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Magnetic coupling constants (2J) of hydroxo- and alkoxo-bridged copper binuclear compounds have been evaluated to determine the accuracy of different density functional methods and to study the magnetic behavior of these compounds. Comparison between the calculated and experimental coupling constants for the complete structures of five compounds shows that the most successful computational strategy is the combination of the B3LYP method with the broken-symmetry approach. Calculations for model compounds of both families yield reasonable approximations to the values of magnetic coupling constants calculated for the full molecular structures. Our calculations show a correlation between the magnetic coupling constant and the Cu−O−Cu bridging angle and with the out-of-plane displacement of the hydroxo or alkoxo groups, in agreement with the experimental data. The counterions of the hydroxo-bridged complexes, when hydrogen bonded to the bridging hydroxo group, determine the extent of the out-of-plane displacement of its hydrogen atom and strongly influence the sign and magnitude of the magnetic interaction. The energy gap between the two singly occupied molecular orbitals is shown to determine the changes in the value of 2J for small structural variations.

A stereochemical study of polyhedral eight-vertex structures is presented, based on continuous shape measures (CShM). Reference polyhedra, shape maps, and minimal-distortion interconversion paths are presented for eight-vertex polyhedral and polygonal structures within the CShM framework. The application of these stereochemical tools is analyzed for several families of experimental structures: 1) coordination polyhedra of molecular transition-metal coordination compounds, classified by electron configuration and ligands; 2) edge-bonded polyhedra, including cubane structures, realgar, and metal clusters; 3) octanuclear transition-metal supramolecular architectures; and 4) coordination polyhedra in extended structures in inorganic solids. Structural classification is shown to be greatly facilitated by these tools, and the detection of less common structures, such as the gyrobifastigium, is straightforward.

The effect of structural parameters on the exchange coupling constant of the title complexes of Cu(II), Ni(II), and Mn(II) is studied by means of density functional calculations on model compounds. The studied parameters are the bridging M−N−M angle, the M−N bond distance, and the out-of-plane shift of the azido bridge. The model compounds in their most stable geometry, as well as some full molecules in their experimental structures, appear in a high-spin ground state showing ferromagnetic coupling in all cases. The atomic spin density distributions of the model compounds are interpreted as resulting from the interplay between electron delocalization and spin polarization.