Results of spin density functional theory (SDFT) calculations were used to construct and check features of a generally applicable semi-quantitative approach to understanding magnetic coupling in gadolinium-containing molecules, clusters, and solids. Using fragments based on structures of metal-rich lanthanide compounds, we have investigated molecular and low-dimensional extended structures, and have shown that open-d-shell clusters facilitate strong ferromagnetic coupling whereas closed-d-shell systems prefer antiferromagnetic coupling. The qualitative features can be interpreted using a perturbative molecular orbital (PMO) model that focuses the influence of the 4f 7- d exchange interaction on the d-based molecular orbitals. The f-d exchange interaction, mediated by spin polarization of both filled and partially-filled metal-metal bonding orbitals, is described for the model system Gd3I6(OPH3)12 n+ using basic perturbation methods. This approach is successful for predicting the magnetic ground state for Gd2Cl3, a semiconducting system for which calculations predict antiferromagnetic ordering of the 4f 7 moments in a pattern consistent with published neutron diffraction data. An attempt to account for the calculated magnetic energies of spin patterns using an Ising model was unsuccessful, indicating that the Ising model is inappropriate. Instead, the d-electron mediated f-f exchange interaction was interpreted using our basic perturbation theory approach. Computed density of states and spin polarization information was used to support the perturbation-theoretic analysis. This method has also been successful evaluating the ground state for Gd[Gd6FeI12]. Using the model [Gd6CoI12](OPH3)6, which has three unpaired electrons in the HOMO, the 4f moments prefer spin alignment with the unpaired electrons in the system and the ferromagnetic 4f 7 spin arrangement is the ground state. We have extended our analysis of R6X12 clusters to include nonmetal interstitial atoms, the bioctahedral cluster compounds Gd10Cl17C4 and Gd10I16C4, and Gd5(O)(OPri)5. Finally, we have shown that we can successfully predict the ground state magnetic structures of several metallic and semiconducting Gd-containing compounds, Gd2Cl3, GdB2C2,alpha-Gd2S3, Gd5Si4, and Gd5Ge4, using semi-empirical calculations which closely simulates the exchange effects exerted by the 4f electrons. In a more speculative vein, ideas concerning the incorporation of anisotropic rare-earth metal atoms to the cluster framework are touched upon.

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