[Ifeffit] more fun with FFTs

....to clarify my earlier remarks... The experimental chi is the amplitude times the sine of the phase, and is of course a real number. However, if you determine the amplitude and phase, you do it by separating the real chi into two complex functions Amplitude*Sin(phase) = (Amplitude*(Exp(I phase) - Exp(- I phase))/(2 I) which have most of their spectral power at distinct locations in the r-space transform. This is done by k->r transform, zeroing one of terms, multiplying by 2I, and backtransforming r->k. The amplitude and phase are easily determined from the real and imaginary parts of the complex result. When using Fourier methods it is most useful to look at chi as the imaginary part of this "complex chi"= Amplitude Exp(I phase), and that was what I meant. It's just like saying the "scattering amplitude" F(k) and phase are two components of the complex scattering ampltude: scattering amplitude = |scattering amplitude| * Exp(I scattering phase). This mathematics is implicit in all of scattering theory and XAFS in particular. Regarding window effects, I think the most useful way to think about them is to realize the Fourier transform of windowed weighted chi is the convolution of the fourier transforms of the k-window and the unwindowed weighted chi (convolution theorem). What the window does is give an r-space transform that is the convolution of a scraggly function (~ sin(x)/x for a sharp k-space cutoff) with the nice peak you (probably) would have had if you had an infinite range of chi. The width of the r-space peaks and the structure of the side lobes is principally due to the fourier transform of the k-space window. If the k-window doesn't have sharp corners (like a box does) its fourier transform will be smoother and there will be less truncation ripple in r-space. That's why tapered windows are helpful. One is free to use arrays of other lengths, or to eschew zero padding altogether, but I don't think the transforms would be very useful at a quarter angstrom sampling, certainly not in the sense they normally are. thanks - grant On Wed, 9 Jun 2004 ifeffit-request@millenia.cars.aps.anl.gov wrote:

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Today's Topics:

1. Re: E0 correction in EXAFS fitting (Matt Newville) 2. more fun with FFT's (Grant Bunker) 3. Re: more fun with FFT's (Scott Calvin)

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Message: 1 Date: Wed, 9 Jun 2004 13:19:22 -0500 (CDT) From: Matt Newville Subject: Re: [Ifeffit] E0 correction in EXAFS fitting To: XAFS Analysis using Ifeffit Message-ID: Content-Type: TEXT/PLAIN; charset=US-ASCII

Dear Wojciech,

It seems like this question has been asked many times, possibly in slightly different form.

Feff's choice of E0 can be off by several eV. Also, Feff is not good at distinguishing formal oxidation state. So believing Feff's E0 may not be the best idea. In my experience, Feff tends to pick an E0 that is relatively far up the main absorption edge, generally several eV above the maximum of the first derivative. That's consistent with the traditional lore that says the max of the first derivative is the Fermi level, not E0 (lowest unoccupied orbital).

If athena/autobk pick E0 to be on a sharp pre-edge peak, you probably want to move it. But the best placement for E0 is not easy to make when there is a large pre-edge peak.

One camp says that since there is absorption, then it's at E_0, and the pre-edge peak is really the absorption edge, followed by a large negative EXAFS 'black line' oscillation that nearly sends mu(E) to zero. The other camp invokes localized states (either excitons or empty molecular orbitals) to say the pre-edge peaks are really quasi-bound transitions, but below the real continuum. I'll try to avoid that debate.

I couldn't tell whether there was a large pre-edge peak followed by the main absorption edge or a very large white line. If I understand, it sounds like Feff is trying to put E0 at the pre-edge peak... is that correct?

I'm sure that leaves unanswered questions, but I hope it helps show the general level of confusion about E0.

--Matt

On Tue, 8 Jun 2004, it was written:

...

Dear Bruce and other mailing list users,

I have a very basic question concerning the choice of E0 in EXAFS data analysis. Recently I have been working on Ru solvated complex. I don?t go into too many details but I can say it?s a pretty large molecule in aqueous solution with 3 ligands containing 6 N atoms and 30 C atoms in D3 symmetry. Now, we have measured the L3 edge XANES and EXAFS of this molecule and I have recently tried to analyze it. Now, what bothers me a lot is the following observation: once I start processing the data (meaning background removal, pre-edge subtraction etc.) AUTOBK in both Ifeffit and Athena ?proposes? to place the edge energy E0 at the inflection point of the spectrum which lies at about 2838-2839 eV (which corresponds to atomic Ru L3 edge absorption energy). You might say it?s ok but I cannot accept this value. The inflection point lies on a huge pre-edge peak which is the 4d bound-to-bound transition (white line) which in principle I don?t want to include in my chi(k) because it?s still below the ionization energy as I understand it. I guess the continuum states should start higher in energy and actually from other spectroscopies one would suspect the E0 to be around 2847 eV (so about 7-8 eV higher in energy space). Now I set my E0 to this value and I started fitting the spectrum with FEFF calculation performed on crystalline structure of the same complex. What I end up with is always E0 correction for the first shell of neighbors (meaning N atoms) between -6 to -7.5 eV. I check in chi.dat and xmu.dat files that in my FEFF calculation the k=0 value was assigned to approx. 2839 eV so it?s the same atomic value again. However I know it shouldn?t be like that (apart from a simple fact that Ru in my compound is in its 2+ oxidation state which surely moves the E0 toward higher energies, doesn?t it?). So, I tried to fool FEFF and make some tricks like shift my data in energy space or fit the white line and subtract it form the data but it always consistently converges to place the E0 value at the first inflection point meaning between 2839-2842 eV. I thought that when fitting the experimental data with FEFF scattering paths one can choose E0 and then refine its value by shifting the FEFF-calculated E0 by the amount which comes out of the fit. So if I have some value of E0 coming out of my fit then I just shift the initial k=0 value as estimated by FEFF using k? -> sqrt( k-E0(2m/h_bar^2) ) (in other words the negative E0 correction would always shift the origin in k-space towards larger k values which means lower values in energy space). Ok, so now my question is the following: is there an explicit way to set E0 value before letting FEFF to do its job or it will always use the tabulated atomic value? So, if I don?t know my E0 a priori how can I refine it for a complex or molecule which has different oxidation state than 0? I mean it?s a serious question in my opinion and I wish I could get some feedback from people who have been doing it for so many years. I hope I made my point clear enough to you. Let me know if you need any more feedback in order to answer my question. I?ll be glad to give more details. Best regards,

Wojciech

********************************************************************* Wojciech Gawelda

Laboratoire de Spectroscopie Ultrarapide (LSU) Institut des Sciences et Ing?nierie Chimiques (ISIC), Facult? des Sciences de Base (SB-BSP) Ecole Polytechnique F?d?rale de Lausanne (EPFL)

CH-1015 Lausanne-Dorigny, Switzerland Tel.: +41 (21) 693 0452 Fax.: +41 (21) 693 0422 E-mail: mailto:wojciech.gawelda@epfl.ch wojciech.gawelda@epfl.ch WWW: http://lsu.epfl.ch http://lsu.epfl.ch *********************************************************************