A single configuration model containing nonorthogonal magnetic orbitals is developed to represent the important features of the antiferromagnetic state of a transition metal dimer. A state of mixed spin symmetry and lowered space symmetry is constructed which has both conceptual and practical computational value. Either unrestricted Hartree–Fock theory or spin polarized density functional theory, e.g., Xα theory, can be used to generate the mixed spin state wave function. The most important consequence of the theory is that the Heisenberg exchange coupling constant J can be calculated simply from the energies of the mixed spin state and the highest pure spin multiplet.

Huisgen's 1,3-dipolar cycloadditions become nonconcerted when copper(I) acetylides react with azides and nitrile oxides, providing ready access to 1,4-disubstituted 1,2,3-triazoles and 3,4-disubstituted isoxazoles, respectively. The process is highly reliable and exhibits an unusually wide scope with respect to both components. Computational studies revealed a stepwise mechanism involving unprecedented metallacycle intermediates, which appear to be common for a variety of dipoles.

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