Topics in Catalysis Vol. 18, Nos. 1–2, January 2002 3 Theoretical interpretation of XAFS and XANES in Pt clusters A.L. Ankudinov a , J.J. Rehr a , J.J. Low b and S.R. Bare b a Department of Physics, University of Washington, Seattle, WA 98195-1560, USA b UOP LLC, Des Plaines, IL 60017, USA This paper first briefly summarizes the dramatic progress over the past decade both in fundamental theory and in the interpretation of XAFS and XANES. These developments have led to several ab initio codes such as FEFF for simulating XAFS and XANES, together with compatible analysis codes which permit an interpretation of the spectra in terms of geometrical and electronic properties of a material. As an example of relevance to catalysis, we discuss recent work which interprets the Pt L-edge XANES of PtX clusters based on the self- consistent FEFF8 code. For pure Pt clusters, we find that self-consistency is important in determining the variation of XANES with cluster size. For PtCl clusters, we show that the presence of a Cl–Pt bond leads to a “hybridization peak,” i.e., a peak in the Cl d-density of states (dDOS) mixed with Pt d-states, which can be used as a measure of Cl content. For Pt–H clusters, we show that hydrogen addition is well correlated with the growth of a broad shoulder above the white line. We find that this feature can be attributed largely to AXAFS, i.e., to a change in the atomic background absorption. We also analyze the effect of a support, in terms of model calculations for a realistic Pt 6 cluster within a zeolite-LTL pore. KEY WORDS: Pt L-edge XANES; catalysis; AXAFS; metal clusters 1. Modern theory of XAFS and XANES The development of modern X-ray absorption theory has paralleled that of modern synchrotron X-ray sources. Ad- vances over the past decade have revolutionized the tech- nique of extended X-ray absorption fine structure (EXAFS) for local structure determinations and essentially replaced the more phenomenological first generation theories. In- deed, the basic theory of EXAFS is now well understood. This development can be regarded as a successful second generation theory and is discussed in detail in a recent re- view [1]. Significant progress has also been made in third generation theories, which are appropriate for the current series of high brilliance X-ray sources, such as the ALS, APS, ESRF, and SPring8. These include theories of X-ray absorption near edge structure (XANES), i.e., the structure within about 30 eV of threshold where multiple-scattering contributions are important, as well as many related spectro- scopies (e.g., X-ray magnetic circular dichroism (XMCD), anomalous X-ray scattering, etc.). Curved-wave multiple- scattering (MS) theory now provides a unified treatment of the structure in both EXAFS and XANES, hence the term XAFS [2]. Thus we will also use the acronym XAS to refer more generally to XAFS and other X-ray spectro- scopies. These theoretical advances have led to the de- velopment of ab initio codes for XAS calculations in arbi- trary systems, for example, CONTINUUM [3], EXCURVE [4], FEFF [2,5,6], GNXAS [7], and WIEN98 [8] as well as various band-structure codes [9]. The EXAFS code development was revolutionary in that it provided accurate theoretical standards which eliminated the need for the tabulated phases and amplitudes of the first generation theories [10,11] and greatly simplified the analysis of experimental data. Despite this progress, a fully quantitative treatment of XAS remains elusive, due to a host of complications, e.g., non-spherical potential corrections and many body effects such as the treat- ment of the core-hole, inelastic losses, and multiplet-effects. Below we very briefly we outline the key developments that have led to the current theory. 2. Key developments in XAS theory The basic formal MS theory of XAS [1,12] is now fairly well established. Formally the X-ray-absorption coefficient µ for a given X-ray energy ¯ hω is given by Fermi’s Golden rule, µ(E) ≈  f |〈i |A · p|f 〉| 2 δ(E − E f ), (1) where E = ¯ hω − E i is the photoelectron energy, A · p is the coupling to the X-ray field, and the sum is over unoc- cupied final states. Most practical calculations are based on the dipole-approximation and the reduction of the Golden rule to a one-electron approximation. However, the ques- tion of precisely which one-electron states to use is not un- ambiguous. Much current work is based on the final state rule, in which the final states are calculated in the presence of an appropriately screened core-hole, and all many-body effects and inelastic losses are lumped into a complex val- ued optical potential. This theory is the basis for FEFF and many other codes. Another commonly used approach for calculating XANES is the atomic multiplet theory [13,14]. However, neither of these approaches is fully satisfactory. The one-electron approach ignores atomic multiplet effects, which are important for transition metal L-shell XAS, while the atomic multiplet theory is uses a crystal-field parameter- ization of solid state effects and ignores delocalized states. Also, due to local field effects, a screened X-ray field can be important, especially for soft X-rays [15]. Corrections to 1022-5528/02/0100-0003/0  2002 Plenum Publishing Corporation