Hi Scott,

I'm not sure what you're suggesting--a real simultaneous fit, which somehow weights the fit in R-space and k-space to arrive at a single set of parameters? Or just two fits in series so that you only hit one button?

first of all let me tell you that the idea of running the fit in R-space somehow disturbs my simple mind, considering that the R-space depends on the processing parameters (window type and width, weight etc). So, I would assume that a fit in k-space would be auspicable. Then, I discovered that EXCURV, the competing program at least for biological XAS, performs the fit BOTH in R-space and in k-space, and I am pretty sure that the parameters it gets are slightly different. then, yes, I was thinking of two different fits hitting the same button (let's say in Diana - or Artemis - instead of having just the option of running the fit either in R- or in k-space, one could have an additional button telling the program to run both fits)

In the first case, I'm not sure I see a big benefit considering that the weighting scheme becomes in effect another opaque parameter that can be used to generate arguments among experts. :)

that I understand, not being an expert... :-)

In the second case, it seems to me more straightforward just to run the fit twice.

OK. probably yes, but if Bruce may think of a slight improvement ... it was just an idea Regards, Stefano -- ____________________________________________ Stefano Ciurli Professor of Chemistry Laboratory of Bioinorganic Chemistry Department of Agro-Environmental Science and Technology University of Bologna Viale Giuseppe Fanin, 40 I-40127 Bologna Italy Phone: +39-051-209-6204 Fax: +39-051-209-6203 "Fatti non foste a viver come bruti, ma per seguir virtute e canoscenza" Dante Alighieri - Inferno - Canto XXVI "Ihr seid bestimmt, nicht Tieren gleich zu leben, Nein, Tugend zu erringen und Erkenntnis" "Ye were not form'd to live the life of brutes, But virtue to pursue and knowledge high"

Hi Bruce and Matt, Ok for all your explanations. Thanks! Stefano -- ____________________________________________ Stefano Ciurli Professor of Chemistry Laboratory of Bioinorganic Chemistry Department of Agro-Environmental Science and Technology University of Bologna Viale Giuseppe Fanin, 40 I-40127 Bologna Italy Phone: +39-051-209-6204 Fax: +39-051-209-6203 "Fatti non foste a viver come bruti, ma per seguir virtute e canoscenza" Dante Alighieri - Inferno - Canto XXVI "Ihr seid bestimmt, nicht Tieren gleich zu leben, Nein, Tugend zu erringen und Erkenntnis" "Ye were not form'd to live the life of brutes, But virtue to pursue and knowledge high"

Hi Matt, Thinking about problems. You once told me that:

Fitting in unfiltered k-space also gives erroneous R-factors, as was recently discussed here.

would you give me a direction to the discussion about this point that I can read? Thanks Stefano -- ____________________________________________ Stefano Ciurli Professor of Chemistry Laboratory of Bioinorganic Chemistry Department of Agro-Environmental Science and Technology University of Bologna Viale Giuseppe Fanin, 40 I-40127 Bologna Italy Phone: +39-051-209-6204 Fax: +39-051-209-6203 "Fatti non foste a viver come bruti, ma per seguir virtute e canoscenza" Dante Alighieri - Inferno - Canto XXVI "Ihr seid bestimmt, nicht Tieren gleich zu leben, Nein, Tugend zu erringen und Erkenntnis" "Ye were not form'd to live the life of brutes, But virtue to pursue and knowledge high"

Hello everybody,

Thinking about problems. You once told me that:

...

Fitting in unfiltered k-space also gives erroneous R-factors, as was recently discussed here.

would you give me a direction to the discussion about this point that I can read?

Pardon my poor knowledge of EXAFS fitting and reliability of the results, but more generally, I wondered if EXAFS fitting in raw unfiltered k-space is always relevant. Let me explain it; I do agree that in certain cases, when the whole structure is known and all EXAFS contributions well modelled by an ab-initio model (e.g., feff), you may well reproduce all oscillations of the EXAFS spectrum, and then fitting in raw k can be OK. However, more often than wanted, the fitting is done with a structural model including only the first few shells. With these shells, we model not only the actual contributions from the neighboring shells, but also that from the more distant shells. Physically, it can be demonstrated that this would not be a problem if the EXAFS signal had a constant amplitude and would spread over an infinite range in k space. However: (a) EXAFS contributions have not a constant amplitude, and (b) they can be recorded over only a few Å-1. So maybe (or even surely, I daresay), the contribution from non-modelled distant shells would affect the structural parameters from the modelled shells. Finally, another issue - for which I would not lay out my neck, though - is the noise. In EXAFS, the signal to noise increases with k, and of course fitting in the raw k space is another way of dealing conveniently with the noise -or relative uncertainty, as we may name it. However, the FT is a way of filtering out some of this noise, and so maximise the signal from a shell. Likewise, fitting in filtered q-space may yield more accurate results, because some of the noise is filtered out. However, I concur that somehow the fact that the uncertainty on the high-q part of the filtered contribution os greater than in the low q-part should be implemented somehow. So there are my own reflexions. Maybe some people have already worked on that, and there are some publications that I've missed (shame on me!). If that's the case, I would welcome any insight. Best regards, Michel Schlegel -- Michel Schlegel Commissariat à l'énergie atomique CEN de Saclay, DEN/DANS/DPC/SCP/LRSI Bat 391 - Piece 205B F91 191 Gif-sur-Yvette Cedex, France Ph: +33 (0)1 69 08 93 84 Fax: +33 (0)1 69 08 54 11

Hello Bruce,

Although I prefer to think about the EXAFS problem in R space, I don't think this is the reason to do the fit in R space. Regardless of which fitting space you use, you are relying on Feff to supply some fraction of all the Fourier components in the data.

We could also used reference-derived phase and amplitude function, as in the good ol'time ;)

The first-shell feff path only has Fourier components (or frequencies, if you prefer) corresponding to the first-shell portion of chi(R). Thus that feff path can only fit those frequencies. That's true in k-space as well as in R-space

True in R-space, and that's why Athena-Ifeffit are doing such a wonderful job at providing windows to fit only selected area of the fourier transform. Almost true also in q-space. In k-space... hmmm, well, I would love to see the mathematical demonstration of it for a limited k-range and a Feff(k) (eventhoug I agree that many people have performed tha fit in k- and R-spaces, and found about the same paramters, so it must be verified somehow).

What's more, I think the problem of non-modelled shells affecting the modelled portion of the data exists in R-space just as much as in k-space. Because of sigma^2 and the finite data range, peaks have width. In R-space, a given path is centered at a particular R-value (or, in other words, its contribution to the spectrum is dominated by a particular frequency). However, the peak has width (it contains frequencies below and above the dominant frequency). Thus longer paths always interfere with shorter paths to some extent.

I think the effect of interfering contributions in the Konigsberger and Prins. What I noticed, though, is that the fit of closer shells can affect that of the furthest shell because of the "spillof" from the first peak. The recciprocal I was not aware of. But I do agree with you on the whole. However, I think that in the FT case, these interences are limited to the nearest shells, whereas in k-space, nothing protects you from shells at, say, 2R and 3R (so to speak. Best regards, Michel -- Michel Schlegel Commissariat à l'énergie atomique CEN de Saclay, DEN/DANS/DPC/SCP/LRSI Bat 391 - Piece 205B F91 191 Gif-sur-Yvette Cedex, France Ph: +33 (0)1 69 08 93 84 Fax: +33 (0)1 69 08 54 11

Hi Michel, On Tue, 20 Sep 2005, Michel Schlegel wrote:

Pardon my poor knowledge of EXAFS fitting and reliability of the results, but more generally, I wondered if EXAFS fitting in raw unfiltered k-space is always relevant.

I would not call your knowledge of EXAFS fitting "poor". I think you've pretty much got every point exactly right. For the original question (why prefer R-space v. k-space or even Q-space for fitting), the difference is only important when there are spectral content (k- and R-range) that you want to ignore. The content you'd want to ignore is most commonly the high-R shells that you don't (yet?) have a model for. That is, if your model could account for all spectral features, fitting in k- and R-space would be equivalent. For the more common case in which the model is more limited than the data, using R-space makes it very easy to specify which components to ignore. Fitting in Q-space is nearly identical to R-space, expect for an issue you point out later.... Being able to limit the spectral content in this way is entirely to get a good measure of the fit statistics. When fitting in original k-space, you cannot say "fit the first shell and ignore the fact that I'm not modelling the second shell". As Michel points out, the limited k-range and the physics of EXAFS does mean there is 'spectral bleeding', so that the frequencies (R-values) for a single 'shell are not perfectly sharp. Looking at any plot of |chi(R)| it is pretty obvious that the peaks are not delta functions, or even particularly sharp. As Michel put it "the contribution from non-modelled distant shells would affect the structural parameters from the modelled shells". This is unavoidable, but is also generally a small effect. The best things to do are to be aware of this possibility and try to model any significant further shells than those you're really willing to say you've got right. This is why we prefer R-space to Q-space and the older approach of 'Fourier Filtering'. It is often difficult and sometimes impossible to really isolate the 'First Shell' from the 'Second Shell', which can make it dangerous to compare isolated 'First Shells' from systems with different 'bleeding' of higher shells. Michel also wrote:

Finally, another issue - for which I would not lay out my neck, though - is the noise. In EXAFS, the signal to noise increases with k, and of course fitting in the raw k space is another way of dealing conveniently with the noise -or relative uncertainty, as we may name it. However, the FT is a way of filtering out some of this noise, and so maximise the signal from a shell. Likewise, fitting in filtered q-space may yield more accurate results, because some of the noise is filtered out. However, I concur that somehow the fact that the uncertainty on the high-q part of the filtered contribution os greater than in the low q-part should be implemented somehow.

The FT does not actually filter out noise. It can be used to filter out the highest frequencies, and so the sharp spikey spectra that oftens shows up in k-weighted chi(k) at high k (where the noise is larger than the signal). Sadly, this is the part of the noise we care the least about: there is also noise with the same frequency (hopefully lower amplitude!) as the signals we're analyziing. That's not removed by ignoring the high frequency components. In general, I would say that fitting in R-space is slightly preferred over fitting in Q-space and much preferred over fitting in k-space. The only real reason it is much preferred to k-space fitting is that you can systematically ignore shells that you are not modelling. Cheers, --Matt