Calculation Of Scattering Factors Research Articles

DiSCaMB: a software library for aspherical atom model X-ray scattering factor calculations with CPUs and GPUs.

It has been recently established that the accuracy of structural parameters from X-ray refinement of crystal structures can be improved by using a bank of aspherical pseudoatoms instead of the classical spherical model of atomic form factors. This comes, however, at the cost of increased complexity of the underlying calculations. In order to facilitate the adoption of this more advanced electron density model by the broader community of crystallographers, a new software implementation called DiSCaMB, 'densities in structural chemistry and molecular biology', has been developed. It addresses the challenge of providing for high performance on modern computing architectures. With parallelization options for both multi-core processors and graphics processing units (using CUDA), the library features calculation of X-ray scattering factors and their derivatives with respect to structural parameters, gives access to intermediate steps of the scattering factor calculations (thus allowing for experimentation with modifications of the underlying electron density model), and provides tools for basic structural crystallographic operations. Permissively (MIT) licensed, DiSCaMB is an open-source C++ library that can be embedded in both academic and commercial tools for X-ray structure refinement.

Hirshfeld atom refinement.

Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly-l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree-Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints - even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu's), all other structural parameters agree within less than 2 csu's. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Åfor temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å(2) as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements - an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.

Scattering factor calculations and dispersion corrections for heavy atoms

Reliable knowledge of the complex X-ray form factor (Re( f) and Im( f)) is required for crystallography, deformation density bonding studies and refractive index studies. Dispersion corrections are important in DAFS, MAD analyses and XAFS studies. Discrepancies between currently used theoretical approaches of 200% exist for numerous elements from 1 to 3 keV X-ray energies, and at higher energies these discrepancies can persist at the 10% level or more. This has suggested that new formulations and new experimental approaches are necessary. Recent tabulations improve upon the theoretical uncertainty in some of these regions by a factor of 10 and reduce the error of this approach to below one standard deviation. Recent experimental developments have begun to probe alternate theory, providing a tool to investigate the significance of relativistic corrections and convergence criteria across a range of atomic number. In part, this has revealed that more theoretical work will be required in future years. Recent advances permit new probes and insights into atomic and solid state physics, as well as to many X-ray optical applications. This paper discusses significant improvements upon the theoretical uncertainty in near-edge regions, reducing the error of this approach to less than one standard deviation.

Recursive calculation of closed-form scattering factors for atomic orbitals

Recurrence relations are derived for calculating closed-form expressions for the Fourier–Bessel transform of electronic charge densities represented by Gaussian- and Slater-type atomic orbitals. The derivation is based on hypergeometric and Legendre function representations of the transform and the use of their recurrence properties. The scattering-factor calculations are discussed in detail. A table of closed-form expressions for Gaussian-type orbitals, not hitherto available, has been calculated using the new method and is available on request.

On electron-diffraction complex scattering factors for tin

The use of Cox and Bonham scattering factors for tin in electron-diffraction studies of a number of tin compounds leads to anomalously low amplitudes of vibration. The anomaly is due to overdamping of the calculated molecular intensities by the phase-angle dependent terms cos(η i η j ). Modified scattering factor calculations eliminate the anomaly.

Coherent Atomic Scattering Factors for the Lithium Hydride Crystal Field

This paper describes an effort made to evaluate the coherent atomic scattering factors for the lithium and hydride ions as they exist in the LiH crystal field. The two electron wave functions chosen to describe these ions are each in turn optimized in the field of positive and negative point charges arranged as the corresponding ions are arranged in the crystal. Using the orbital exponents obtained from the minimization process, atomic scattering factor calculations are made in the usual way. The factors for ${\mathrm{Li}}^{+}$ are unchanged. Interesting effects are noted for the ${\mathrm{H}}^{\ensuremath{-}}$ scattering factors.The energy of the ions in the field of point charges is related to the crystal cohesive energy. Specifically, neglecting the zero-point energy correction, the calculated open configuration results were -236.3 and -227.4 kcal/mole when compared with computed and experimentally determined free ${\mathrm{H}}^{\ensuremath{-}}$ reference energies, respectively. The experimental cohesive energy is -218.5 kcal/mole.Finally, it was noted that the ${\mathrm{H}}^{\ensuremath{-}}$ ion contracts in the crystal field. A possible explanation for this effect is given.