Revisited relativistic Dirac-Hartree-Fock X-ray scattering factors. II. Chemically relevant cations and selected monovalent anions for atoms with Z = 3-112

The previously described approach for determination of the relativistic atomic X-ray scattering factors (XRSFs) at the Dirac-Hartree-Fock level [Olukayode et al. (2023). Acta Cryst. A79, 59-79] has been used to evaluate the XRSFs for a total of 318 species including all chemically relevant cations [Greenwood & Earnshaw (1997). Chemistry of the Elements], six monovalent anions (O^-, F^-, Cl^-, Br^-, I^-, At^-), the ns¹np³ excited (valence) states of carbon and silicon, and several exotic cations (Db⁵⁺, Sg⁶⁺, Bh⁷⁺, Hs⁸⁺ and Cn²⁺) for which the chemical compounds have been recently identified, thus significantly extending the coverage relative to all the earlier studies. Unlike the data currently recommended by the International Union of Crystallography (IUCr) [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554-589], which originate from different levels of theory including the non-relativistic Hartree-Fock and correlated methods, as well as the relativistic Dirac-Slater calculations, the re-determined XRSFs come from a uniform treatment of all species within the same relativistic B-spline Dirac-Hartree-Fock approach [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287-303] that includes the Breit interaction correction and the Fermi nuclear charge density model. While it was not possible to compare the quality of the generated wavefunctions with that from the previous studies due to a lack (to the best of our knowledge) of such data in the literature, a careful comparison of the total electronic energies and the estimated atomic ionization energies with experimental and theoretical values from other studies instils confidence in the quality of the calculations. A combination of the B-spline approach and a fine radial grid allowed for a precise determination of the XRSFs for each species in the entire 0 ≤ sin θ/λ ≤ 6 Å^-1 range, thus avoiding the necessity for extrapolation in the 2 ≤ sin θ/λ ≤ 6 Å^-1 interval which, as was shown in the first study, may lead to inconsistencies. In contrast to the Rez et al. work [Acta Cryst. (1994), A50, 481-497], no additional approximations were introduced when calculating wavefunctions for the anions. The conventional and extended expansions were employed to produce interpolating functions for each species in both the 0 ≤ sin θ/λ ≤ 2 Å^-1 and 2 ≤ sin θ/λ ≤ 6 Å^-1 intervals, with the extended expansions offering a significantly better accuracy at a minimal computational overhead. The combined results of this and the previous study may be used to update the XRSFs for neutral atoms and ions listed in Vol. C of the 2006 edition of International Tables for Crystallography.

GRASP Manual for Users

grasp is a software package in Fortran 95, adapted to run in parallel under MPI, for research in atomic physics. The basic premise is that, given a wave function, any observed atomic property can be computed. Thus, the first step is always to determine a wave function. Different properties challenge the accuracy of the wave function in different ways. This software is distributed under the MIT Licence.

Revisited relativistic Dirac-Hartree-Fock X-ray scattering factors. I. Neutral atoms with Z = 2-118

In this first of a series of publications, the X-ray scattering factors for neutral atoms are revisited. Using the recently developed DBSR_HF program [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287-303] the fully relativistic Dirac-Hartree-Fock ground-state wavefunctions for all atoms with Z = 2-118 (He-Og) have been calculated using the extended average level scheme and including both the Breit interaction correction to the electronic motion due to magnetic and retardation effects, and the Fermi distribution function for the description of the nuclear charge density. The comparison of our wavefunctions with those obtained in several previous studies in terms of the total and orbital (spinor) electronic energies, and a number of local and integrated total and orbital properties, confirmed the quality of the generated wavefunctions. The employed dense radial grid combined with the DBSR_HF's B-spline representation of the relativistic one-electron orbitals allowed for a precise integration of the X-ray scattering factors using a newly developed Fortran program SF. Following the established procedure [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554-589], the resulting X-ray scattering factors have been interpolated in the 0 ≤ sin θ/λ ≤ 2 Å^-1 and 2 ≤ sin θ/λ ≤ 6 Å^-1 ranges using the recommended analytical functions with both the four- (which is a current convention) and five-term expansions. An exhaustive comparison of the newly generated X-ray scattering factors with the International Union of Crystallography recommended values and those from a number of previous studies showed an overall good agreement and allowed identification of a number of typos and inconsistencies in the recommended quantities. A detailed analysis of the results suggests that the newly derived values may represent an excellent compromise among all the previous studies. The determined conventional interpolating functions for the two sin θ/λ intervals show, on average, the same accuracy as the recommended parametrizations. However, an extension of each expansion by only a single term provides a significant improvement in the accuracy of the interpolated values for an overwhelming majority of the atoms. As such, an updated set of the fully relativistic X-ray scattering factors and the interpolating functions for neutral atoms with Z = 2-118 can be easily incorporated into the existing X-ray diffraction software with only minor modifications. The outcomes of the undertaken research should be of interest to members of the crystallographic community who push the boundaries of the accuracy and precision of X-ray diffraction studies.

Comment on "Theoretical Confirmation of the Low Experimental 3C/3D f-Value Ratio in Fe xvii"

A Comment on the Letter by Mendoza and Bautista [Phys. Rev. Lett. 118, 163002 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.163002].

Concurrent Vector Algorithms for Spline Solutions of the Helium Pair Equation

An algorithm for the solution of the pair equation for helium is described, suitable for concurrent vector pro cessors. Emphasis is placed on minimizing memory re quirements so that the technique may be extended to systems with more electrons. The pair function is ex panded in a series of partial waves whose radial factor is represented by a tensor product of B-splines. Perfor mance is analyzed for the ground and first excited 1 S state, and for the lowest 3 S and 1,3 P states. An odd-even, column Nesbet algorithm is derived for solving the gen eralized eigenvalue problem and is shown to converge in all cases.