XANES calculations

Fig. 4. K-edge XANES calculated for the model carbonyl molecule X(CO)6 for various angles of rotation, 0, of the oxygen shell. From Pendry (233).

Currently the feeling is that more structural information, for example, locations and site symmetries of the atoms in a particular shell, is contained in the XANES region of an edge absorption spectrum than in EXAFS. However, the large cluster size ( 102 atoms) required for XANES calculations is a considerable drawback. 

The XANES of carbonates have been studied by Madix et al. (1988), who observed a transition at 290 eV to an orbital they identified as 7T c o corresponding to the Za/ orbital in Fig. 5.25, about 1 eV above the C li ionization potential (Fig. 5.27 Tegeler et al., 1980). The carbon x-ray emission spectrum and XANES calculated for C(OH)j by Tossell (1986) are compared with experimental values in Table 5.12 and show reasonable agreement. Note that the previously calculated C Is ionization potential of Tossell (1986) was too high by almost 20 eV (306.4 versus 288.8 eV), leading to the erroneous conclusion that the C Is— XANES peak lay below the C Is ionization threshold. As observed in numerous other cases, the core ct resonance (C ls- 4e in this case) is sensitive to nearest-neighbor distance and is thus a measure of R(C-0). 

The final states may be mixed with other orbitals and can be used to determine the coordination environment of an element in a compound, its electron density and oxidation state. The intensity can be used to accurately determine relative oxidation state ratios. Furthermore, XANES can be used to determine relative amounts of species by linear combination of individual compounds. In recent years, the codes for XANES calculation (especially John Rehr s FEFF code), have significantly improved and it can be expected that theoretical models of compounds will be accurately determined by XANES measurement and calculation in the future. 

An example of the use of ab initio XANES calculations to determine nanoparticle structure is the Zn/ferrihydrite sorption system examined by Waychunas et al. (2001). In the case of sorption complexes the XAI S spectrum of the sorbed species will contain information about the local structure of the substrate, and thus the structural nature of the full sorption complex. In the Zn/ferrihydrite system it was observed via EXAFS that the number of Fe next nearest neighbors about the sorbed Zn ion decreased as the Zn sorption density increased. Direct calculation of the XANES structure identified MS paths that changed in number as a function of cluster size (and thus number of neighbor Fe atoms), and gave rise to XANES features that changed in intensity (Fig. 32). These changes agreed well with the structural interpretation of the EXAFS and the crystal chemistry of Zn-Fe hydroxides. 

The key role of the second shell in the spectra of ferro-cyanides is demonstrated in Fig. 12. The multiple scattering XANES calculation for a single shell of FeQ is... 

The main area of application of XANES calculations is in structural research, and obviously the translational symmetry necessary for a A -space calculation of XANES is of limited use in this context. However A-space calculations on crystalline materials are of interest when investigating the influence of various approximations. Programs which find a DFT ground state and also have an option for a XANES calculation are now available from a number of sources, using full-potential linear augmented plane wave (FPLAPW) or linearized muffin-tin orbital (LMTO) schemes. To date none of these schemes include the effects of a core hole. 

An example of a comparison between theory and experiment illustrating the state of the art for XANES calculations based on multiple-scattering theory, begins with Fig. 1, where we show our results for CI2. Here the molec-... 

The main motivation for XANES calculations derives from the needs of... 

One C ui extrapolate from our previous calculations to conclude that it should be possible to perform XANES calculations for modest sized clusters contmning several tens of atoms. We anticipate that the combination of a full-potential real-space cluster calculational method with density functional... 

Increasing numbers of groups are now engaging in calculations of excited state structural dynamics from first principles in isolated molecular systems and with relatively small molecules of light elements. However, only very limited calculations of excited state structural dynamics with heavy elements are available these calculations provide not only excited state structures but also dynamics, as well as potential energy surfaces around the metal centers, enabling accurate XANES calculations. This is not uniquely for XTA analyses, but for the whole field of XAS including steady-state measurements. 

It will be shown that, upon interaction with water or ammonia, the T -like symmetry of the Ti(IV) centers in TS-1 is strongly distorted, as testified by UV-Vis, XANES, resonant Raman spectroscopies [45,48,52,58,64,83,84], and by ab initio calculations [52,64,74-76,88]. As in Sect. 3 for the dehydrated catalyst, the discussion follows the different techniques used to investigate the interaction. 

Final detennination of the structure was made by proposing a structural model with Cu sitting in threefold hollow sites and O atoms on atop sites with respect to the Cu atoms (Fig. 27.16). A program, FEFFIT, was used to analyze the data (Stem et al., 1995). This calculates the phase and amplitude parameters for the various backscatters. The EXAFS for the parallel polarization could be fitted six Cu-Cu interactions at a bond distance of 2.67 A and three Cu-Pt interactions at 2.6 A. For the perpendicular polarization, the data could be fitted one Cu-0 interaction at 1.96 A and three Cu-Pt interactions at 2.6 A. The Cu-Pt bond length is shorter than the sum of the metallic radii of Cu and Pt, which is 2.66 A. This indicates a Cu oxidation state different from zero, which agrees with the XANES results. 

In order to gain information on the environments of certain atoms in dissolved species, in melts or in solids (crystalline or noncrystalline), which are not accessible to diffraction studies for one reason or another, X-ray absorption spectrometry (XAS) can be applied, with the analysis of the X-ray absorption near-edge structure (XANES) and/or the extended X-ray absorption fine structure (EXAFS). Surveys of these methods are available 39,40 a representative study of the solvation of some mercury species, ElgX2, in water and dimethylsulfoxide (DMSO) by EXAFS and XANES, combined with quantum-chemical calculations, has been published.41... 

Fig. 21 a Normalized As K-edge XANES spectra for FeAs and some FeAsi j,Py members, measured in transmission mode, b Orbital projections of conduction states calculated from FeAs and FeAso.5oPo.50 (the Fermi edge is at OeV). Reprinted with permission from [61]. Copyright Elsevier... 

NMR investigations [129, 132, 133], EXAFS and XANES studies [134-136], and theoretical calculations [127, 137, 138] performed on higher-order cyanocuprates strongly suggested that the cyanide anion was not bound to copper in these R2Cu(CN)Li2 species. Additional evidence was provided by the first X-ray crystal structure determinations of higher-order cyanocuprates ](C(5H4CH2NMe2-2)2 Cu(CN)Li2] [139] (Fig. 1.34) and [(tBu)2Cu(CN)Li2] [130] (Fig. 1.35). 

In solid state physics, the sensitivity of the EELS spectrum to the density of unoccupied states, reflected in the near-edge fine structure, makes it possible to study bonding, local coordination and local electronic properties of materials. One recent trend in ATEM is to compare ELNES data quantitatively with the results of band structure calculations. Furthermore, the ELNES data can directly be compared to X-ray absorption near edge structures (XANES) or to data obtained with other spectroscopic techniques. However, TEM offers by far the highest spatial resolution in the study of the densities of states (DOS). 

Fig. 2. a) Required number of incoming x-ray photons to observe time-resolved EXAFS of transition metal compounds in H20 solution with a signal-to-noise ratio S/N = 1. No ligand or counterion contributions were included (see Fig. 1). Input parameters are /= 10%, %= 1 % (relative to the absorption edge jump of the selected element). The maxima of curves 2) in Fig. 1 for Fe and Ru correspond to the data points for these elements, b) Feasibility range for time-resolved x-ray absorption spectroscopy. The shaded region indicates the required x-ray dose per data point as a function of the fraction of activated species for the calculated EXAFS experiments on transition metal compounds shown in a). Curves (1) to (3) are extrapolated from experimental results (see section 3. for details) of time-resolved XANES.

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