M. Atanasov, C. Daul and H. U. Güdel
Modelling of Anisotropic Exchange Coupling in Rare-Earth–Transition-Metal Pairs:
Applications to Yb³⁺-Mn²⁺ and Yb³⁺-Cr³⁺ Halide Clusters and Implications to the Light Up-Conversion
in "Computational Chemistry: Reviews of Current Trends", Volume 9
Ed. Jerzy Leszczynski
World Scientific Publishing, Singapore, ISBN 981-256-097-1, 153-194 (2005)                 

Abstract: A procedure for calculating magnetic exchange coupling constants in rare earth (RE)-transition metal (TM) dimers is presented. In a first step RE-TM transfer (hopping) integrals between orbitals carrying unpaired (magnetic) electrons on RE and TM are determined from a MO-calculation utilising the concept of orbital exchange pathway and effective Hamiltonian theory. In a second step, many-electron wave-functions for ground or excited electronic states on RE and TM are constructed in which spin-orbit coupling (which dominates for the RE) is fully (variationally) taken into account. Finally, the data from steps 1 and 2 are combined to obtain numerical values for kinetic exchange integrals (within Anderson's superexchange theory) utilising a non-Heisenberg (orbital dependent) exchange operator. The MO's corresponding to the d(Mn) and f(Yb) magnetic orbitals have been used to also calculate ferromagnetic contributions to the exchange coupling. The model is applied to Yb³⁺-Mn²⁺ dimers with corner, edge and face shared octahedra and Cl^– and Br^– ligands. For that purpose we utilise a spectroscopically adjusted (to spectra of single nucleous octrahedral Mn²⁺, Cr³⁺ and Yb³⁺ complexes) parameterisation of the Extended Hückel theory. The expediency of the approach is discussed based on a comparison between calculated and experimental (available from inelastic neutron scattering experiments) anisotropic exchange parameters in Br₃Cr³⁺-m(Br₃)-Yb³⁺Br₃ dimers. Ferromagnetic exchange parameters for the ground state and the lowest emitting excited state increase from corner to edge to face Mn-Cl-Yb sharing thus varying in the same way as the efficiency of the up-conversion found for such species. This lends support for an exchange mechanism for this phenomenon postulated previously.