Open shell transition local spin

In this chapter, we review quantum chemical theories developed to describe chemical bonding in open-shell (transition metal) compounds. We review some important electronic structure methods that provide us with the central ingredient for an analysis of the chemical bond, the electronic wave function. We then discuss how information from the electronic wave function is extracted for a qualitative interpretation of the electronic structure. For this purpose, different approaches are described to extract local quantities from quantum states. An example is the local spin concept, which can be employed to study spin-spin interactions in terms of a Heisenberg coupling model. Finally, the difficulty of describing electronic structures of open-shell molecules accurately is highlighted as an example. 

In molecules, the interaction of surrogate spins localized at the atomic centers is calculated describing a picture of spin-spin interaction of atoms. This picture became prominent for the description of the magnetic behavior of transition-metal clusters, where the coupling type (parallel or antiparallel) of surrogate spins localized at the metal centers is of interest. Once such a description is available it is possible to analyze any wave function with respect to the coupling type between the metal centers. Then, local spin operators can be employed in the Heisenberg Spin Hamiltonian. An overview over wave-function analyses for open-shell molecules with respect to local spins can be found in Ref. (118). 

It has been long known that for a given transition-metal cluster the open-shell and the closed-shell species may differ. Typically, metal-ligand bond lengths are elongated for the open-shell structures, where the metal centers carry local spins and electrons occupy antibonding orbitals, in comparison to their closed-shell... 

The lowest absorption (and the emission) transition is ligand localized on the right-hand side and charge transfer on the left-hand side of Fig. 22. In between is an intermediate region. Since the excited states arc open shell, spin-singlets and spin-triplets appear. This simple approximation can be extended by including more excited configurations. 

Transition state geometries for reactions of open-shell molecules, particularly radical ions, pose special problems for DFT methods. In contrast to closed-shell systems whose ground state wavefunction is always totally symmetric, rearrangements of radicals and radical ions frequently involve crossings of states of different symmetry. In this situation, the molecule must lose symmetry to effect an adiabatic passage from reactants to products. In radical ions this loss often involves a localization of spin and charge, and it seems that DFT methods tend to oppose this localization. 

Transitions from a localized to an itinerant state of an unfilled shell are not a special property of actinides they can, for instance, be induced by pressure as they rue in Ce and in other lanthanides or heavy actinides under pressure (see Chap. C). The uniqueness for the actinide metals series lies in the fact that the transition occurs naturally almost as a pure consequence of the increase of the magnetic moment due to unpaired spins, which is maximum at the half-filled shell. The concept has resulted in re-writing the Periodic Chart in such a way as to make the onset of an atomic magnetic moment the ordering rule (see Fig. 1 of Chap. E). Whether the spin-polarisation model is the only way to explain the transition remains an open question. In a very recent article by Harrison an Ander-... 

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