Hi Wojciech, I have another suggestion. It is my secret, completely untested belief (which I am now revealing to everyone on this mailing list!), that some of the cases of "successful" fits using multiple E0's are masking problems caused by not considering a third cumulant. For those who may not know the role of this parameter, it in essence measures asymmetry in the distribution associated with a path. For example, if a pair of atoms are more likely to separated by a distance considerably larger than the mean separation than by a distance considerably smaller than the mean separation, then the third cumulant is positive. (The mathematical definition is that the third cumulant is the mean cube of the difference from the mean, in the same sense that sigma2 is the mean square of the difference from the mean.) In most cases, the third cumulant is small. Nevertheless, if it were 0 in all cases, then materials would not show any expansion with temperature! Through symmetry arguments, it is pretty clear that the third cumulant is most likely to be significantly nonzero for nearest-neighbor paths. What does this have to do with fitting different E0's? E0 and the third cumulant both affect the phase of the EXAFS signal, although they are weighted in different ways by k. Nevertheless, if a nonzero nearest-neighbor third cumulant is called for, allowing a different E0 for the nearest-neighbor instead would probably also improve the fit statistically. In this case, however, while the use of a third cumulant can be justified on physical grounds relatively easily, the use of a separate E0 is an arbitrary non-physical attempt to improve the statistics. So as far as I am concerned, I am more inclined, if my fit is not quite working out, to try allowing the third cumulant for paths in the first coordination shell to vary than I am to introduce multiple E0's. In fact, I usually do this at some point during the fitting process even if my fit is behaving fairly well to reassure myself that the third cumulant is 0 to within the uncertainty of the fit, and that constraining it to 0 is not distorting the values of the parameters I am interested it. Take all of this with a grain of salt; I wrote my dissertation on the third cumulant, and, to paraphrase Bruce, since I've spent a lot of time making a nice hammer, everything tends to look like a nail... --Scott Calvin Sarah Lawrence College
I would like to address a couple of questions which are partially related to my recent struggles in fitting some EXAFS data. I'm trying to fit my data using several shells of different neighbors including a few single scattering paths and also so multiple scattering contributions (mainly collinear multiple scattering paths) all calculated with the help of FEFF 8.20. Now, I found once in the FEFFIT manual the following suggestion: one might consider using several different E0's for different paths in order to improve the fit. Ok, the explanation was based on some approximations coming from FEFF code which include incomplete core-hole shielding, lack of angular variations of the valence charge distribution and charge transfer between atoms in polar materials. My question is the following: does anyone of you have some experience with such procedure? And if yes, shall than distinguish between the first shell of nearest neighbors and the rest of the atoms in terms of their E0 corrections (using 2 parameters)? Or perhaps one can use separate E0's for each path?