Relativistic correction of atomic scattering factors for high-energy electron diffraction

Abstract

Relativistic electron diffraction depends on linear and quadratic terms in the electric potential, the latter being neglected in the frequently used relativistically corrected Schrödinger equation. Conventional tabulations for electron scattering and its large-angle extrapolations can be amended in closed form by a universal correction based on the screened Coulomb potential squared.

Refinement of X-ray and electron diffraction crystal structures using analytical Fourier transforms of Slater-type atomic wavefunctions in Olex2

“…The Gaussian functions are often extended by adding a constant. These can be found in, and are used automatically by, software such as olex2.refine (Dolomanov et al, 2009) or SHELXL (Sheldrick, 2015) While these functions prove to be very useful for fast determinations of atomic connectivity, there are downsides, and a need for re-evaluation has recently been shown in the literature (Thorkildsen, 2023;Olukayode et al, 2023a,b), This requirement has led to a variety of developments in recent years, ranging from high-quality X-ray scattering factors from freshly calculated wavefunctions to relativistically corrected electron diffraction scattering factors (Thorkildsen, 2023;Olukayode et al, 2023a,b;Yonekura et al, 2018;Lentzen, 2019). The main reason for the routine use of Gaussian-type functions in crystallography is the same as in quantum mechanical computations: the required calculations are more straightforward to perform and require less computational power, making them attractive even though a trade-off in accuracy must be made (Magalha ˜es, 2014).…”