Evaluation of Sternheimer Nuclear Quadrupole Shielding Functions and their Application to the Determination of the ⁵⁷Fe^m Nuclear Quadrupole Moment from X-ray-Determined Charge Densities

The Sternheimer function γ(r) describes the shielding/antishielding of the electric field gradient (EFG) at the nuclear position due to polarization induced in the atomic density by the quadrupolar components of the density distribution. The functions for Fe, Fe²⁺ and Fe³⁺ have been derived by means of Sternheimer's procedure [Sternheimer (1986). Z. Naturforsch. Teil A, 41, 24–36], using a finite-difference method for solving the radial equations for the perturbed wave functions and numerical integration for the calculation of γ(r) . The shielding factors R, due to the contributions from the electron density of the atom at the nucleus of which the EFG is being considered (the `central contributions'), are derived from the γ functions. Results are given for near-Hartree–Fock atomic and ionic wavefunctions [Clementi & Roetti (1974). At. Data Nucl. Data Tables, 14, 177–478]. Contributions to the shielding from the core and valence electrons are separated. Since the X-ray multipole formalism describes a flexible valence shell but uses a frozen core, only γ^core and R^core are used in the calculation of Mössbauer splittings from the experimental charge densities. The effect on the shielding of X-ray-determined radial expansion/contraction of the valence shells [Coppens, Guru Row, Leung, Stevens, Becker & Yang (1979). Acta Cryst. A35, 63–72] is evaluated. The combination of spectroscopic nuclear quadrupole splittings and X-ray charge densities on iron pyrite (FeS₂), sodium nitroprusside {[Na₂Fe(NO)(CN)₅].2H₂O} and [Fe(TPP)(pyridyl)₂] leads to unweighted and weighted average values for Q(⁵⁷Fe^m) of 0.12 (3) and 0.11 (2) × 10⁻²⁸ m², respectively, when the core shielding factors are used.