce said, but since you asked:
1)Does the equation for bond distance resolution (r = pi/2deltak) only apply to SS?
No. It applies to all EXAFS.
I have held the opinion that this can be applied to MS analysis
You have been right.
however I have recently been informed that this equation does not correctly describe distance > resolution in MS analyses. The paper in Coord. Chem. Rev. 2005, 249, 141-160 describes this > and is this concordant with the views of the wider EXAFS community?
You were mis-informed. This paper is profoundly wrong, and is not concordant with the views of the wider EXAFS community, as defined by the standards and criteria documents at http://www.i-x-s.org/OLD/subcommittee_reports/sc/err-rep.pdf This paper states that the number of independent points in an XAFS data set is: N_i = [ 2*(rmax - rmin) * (kmax -kmin) / pi ] + Sum D*(N-2) + 1 Here rmin,rmax,kmin, and kmax are the spectral ranges. I cannot tell what the sum is over, but D is the "dimension with a restrained part of the model (ie, three for a three-dimensional model)" and N is "the number of independent atoms within the restrained group of the model". The ( Sum D*(N-2) ) term asserts that the number of independent points in the data is dependent on the model. This is complete nonsense. For what it's worth, the standards and criteria report cited above recommends using N_i = [ 2*(rmax - rmin) * (kmax -kmin) / pi ] rounded to the nearest integer. The report is has a bit more to say, but note that it is carefully (and deliberately) silent on "+1", "+2", etc. This is because N_i is an estimate of the maximum number of parameters that can be extracted from a signal. If you're quibbling whether to add 1 or 2 to this number, it probably means you should really subtract 4. Now, one may apply a variety of modeling approaches (tricks?? assumptions??) to the analysis of multiple scattering in highly constrained three-dimensional models that are often associated with organo-metallics. For example, a histidine ring attached to a metal will give multiple scattering, and you can usually assert that the ring is rigid, though you may need to refine its location and orientation relative to the metal. That makes the bond distances and angles (and MS amplitudes) for all the scattering paths from this ring all dependent on a reduced number of variables. It does not add information to the data. Cheers, --Matt
participants (3)
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Bruce Ravel -
MarkBondin -
Matt Newville