Debye-Waller factors for MS paths
Dear everyone, One of the features of constructing models with Ifeffit is that we are forced to think long and hard about the parameters to use for each path. In particular I have had a great deal of difficulty in deciding how to approach the Debye-Waller factors for with multiple scattering (MS) paths. The ideal approach is to define the D-W factors for the MS paths in terms of the factors for the single scattering paths. That way you add no further variables to the model. But if you think about it you will realise that you cannot simply add all the relevant SS factors up to get a sum for your MS path - it all depends on the geometry, the direction of vibration, correlation of vibrations, etc. Its all a bit tricky for those of us dealing with intense MS paths. So what I am asking is, does anyone know of a general method or approach to define the Debye-Waller factors for MS paths (in terms of SS paths or otherwise)? How do all you Ifeffiters deal with the problem? I've found a few papers that discuss it (listed below) but they generally assume that all vibrations are uncorrelated, which is seldom a realistic situation in continuous solids. Munoz-Paez, A. (2000). Inorganic Chemistry 39(17): 3784-3790. Sakane, H. (1998). Journal of the American Chemical Society 120(40): 10397-10401. Haskel, D. (1998). PhD thesis, University of Washington. (appendix) http://www.aps.anl.gov/xfd/people/haskel/PS/thesis.ps Is there anything out there that I've missed? I'd be particularly interested in anything relating to continuous solids or correlated vibrations. Comments/questions/pearls of wisdom very welcome. Peter Peter Southon Research Fellow - School of Chemistry University of Sydney, NSW 2006, Australia +61 2 9351 4425
Hi Peter, On Wed, 14 Jan 2004, Peter Southon wrote:
So what I am asking is, does anyone know of a general method or approach to define the Debye-Waller factors for MS paths (in terms of SS paths or otherwise)? How do all you Ifeffiters deal with the problem? I've found a few papers that discuss it (listed below) but they generally assume that all vibrations are uncorrelated, which is seldom a realistic situation in continuous solids.
Shelly gave excellent advice for how to deal with this problem, but the overall answer to 'is there a general method for defining MS Debye-Waller Factors' is still no.
Is there anything out there that I've missed? I'd be particularly interested in anything relating to continuous solids or correlated vibrations. Comments/questions/pearls of wisdom very welcome.
There has been some work to use a set of force constants to generate MS DWFS, and attempts made to generate these from (close to) first principles. There was work along these lines by A. Poiarkova and Rehr (including Poiarkova's thesis) which describes generating DWFs this way. Probably A Poiarkova and JJ Rehr, PRB 59 948-957 (1999) is the best reference. This approach aimed to calculate the DWFs, not to necessarily model/fit them. This work could, in principle, be turned around to allow a parameterized fit using a few force constants that generated the appropriate sigma2. Similar work has been done (or is being done) by N. Dimakis and G. Bunker (I'll probably get in trouble for calling them similar, as the approaches are pretty different, but both aim to calculate EXAFS DWFs from nearly first principles). I believe N Dimakis and G Bunker, PRB 65 201103(R) (2002) is the place to start. To me, this work seems to be a little more straightforward to parameterize for a fit, but it would be real work to try to put such capabilities into ifeffit. I don't have a good feel for how general either of these approaches is or what the prospects of using them "in general" is. Hopefully John or Grant can correct anything I've misrepresented!! It sure would be nice to have something like this available in ifeffit, wouldn't it? --Matt
Matt, Peter, et al. On Wed, 14 Jan 2004, Matt Newville wrote:
Similar work has been done (or is being done) by N. Dimakis and G. Bunker (I'll probably get in trouble for calling them similar, as the approaches are pretty different, but both aim to calculate EXAFS DWFs from nearly first principles). I believe N Dimakis and G Bunker, PRB 65 201103(R) (2002)
is the place to start. To me, this work seems to be a little more straightforward to parameterize for a fit, but it would be real work to try to put such capabilities into ifeffit.
I am suspect that Grant Bunker reads the list but if he doesn't I can at least tell you what I know. Their method uses first principles to calculate DW factors for target molecules (imidazole, for example). They then use these calculations to parametrize the DW parameters for systems containing this molecule. It is an extremely computationally intensive approach which may or may not be possible for extended solids. However, for molecules, it is very promising because you can build up a data base, determine analytic parameters and then use it for all similar molecules. Carlo -- Carlo U. Segre -- Professor of Physics Associate Dean for Special Projects, Graduate College Illinois Institute of Technology Voice: 312.567.3498 Fax: 312.567.3494 Carlo.Segre@iit.edu http://www.iit.edu/~segre
I have to agree with Matt Newville, that "The overall answer to 'is there a general method for defining MS Debye-Waller Factors' is still no." One of the reasons for this is that there seems to be insufficient information in the experimental spectra, even with temperature dependent data, to determine all the relevant MS DW factors with reasonable accuracy. In my view it is more efficient to fit, not to the DW factors directly, but instead to the much smaller number of spring constants that implicitly define all the MS DW factors. Krappe and Rossner have implemented this with their Bayesian analysis approach [Phys. Rev. B66, 184303 (2002)] with reasonable results. They used the fast recursion approach of Poiarkova and myself [J. Synchrotron Rad. 8, 313 (2001)] to caclulate the MS DW factors from the springs. The recursion method is implemented in FEFF8 to 2nd order, but it is reasonably straightforward to extend it, as Krappe and Rossner have done. An advantage of their Bayesian approach is that one can take advantage of a priori data, such as ab initio calculations of spring constants (e.g., as Grant has described or from other ab initio codes like GAUSSIAN, WASP, etc.) as good starting points in a fit and for calculations of the spring constants that cannot (due the limited information in the data) be fit. Work along these lines is in progress here at UW, which hopefully, will help with the goal "It sure would be nice to have something like this available in ifeffit" J. Rehr
participants (4)
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Carlo U. Segre -
John J. Rehr -
Matt Newville -
Peter Southon