Overlap Contribution to the Isomer Shift of Iron Compounds

The electron density ${\Psi }^2\mathrm{}\left(0\right)\mathrm{}$ at the iron nucleus in oxides is calculated as a function of the Fe-O distance, by taking into account the overlap of the inner shells of iron with the oxygen $2p$ wave functions. The calculation shows the importance of the intershell terms, which effectively reduce the overlap-induced electron density. By comparing these results with the high-pressure isomer-shift measurements of divalent iron in CoO, the relative change of the ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ nuclear radius is found to be less than -4.0×${10}^{-4\mathrm{}}$. The overlap effect provides an important amplification mechanism for the contribution of $4s$ bonding to ${\Psi }^2\mathrm{}\left(0\right)\mathrm{}$. On the basis of this mechanism, large increases in ${\Psi }^2\mathrm{}\left(0\right)\mathrm{}$ observed on going from ${\mathrm{Fe}}^{2+}$ to ${\mathrm{Fe}}^{3+}$ salts can be explained by a reasonable increase in the amount of $4s$ bonding.