Theoretical X-ray absorption fine structure (XAFS) standards are developed for arbitrary pairs of atoms throughout the periodic table (Z < 94). These standard XAFS spectra are obtained from ab initio single-scattering XAFS calculations, using an automated code, feff, which takes into account the most important features in current theories: (i) an exact treatment of curved-wave effects; (ii) approximate molecular potentials derived from relativistic atoms, (iii) a complex, energy-dependent self-energy; (iv) a well defined energy reference, feff also yields tables of XAFS phases and amplitudes as well as mean-free paths. Sample results are presented and compared with experimental results and with earlier work. We find that these theoretical standards are competitive with experimental standards, permitting XAFS analysis at lower wavenumbers and yielding distance determinations typically better than 0.02 Á and coordination numbers typically better than 20%. These standards also provide theoretical tests of chemical transferability in XAFS.

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In the classical limit, a simple relation has been shown to exist between the thermal expansion coefBcient a and the cumulants of the vibrational amplitude that are measured in x-ray-absorption fine structure (XAFS), i.e. , nrTo /cr l = 1/2, where cr is the mean-square vibrational amplitude, the third cumulant, T the absolute temperature, and r the equilibrium bond length. We generalize this relation to the quantum case using a correlated Einstein model and thermodynamic perturbation theory, and find arTo /o = [3z(l + z) ln(1/z)]/[(1 -z)(1+ 10z+ z )], where z = exp( -e~/T), and e~is the Einstein temperature. This result is found to be in agreement with the measured thermal expansion coefFicient and XAFS cumulants in RbBr at 30 K and 125 K.

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An approach is presented for theoretical calculations of the Debye-Waller factors in x-ray absorption spectra. These factors are represented in terms of the cumulant expansion up to third order. They account respectively for the net thermal expansion σ(1) (T ), the mean-square relative displacements σ 2 (T ), and the asymmetry of the pair distribution function σ (3) (T ). Similarly, we obtain Debye-Waller factors for x-ray and neutron scattering in terms of the mean-square vibrational amplitudes u 2 (T ). Our method is based on density functional theory calculations of the dynamical matrix, together with an efficient Lanczos algorithm for projected phonon spectra within the quasiharmonic approximation. Due to anharmonicity in the interatomic forces, the results are highly sensitive to variations in the equilibrium lattice constants, and hence to the choice of exchangecorrelation potential. In order to treat this sensitivity, we introduce two prescriptions: one based on the local density approximation, and a second based on a modified generalized gradient approximation. Illustrative results for the leading cumulants are presented for several materials and compared with experiment and with correlated Einstein and Debye models. We also obtain Born-von Karman parameters and corrections due to perpendicular vibrations.