R. Reschke

Numerical integration of overlap and ligand contributions to the electric field gradient

The total electric field gradient (EFG) tensor Vpqis calculated by numerical integration of threedimensional integrals. Each of them is solved a) by integrating over one dimension analytically and b) by integrating over the remaining two dimensions on the basis of a Gauss-type integration rule. The use of 100 abscissas in the twodimensional numerical integration scheme yields satisfactory accuracy which was checked by evaluating overlap integrals; an increase to 400 abscissas does not increase the result drastically. Calculating quadrupole splittings ΔEQfrom numerically integrated electric field gradient tensors Vpqwe observe that depending a) on the amount of covalency and b) on the amount of deviation from octahedral or tetrahedral symmetry, involved in a molecular system, overlap and ligand contributions to Vpqplay an important role. Especially for the sandwich compound ferrocene, Fe(C5H5)2, we find a significant difference between ΔEQnum. int.which follows from the numerical integration method, and ΔEQconventionalwhich is derived from effective charges.

Electronic structure, electron density, electric field gradient-, magnetic susceptability- and G-tensor of K3Fe(CN)6

Abstract Molecular orbital calculations are presented for the electronic structure of K 3 Fe(CN) 6 based on clusters of formula K 8 Fe(CN) 5+ 6 , using a semi-empirical molecular orbital method including mixing of low-lying electronic configurations and spin-orbit coupling. The energy splittings obtained are in qualitative agreement with ligand field studies from several workers, excluding those of Merrithew and Modestino. While other authors interpret either Mossbauer data, or ESR results, or susceptibility values only, we obtain from the electron structure calculations charge densities at the iron nucleus, and electric field gradient, magnetic susceptibility and gyromagnetic tensors, which consistently interpret experimental Mossbauer-, EST- and magnetic anisotropy results. From the electronic structure calculations as well as from the reanalysis of experimental quadrupole line intensities (obtained by Oosterhuis and Lang) we derive that orthorhombic polytypism of K 3 Fe(CN) 6 has to be considered for a consistent interpretation of the experimental data. The successful correlation between calculation and experiment in an energy range of about 300 K above the electronic groundstate is a measure for the adequacy of our electronic structure calculations in this low-energy range.