Relativistic electron densities and isomer shifts of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ in iron-oxygen and iron-fluorine clusters and of iron in solid noble gases

Relativistic calculations of various electronic configurations of the iron atom are used in conjunction with Huckel-type molecular-orbital and limited-configuration-interaction calculations of iron-containing clusters to determine electron densities at the iron nucleus. The calculations include all effects of the overlap of iron core and ligand orbitals, and the effect of potential distortion of iron-core orbitals due to molecular configurations $3d^{m}4s^n$. Using the calculated electron densities and experimental isomer shifts, the relative change in the ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ nuclear-charge radius is deduced from studies of Fe$\mathrm{O}_6^{}{}_{}{}^{-9\mathrm{}}$ and Fe$\mathrm{O}_6^{}{}_{}{}^{-10\mathrm{}}$ as (-8.72 ± 1.02) × ${10}^{-4\mathrm{}}$, from studies of Fe$\mathrm{F}_6^{}{}_{}{}^{-3\mathrm{}}$ and Fe$\mathrm{F}_6^{}{}_{}{}^{-4\mathrm{}}$ as (-9.18 ± 0.56) × ${10}^{-4\mathrm{}}$, and from iron monomers and dimers dissolved in solid noble gases as (-7.12 ± 0.59) × ${10}^{-4\mathrm{}}$ or (-8.65 ± 0.71) × ${10}^{-4\mathrm{}}$, depending upon the assumed dimer geometry. From all these studies we obtain for the relative change in charge-radius value an average of (-8.85 ± 0.9) × ${10}^{-4\mathrm{}}$, in reasonable agreement with the work of several other investigators.