The effect of nonorthogonality in the broken symmetry approach to magnetic coupling has been explicitly considered for the first time in Hartree−Fock and a variety of DFT methods. On the basis of the results for three different systems, representative of a variety of physical situations it is shown that the most often quoted trend concerning the much larger degree of delocalization of magnetic orbitals obtained from DFT, as opposed to Hartree−Fock, is not fully justified. A new and simple way to relate the overlap integral entering into the calculation and the spin density is proposed and tested in a variety of model systems.

The performance of the M06 family of exchange-correlation potentials for describing the electronic structure and the Heisenberg magnetic coupling constant (J) is investigated using a set of representative open-shell systems involving two unpaired electrons. The set of molecular systems studied has well defined structures, and their magnetic coupling values are known experimentally. As a general trend, the M06 functional is about equally as accurate as B3LYP or PBE0. The performance of local functionals is important because of their economy and convenience for large-scale calculations; we find that M06-L local functional of the M06 family largely improves over the local spin density approximation and the generalized gradient approximation.

The magnetic interactions in organic diradicals, dinuclear inorganic complexes and ionic solids are presented from a unified point of view. Effective Hamiltonian theory is revised to show that, for a given system, it permits the definition of a general, unbiased, spin model Hamiltonian. Mapping procedures are described which in most cases permit one to extract the relevant magnetic coupling constants from ab initio calculations of the energies of the pertinent electronic states. Density functional theory calculations within the broken symmetry approach are critically revised showing the contradictions of this procedure when applied to molecules and solids without the guidelines of the appropriate mapping. These concepts are illustrated by describing the application of state-of-the-art methods of electronic structure calculations to a series of representative molecular and solid state systems.

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The performance of the complete active space second-order perturbation theory (CASPT2) to accurately predict magnetic coupling in a wide series of molecules and solid state compounds has been established. It is shown that CASPT2, based on a reference wave function that only includes the effects described by the Anderson or Hay−Thibeault−Hoffmann model, correctly reproduces all experimental trends. For a complete quantitative agreement with experiment (or with accurate results arising from the difference dedicated configuration interaction method), it is necessary to include effects that go beyond the Anderson model in the reference wave function. The CASPT2 method is computationally less demanding than CI based methods and, hence, allows us to extend the study of magnetic coupling parameters to larger molecules or systems with elevated spin moments. Moreover, CASPT2 provides a reliable and accurate alternative to density functional based methods that require the use of a broken symmetry approach.