J. J. Rehr

Analysis of multiple-scattering XAFS data using theoretical standards

Abstract Theoretical standards for scattering amplitudes and phase shifts are often necessary for XAFS analysis, as for cases in which multiple scattering paths are important over the R-range of interest. Even when not necessary, they are often more convenient and reliable than experimental standards. We discuss several important considerations that must be taken into account to successfully compare ab initio theoretical calculations from FEFF to experimental XAFS spectra, and present a computer program, FEFFIT, to assist in using FEFF to get reliable information from experimental XAFS data.

Parameter-free calculations of X-ray spectra with FEFF9

We briefly review our implementation of the real-space Greens function (RSGF) approach for calculations of X-ray spectra, focusing on recently developed parameter free models for dominant many-body effects. Although the RSGF approach has been widely used both for near edge (XANES) and extended (EXAFS) ranges, previous implementations relied on semi-phenomenological methods, e.g., the plasmon-pole model for the self-energy, the final-state rule for screened core hole effects, and the correlated Debye model for vibrational damping. Here we describe how these approximations can be replaced by efficient ab initio models including a many-pole model of the self-energy, inelastic losses and multiple-electron excitations; a linear response approach for the core hole; and a Lanczos approach for Debye-Waller effects. We also discuss the implementation of these models and software improvements within the FEFF9 code, together with a number of examples.

Coordination chemistry of Ti(IV) in silicate glasses and melts: I. XAFS study of titanium coordination in oxide model compounds

Abstract The coordination environment of Ti(IV) in a variety of Ti-bearing crystalline oxide and silicate model compounds has been studied using Ti K-edge x-ray absorption fine structure (XAFS) spectroscopy at ambient temperature and pressure in order to provide a quantitative basis for interpreting Ti K-edge XAFS spectra of silicate glasses and melts (Parts II, III, and IV) Farges and Brown, 1996; Farges et al., 1996a,b). Pre-edge features of Ti K-edge XAFS spectra can be used to derive accurate information on the local coordination environment of Ti only if both pre-edge position and heights are considered. Using these features, it is also possible to distinguish between one coordination environment vs. a mixture of several others (e.g., [5]Ti vs. [4]Ti + [6]Ti). Quantitative analysis of the Ti x-ray absorption near edge structure (XANES) spectra, based on ab-initio multiple-scattering calculations for a variety of Ti-containing clusters and anharmonic analysis of the normalized XAFS oscillations, show that O first neighbors and alkali/alkaline-earth second neighbors around Ti contribute to the XAFS spectra. However, second neighbors are more prominent in the XANES region because the effects of disorder associated with these contributions are less important in this region than in the extended XAFS (EXAFS) region. Therefore, XANES spectra can be used to probe the degree of disorder in the medium-range structural environment around Ti in crystalline and amorphous materials, including Ti-bearing aperiodic structures, such as metamict, glassy, and molten compounds.

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X-RAY-ABSORPTION FINE STRUCTURE IN EMBEDDED ATOMS

Oscillatory structure is found in the atomic background absorption in x-ray-absorption fine-structure (XAFS) measurements. This atomic XAFS (AXAFS) arises from scattering within an embedded atom, and is analogous to the Ramsauer-Townsend effect. Calculations and measurements confirm the existence of AXAFS and show that it can dominate contributions such as multielectron excitations. The structure is sensitive to chemical effects and thus provides a probe of bonding and exchange effects on the scattering potential.

Coordination chemistry of Ti(IV) in silicate glasses and melts: II. Glasses at ambient temperature and pressure

Abstract The coordination environment of Ti(IV) in a number of Ti-silicate and Ti-aluminosilicate glasses has been determined by x-ray absorption fine structure (XAFS) spectroscopy at the Ti K-edge at ambient temperature and pressure. These glasses contain 2.7–30.5 wt% TiO2 and varying amounts of Na2O, K2O, or CaO (5.0–38.7 wt%) and Al2O3 (0–11.9 wt%), and have NBO/T ratios ranging from 0.07–0.81. Quantitative analysis of the Ti XANES spectra, based on ab initio multiple-scattering calculations for a variety of Ti-containing clusters, and anharmonic analysis of the normalized XAFS oscillations suggest the presence of three types of atoms around Ti: O first neighbors, (Si, Ti)-second neighbors, and alkali third neighbors. Five-coordinated Ti, [5]Ti, is the dominant Ti species in the glasses most concentrated in Ti (> 16 wt% TiO2) and is located in distorted square pyramids ([5]TiO)O4), with one short Ti O titanyl distance (1.67–1.70 ± 0.03A) and four long Ti O distances (1.94–1.95 ± 0.02A). In addition, minor amounts of [4]Ti were detected, the proportion of [4]Ti increasing in the order: Na glasses The presence of Ti-(Si, Ti) correlations near 3.2–3.4 ± 0.1A, as in crystalline Na2([5]TiO)SiO4, is consistent with [5]TiO5 and SiO4/TiO5 polyhedra sharing corners in these glasses, with Ti O-(Si, Ti) angles of ≈120°–130° ± 10°. Quantitative analysis of the Ti K-edge XANES for the K-bearing glasses suggests the presence K around Ti, in good agreement with bond-valence predictions, which indicate that [5]Ti is most likely to bond to both nonbridging oxygens (one O in short Ti O titanyl bonds) and bridging oxygens (four O in long Ti O bonds), thus can act as a new type of Q4 specie with one additional nonbridging oxygen. Then, we propose [5]Ti to behave simultaneously a network former and a network modifier, with the network former role dominant. Bond valence models explain why the relative proportions of [4]Ti and [5]Ti change when the type of low field strength cation or the type of network-forming cation (Si vs. P) changes in oxide glasses. These models also provide a structural basis for the study of glasses and melts at higher temperatures (see Part III of this study).

Real-time time-dependent density functional theory approach for frequency-dependent nonlinear optical response in photonic molecules

We present ab initio calculations of frequency-dependent linear and nonlinear optical responses based on real-time time-dependent density functional theory for arbitrary photonic molecules. This approach is based on an extension of an approach previously implemented for a linear response using the electronic structure program SIESTA. Instead of calculating excited quantum states, which can be a bottleneck in frequency-space calculations, the response of large molecular systems to time-varying electric fields is calculated in real time. This method is based on the finite field approach generalized to the dynamic case. To speed the nonlinear calculations, our approach uses Gaussian enveloped quasimonochromatic external fields. We thereby obtain the frequency-dependent second harmonic generation beta(-2omega;omega,omega), the dc nonlinear rectification beta(0;-omega,omega), and the electro-optic effect beta(-omega;omega,0). The method is applied to nanoscale photonic nonlinear optical molecules, including p-nitroaniline and the FTC chromophore, i.e., 2-[3-Cyano-4-(2-{5-[2-(4-diethylamino-phenyl)-vinyl]-thiophen-2-yl}-vinyl)-5,5-dimethyl-5H-furan-2-ylidene]-malononitrile, and yields results in good agreement with experiment.

Sensitivity of Pt x-ray absorption near edge structure to the morphology of small Pt clusters

A theoretical study of the sensitivity of Pt L3 x-ray absorption near edge structure (XANES) to the size and shape in small Ptn clusters is reported. Calculations, based on a full multiple scattering, self-consistent field, real-space Green’s function approach implemented in the ab initio FEFF8 code, show that XANES provides a characteristic signature of cluster shape. For example, the calculated white line intensity exhibits a large variation for small cluster sizes and geometry, but becomes independent of cluster size for large clusters. A strong polarization dependence of the white line is predicted for two-dimensional clusters. For three-dimensional clusters the polarization dependence is smaller, but can be used as a measure of the “flatness” of a cluster. A series of semirelativistic all-electron, full potential density functional calculations was also performed for several Ptn clusters. These calculations show the existence of intrinsic static disorder in these clusters due to nonisotropic shrinkag...

Recent Developments in Multiple-Scattering Calculations of XAFS and XANES

Curved-wave multiple-scattering (MS) theory provides a unified treatment of XAFS, encompassing both EXAFS and XANES, as well as a formal equivalence between exact treatments and the (MS) expansion carried to all orders. Recent developments in the theory of XAFS are reviewed with an emphasis on progress in curved-wave MS calculations and on understanding the nature of MS contributions in EXAFS and XANES. In particular we discuss a unified ab initio MS treatment of XAFS based on a scattering matrix formalism which has sufficient speed and accuracy to treat high-order MS in extended systems. We find that neither low-order MS nor full MS theories are fully satisfactory. Instead, sufficiently high-order MS appears to be necessary for the convergence of both EXAFS and XANES calculations. Our approach also gives a MS interpretation of the σ* shape-resonances observed in XANES. We demonstrate that these peaks result from coherent, high-order MS. We also obtain a generalization of the Natoli rule correlating the resonance locations with bond length.

Bethe-Salpeter equation calculations of core excitation spectra

We present a hybrid approach for Bethe-Salpeter equation (BSE) calculations of core excitation spectra, including x-ray absorption (XAS), electron energy loss spectra (EELS), and nonresonant inelastic x-ray scattering (NRIXS). The method is based on ab initio wave functions from the plane-wave pseudopotential code ABINIT; atomic core-level states and projector augmented wave (PAW) transition matrix elements; the NIST core-level BSE solver; and a many-pole self-energy model to account for final-state broadening and self-energy shifts. Multiplet effects are also approximately accounted for. The approach is implemented using an interface dubbed OCEAN (Obtaining Core Excitations using ABINIT and NBSE). To demonstrate the utility of the code we present results for the K edges in LiF as probed by XAS and NRIXS, the K edges of KCl as probed by XAS, the Ti L2,3 edge in SrTiO3 as probed by XAS, and the Mg L2,3 edge in MgO as probed by XAS. These results are compared with experiment and with other theoretical approaches.