New analytical scattering-factor functions for free atoms and ions

New analytical X-ray scattering-factor representations valid for the full range of sin Θ/λ from 0.0 to 6.0 Å⁻¹ have been developed from fits of a linear combination of five Gaussians to the values of the scattering factors tabulated in International Tables for Crystallography (1992) [Vol. C. Dordrecht: Kluwer Academic Publishers]. The resulting functions for both neutral atoms and ions are compared with the existing parametrizations, which are applicable for 0.0–2.0 Å⁻¹ and 2.0–6.0 Å⁻¹, respectively. The quality of the new parametrization involving 11 parameters per atom (ion) compares well with the previous work or is even superior. Examples are discussed, some errors in International Tables for Crystallography, Vol. C are indicated and a warning is given that most of the previously published four Gaussian expansions for ions are inadequate for calculations involving sin Θ/λ ≥ 2.0 Å⁻¹.