Dear Igor,
 
Your problem is very interesting: the dependance of EXAFS analysis results on the FEFF model, and I am cc'ing my response to the group. Obviously, there does not exist a unique way to solve it. It is also true that it is important to know which set of results to choose because if you apply s02 to analyze your unknown compounds, whether it is 0.8 or 1.0 matters. There are several approaches that keep you from breaking your head trying to understand the underlying physics between SCF and nSCF and which of the two values of E0 are better . To choose which model is better, you have to approach it systematically by applying these models (SCF, nSCF and SS) to different systems where you know what debye waller factors should be (e.g., by performing temperature-dependent studies and comparing the resuls you obtained for DWF against those predicted by Einstein or Debye models. This has been done by many and it is a foolproof method. However, it is hard to do temperature dependent studies in solutions, and thus your options may be limited. You can also analyze pure Cu foil data measured in the same conditions at the same beamline, and obtian its S02 (it should be about 0.95 as I remember) and then impose it on your Cu2+ complex. However, this procedure does not allow the S02 in aqueous solutions to be slightly different than in the bulk Cu compounds, and we know that they may be different because the chemistry is strongly different, chemical potentials are discontinuous, and the argument of chemical transferrability of amplitudes and phases may not work. Also, it doesn't answer the question which FEFF calculation to prefer for the analysis of the complexes, but it helps a bit because it gives you some ballpark estimate what S02 should be.
 
So, the first approach is to take S02 from Cu foil or Cu oxide data and impose it on the Cu in solution data. It may be a good start. By the way, in your case, both answers deviate by 10% from the average value: S02 = 0.9. That means, if you do not know which model is more reliable, pick 0.9 and your coordination numbers will be defined with 10% accuracy. It is a good accuracy in case of solutions.
 
The second important question is what to do with E0 and distances. They do correlate, as your results show, and they should. However, the first nearest neighbor (equatorial) distances are identical between the two models. The second, axial, distances are different but overlap within the uncertainties. May be that one should be preferred that gives more realistic E0? Unfortunately, E0 is loosely defined in XAFS analysis (FEFF sets it at the muffin tin level) and it can be within 10-20 eV above Fermi energy. Since Fermi energy must be below 1s-3d transition energy, both of your results are, technically, legitimate. Unfortunately, there is no way to tell what should be the r_axial - partly, because it depends on pH and other factors, but it looks like both your models do give good agreement with expectations.
 
What all these models have in common is that they are all based on theoretical calculations which means that they contain a black box and are hard to check experimentally. Some time ago, I adjusted FEFFIT to solve these problems by "bypassing" the black box part of them. I used an old-fashioned way of EXAFS analysis by using experimental standards instead of theoretical standards. For example, if you are certain that Cu2+ in aqueous solution is octahedrally coordinated, you can use this data set as experimental standard. If you extract the scattering amplitude and phase from this data set, the amplitude function will contain f(k) and S02 in it, and thus it spares you from trying obtaining it from the fit unambigously. Moreover, the phase function will have E0 and delta(k) informations in it as well, and if you align your standard and unknown in energy, the best results for delta r will be less model dependent if you relied on E0 obtained by FEFF.
 
Here is a short paper where this method is explained in detail. 
 
http://pubweb.bnl.gov/people/frenkel/EXP-FEFF/thiols.pdf
 
Regards,
 
Anatoly
 
Anatoly Frenkel
Yeshiva University
anatoly.frenkel@yu.edu

 

-----Original Message-----
From: Igor Frota de Vasconcelos [mailto:idevasco@nd.edu]
Sent: Tuesday, February 08, 2005 9:39 AM
To: Frenkel, Anatoly
Subject: Re: About Cu2+ xafs

Dear Dr. Frenkel,

Thanks for your message!

I will try put the whole story in a nut shell without leaving important details out! I am working with two different models for my hydrated Cu2+.

The first one is a simple one with four water molecules on the equatorial plane, and two in the z axis. The four equatorial O's are 2 A away from the central Cu while the two axial O's are 2.29 A. I positioned the hydrogen atoms according to some molecular dynamics simulations of hydrated Cs and Pb (MD simulation of hydrated Cu2+ is harder because of the Jahn-Teller distortion). I also put eight water molecules in a second shell at 3.95 A to try to minimize truncation effects in the self-consistent calculation. I then used feff8.20 to calculate paths self-consistently (I will call this SCF) and not self-consistently (nSCF).

The other model is the one you suggested in the mailing list (I'll call this one SS).

The results using the latest linux based horae package are (the subscripts e and a denote equatorial and axial O's (I did not include results from multiple-scattering and hydrogen paths):

1) SCF:

S02     =     0.9982900   +/-      0.0616710  
E0      =    -7.5800660   +/-      0.5694190 
dr_e    =    -0.0443480   +/-      0.0034370   =>  r_e = 1.955652 +/- 0.0034370
ss_e    =     0.0069170   +/-      0.0004820 
dr_a    =    -0.0760780   +/-      0.0346330   =>  r_a = 2.213922 +/- 0.0346330
ss_a     =     0.0320830   +/-      0.0076460  

  Reduced chi-square                  : 466.198889482
  R-factor                                    : 0.000652086
  Measurement uncertainty (R)  : 0.000306860

2) nSCF:

S02        =     0.7977480   +/-      0.0758730  
d_E0      =     1.1833490   +/-      0.8799960  
dr_e      =    -0.0448740   +/-      0.0057950    =>  r_e = 1.955126 +/-      0.0057950
ss_e        =     0.0051430   +/-      0.0008710  
dr_a       =    -0.0107380   +/-      0.0451450   =>  r_a = 2.279262  +/-   0.0451450
ss_a       =     0.0338300   +/-      0.0138210  

  Reduced chi-square                  : 2078.758619285
  R-factor                                    : 0.003396526
  Measurement uncertainty (R)  : 0.000306860

3) SS:

S02        =     0.8082010   +/-      0.0866670  
d_E0      =     1.1847890   +/-      1.6045490  
dr_e       =    -0.0329940   +/-      0.0067630   =>  r_e = 1.957006  +/-   0.0067630
ss_e       =     0.0049640   +/-      0.0008280   
dr_a       =    -0.0959300   +/-      0.1364220   =>  r_a = 2.194070   +/-    0.1364220 
ss_a       =     0.0460070   +/-      0.0358600   


The nSCF and SS results are very similar but some SS errors are significantly larger. Therefore I will base my comments and comparisons on the SCF and nSCF results.

As you can see, the structural parameters are pretty much within error! S02 and d_E0 however, differ quite a lot. Although the d_E0 of 1.18 from the nSCF seems more reasonable than the -7.58 value from the SCF, the SCF fit is much better (lower reduced chi-square and R-factor). The S02 values are not within error. My problems are, then, two-folded:

The first is a practical one: I don't know which S02 and d_E0 to pick and it is really bad because nailing them down (specially S02) is the whole purpose of the analysis of this standard.

The second problem is of philosophical nature and more important than the first one because its clarification will provide the answer for the first problem and also some peace of mind. I do not understand why the E0 corrections (d_E0's) are so different. The fact that the correction obtained from SCF calculation is larger (and apparently worse) than that obtained from the nSCF calculation (absolute values) seems counter intuitive to me. The E0 value I picked for background subtraction is 8989 eV, and applying the corrections, I find an edge energy of 8990.1 eV and 8981.5 eV respectively.  This second value falls in the pre-edge region, pretty much on the 1s-3d transition bump. Despite the evidences, I tend to trust the SCF's d_E0 value the most but would like to understand the physics (or lack of) behind the different feff calculations!

I apologize if I bored you with unecessary details! Thank you very much for your attention and willingness to help! I really appreciate it!

Best regards,

Igor

Anatoly Frenkel wrote:
Dear Igor,
 
I am getting back to your question now. It would help if I knew what E0 value you are getting. What is the value of s02 that you are obtaining? How are you modeling the Cu2+ standard compound? Are you using a bulk reference of a Cu-O bond (e.g., by using CuO oxide, or you are using a method in one of the IFEFFIT posts that I suggested (by using SS and OVERLAP cards)?
 
If you tried one but not another, it is important that you compare them because the small clusters have all sort of truncation effects that cumulatively change photoelectron scattering amplitude and phase from those in the bulk.
 
If both models produce similar FEFF paths for the first nearest Cu-O distance, it does not matter which one to choose in order to fit the standard compound. If they are different, use them separately when you fit the EXAFS data, and see which one gives you a more reasonable values of s02 and E0.
 
I'll wait until I have a feedback from you because without knowing exactly what you are doing it is hard to give advice on what to do.
 
From my experience with different Cu2+ complexes, these systems can be reliably analyzed. Let me know where you are getting stuck.
 
Regards,
 
Anatoly

[Anatoly Frenkel] 
 
 
From: Igor Frota de Vasconcelos [mailto:idevasco@nd.edu]
Sent: Wednesday, January 26, 2005 12:16 PM
To: Frenkel, Anatoly
Subject: About Cu2+ xafs

Dear Dr. Frenkel,

I am Igor Vasconcelos and I work under the supervision of Dr. Bruce
Bunker at the University of Notre Dame's Physics department.

I am currently working with some XAFS data on Cu(II) adsorbed on
bacterial cell walls. I started out with (Cu(H2O)6)+2 standard to have a
better feeling about the Cu+2 systems and to obtain a reliable estimate
of S02 to use in the samples' fits.

I am using SCF FEFF8.20 paths to fit the data and, although structural
parameters make sense, I have exhausted my resources and still haven't
understood a rather strange Eo value I am getting. I suspect it has to
do with the way feff performs the calculations. I understand you have an
extensive knowlegde on this system and I am hopeful you will be willing
to provide me some help. I have followed recent posts in the ifeffit
mailing list from you and I have two of your papers (Env. Science Tech.
1998 and 2000) on the  subject as references.

I would be very grateful if you would take the time to receive my
question and answer it, in case you have the time and the inclination.

I am looking forward to hearing from you. Thank you in advance for your
attention,

Igor


--
IGOR F. VASCONCELOS
Department of Physics
University of Notre Dame
225 Nieuwland Science Hall
Notre Dame, IN   46556    USA

phone: (1 574) 631 5650
fax:   (1 574) 631 5952
e-mail: idevasco@nd.edu
www.nd.edu/~idevasco 


-- 
IGOR F. VASCONCELOS
Department of Physics
University of Notre Dame
225 Nieuwland Science Hall
Notre Dame, IN   46556    USA
phone: (1 574) 631 5650
fax:   (1 574) 631 5952
e-mail: idevasco@nd.edu
www.nd.edu/~idevasco