Relativistic X-ray Elastic Scattering Factors for He–Ar from Dirac–Hartree–Fock Wave Functions

Abstract

X-ray and electron elastic scattering factors for He through Ar ground states have been computed from Dirac-Hartree-Fock (DHF) wave functions. Differing from earlier studies, the present DHF wave functions are not restricted to single configurations and will go into the nonrelativistic Hartree-Fock (HF) ground states when the speed of light c --, ~. The relativistic effects have been analyzed through the differences of scattering factors calculated at DHF and HF levels of theory. It has been found that the effects become stronger as the nuclear charge increases and anomalous behavior observed in the literature for C, N, O, Si, P and S is due to the use of either single-or average-energy multiconfiguration DHF wave functions to extract the relativistic effects for these systems preventing attainment of the correct nonrelativistic limit. Scattering factors of common ions of the first-and second-row elements and the valence state of C and Si are also given.

Experimental Determination of the Electron Density Topology in a Non-centrosymmetric Transition Metal Complex: [Ni(H3L)][NO3][PF6] [H3L =N,N‘,N‘‘-Tris(2-hydroxy-3-methylbutyl)-1,4,7-triazacyclononane]

“…One possible explanation for the high correlation is the inadequacy of the Clementi Hartree−Fock scattering factors, which incorporate neither correlation nor relativistic effects. These are probably significant for an element of such a high atomic number …”

Ionic scattering factors of atoms that compose biological molecules

“…A practical approach to this problem is placing positive charges outside a given radius around the ion (Watson, 1958;Schmidt & Weiss, 1979;Rez et al, 1994), but the resultant scattering curves differ significantly in the range sin/ < 0.4 Å À1 , depending on the size of the radius (Schmidt & Weiss, 1979). Previous studies (Wang et al, 1996;Macchi & Coppens, 2001) showed that the Dirac-Fock calculation yielded good solutions for O À and halides with no surrounding positive charges. Based on these studies, we carried out MCDF Plots of typical X-ray (upper row) and electron (lower row) scattering factors from the literature [e.g.…”

“…Relativistic effects are known to be small for light atoms (e.g. Wang et al, 1996). Despite this, we included relativistic effects as most of the scattering factors in Colliex et al (2006) adopted the relativistic calculation, even for the atoms concerned in this study.…”

“…The scattering factors of atoms and ions for X-rays and electrons were calculated (e.g. Doyle & Turner, 1968;Schmidt & Weiss, 1979;Rez et al, 1994;Wang et al, 1996;Su & Coppens, 1997;Macchi & Coppens, 2001) and parameterized previously (e.g. Doyle & Turner, 1968;Rez et al, 1994;Waasmaier & Kirfel, 1995;Peng et al, 1996;Su & Coppens, 1997;Peng, 1998;Macchi & Coppens, 2001;Colliex et al, 2006), but there have been no reported scattering factors for chemically unstable ions involved in proteins and protein complexes except for O À .…”

Relativistic effects on x-ray structure factors

“…[9,[17][18][19][20][21][22][23] The aim of the present study is a systematic investigation of relativistic effects on X-ray structure factors. While this topic has been studied for atomic form factors f (r * ) in the past, [24][25][26][27] there exists up to date no thorough study in this respect on structure factors F(r * ) based on a fully-relativistic reference. However, results from a previous study on relativistic effects on the topology of the electron density suggest, that especially for third row transition metal elements relativistic effects need to be taken into account in order to obtain accurate electron density distributions.…”