Theory of EXAFS

We will consider the theoretical description of EXAFS based on the single-scattering short-range order formalism. The EXAFS can 

Here p E) is the total absorption coefficient at energy E and /jl0 is the smooth atomlike absorption coefficient. In order to be able to extract structural information from the EXAFS, we need to go from the energy to the wave vector form using the formulation  

Here I have divided the expression into two terms which correspond to an amplitude factor (a) and an oscillatory component (b). I will now consider each of these terms in some detail. 

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In the theory of EXAFS it is usual to consider the wave vector k of the wave associated with the photoelectron rather than the wavelength X. They are related by... 

Theories of EXAFS (26.30) based on the scattering of an ejected photoelectron by atoms in the coordination shells surrounding the central absorbing atom give an expression for xW of the following form ... 

E.A. Stem. Theory of EXAFS. In D.C. Koningsberger and R. Prins, editors, X-Ray Absorption. Chemical Analysis, Volume 92. John Wiley Sons, New York, 1988. 

Stern EA (1988) Theory of EXAFS. In Koningsberger DC, Prins R (eds) X-ray absorption. 

The theory of EXAFS has not yet been extended beyond elements. Obviously it will be there that the advantages of EXAFS will show up, because the environments of atoms of different species will be recorded separately, something one diffraction experiment alone cannot achieve. Therefore EXAFS promises to provide valuable complementary information about the short-range order of amorphous semiconducting compounds and alloys, Sayers, Lytle and Stern (1972). 

There have been a number of recent review articles on the application of EXAFS spectroscopy to the study of metalloproteins [1-8]. The theory of EXAFS spectroscopy and the historical development of the field have also been extensively discussed [1-5,7-19]. Here we will briefly cover the practical aspects of data analysis for biological heme (iron porphyrin) systems eind the appropriate model complexes. We will then focus on the EXAFS of two types of biological heme system (a) thiolate-ligated heme enzymes and (b) oxo-ferryl [oxo-iron (IV), Fe =0] states of heme enzymes. All of the enzymes discussed herein have in common the iron protoporphyrin IX ( heme ) as the prosthetic group, Fig. 1. 

FEiFF stands for the effective scattering amplitude feff, an important ingredient in the theory of EXAFS (extended X-ray absorption fine structure) FEFF Project, Physics Department, University of Washington. See their World Wide Web address at http //leonardo.phys.washington.edu/feff. 

The discovery of the phenomenon that is now known as extended X-ray absorption fine structure (EXAFS) was made in the 1920s, however, it wasn t until the 1970s that two developments set the foundation for the theory and practice of EXAFS measurements. The first was the demonstration of mathematical algorithms for the analysis of EXAFS data. The second was the advent of intense synchrotron radiation of X-ray wavelengths that immensely facilitated the acquisition of these data. During the past two decades, the use of EXAFS has become firmly established as a practical and powerfiil analytical capability for structure determination. ... 

Allen GC, Warren KD (1974) The Electronic Spectra of the Hexafluoro Complexes of the Second and Third Transition Series. 19 105-165 Alonso JA, Baibas LC (1993) Hardness of Metallic Clusters. 80 229-258 Alonso JA, Baibas LC (1987) Simple Density Functional Theory of the Electronegativity and Other Related Properties of Atoms and Ions. 66 41-78 Andersson LA, Dawson JH (1991) EXAFS Spectroscopy of Heme-Containing Oxygenases and Peroxidases. 74 1-40 Antanaitis BC, see Doi K (1988) 70 1-26... 

Full derivations of the theory were presented by Lee and Pendry and Ashley and Doniach in 1975. They showed that a complete quantitative description of th EXAFS process was possible and that accurate bond lengths and coordination numbers could be extracted from the analysis of EXAFS data. Lee and Pendry also showed that at high photoelectron energies, the curvature of the electron wave can be neglected and thus the theory can be greatly simplified into what has beeome known as the plane-wave approximation. This approximation results in an expression equivalent to that derived by Stem semi-empirically ... 

X-ray Absorption Principles, Applications and Techniques of EXAFS, SEXAFS and XANES. R. Prins, D. Koningsberger, Eds., Wiley (1987). (Good general Introduction overview of theory and applications.)... 

Bromley ST, Sankar G, Catlow CRA, Maschmeyer T, Jenkins BEG, Thomas JM (2001) New insights into the structure of supported bimetallic nanocluster catalysts prepared from carbonylated precursors a combined density functional theory and EXAFS study. Chem Phys Lett 340 524... 

C. M. Barker, D. Gleeson, N. Kaltsoyannis, C. R. A. Catlow, G. Sankar, J. M. Thomas, On the structure and coordination of the oxygen-donating species in TiMCM-41/TBHP oxidation catalysts A density functional theory and EXAFS study, Phys. Chem. Chem. Phys. 4 (2002) 1228. 

Ashley, C.A. and Doniach, S. Theory of extended X-ray absorption edge fine structure (EXAFS) in crystalline solids." Phys. Rev. B11 1279-1288 1975. 

Details of EXAFS theory and analysis are given in numerous reviews and books The main features only will be recalled in this paper. 

We have detailed the different fields of application in the case of EXAFS because this technique is now routinely used. This is not yet the case of XANES though there is a growing interest in this field. The reason for this delay may be that, until recently, there was no general theory to explain the phenomenon and to allow accurate modelization. Anyhow, the literature gives some examples in the same fields as EXAFS. We selected three of them to illustrate the potentialities of the method. 

Kincaid BM, Eisenberger P (1975) Synchrotron radiation study of the X-edge photoabsorption spectra of Kr, Br2 and GeCU comparison of theory and experiment. Phys Rev Lett 34 1361-1364 Koch EE (1983) Handbook on Synchrotron Radiation (Vol. lb). North-Holland, New York, 506 p Koningsberger DC, Prins R (1988) X-ray absorption Principles, Applications, Techniques of EXAFS, SEXAFS, and XANES. Wiley, New York, 673 p Kossel W (1920) Zum Bau der Rontgenspektren. Z Phys 1 119-134... 

Lee PA, Beni G (1977) New method for the calculation of atomic phase shifts apphcations to extended X-ray absorption fine stracture (EXAFS) in molecules and crystals. Phys Rev B 15 2862-2883 Lee PA, Citrin PH, Eisenberger P, Kincaid BM (1981) Extended X-ray fine stracture Its strength and limitations as a stractnral tool. Rev Modem Phys 53 769-806 Lee PA, Pendiy JB (1975) Theory of extended X-ray absorption fine stractrrre. Phys Rev B11 2795-2811 Li D, Bancroft, GM Fleet, ME Feng, XH (1995a) Silicon X-edges XANES spectra of silicate minerals. Phys Chem Minerals 22 115-122... 

Stem EA (1974) Theory of extended X-ray absorption fine stractrrre. Phys Rev B10 3027-3037 Stem EA, Heald SM (1983) Basic principles and appheatiorrs of EXAFS pp. 955-1014 In EE Koch (ed) Handbook on Synchrotron Radiation (Vol. lb). North-Holland, New York Stohr J, Jaeger R, Feldhaus J, Brennan S, Norman D, Apai G (1980) Extended absorption fine stractrrre studies above the carbort, nitrogen, oxygert, and fluorine K absorption edges. Appl Optics 19 3911-3919... 

Yokoyama, T., 1995, Theory and parameters of EXAFS, in X ray Absorption Fine Structure for Catalysts and Surfaces, ed. Y. Iwasawa (World Scientific, Singapore) ch. 2, p. 9. 

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