Magnetic Interactions in Molecules and Solids by Coen Graaf & Ria Broer

Author:Coen Graaf & Ria Broer
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The first step in the procedure consist of an inspection of the coordination sphere of the magnetic centers to determine the shape and symmetry of the optimal local magnetic orbitals. This can either be done through calculation or by ligand field reasoning. Our first example is a binuclear complex of Cu and V with a double alkoxo-bridge. The copper ion has a electronic configuration. This means that all 3d-orbitals are doubly occupied except the orbital, which is highest in energy because it directly points to the atoms of the first coordination sphere. The vanadium ion is covalently bound to the apex oxygen and the resulting vanadyl group has a formal oxidation state of VO(II) with one unpaired electron in the orbital of lowest energy, the largely non-bonding V- orbital. Figure 4.6 shows the two magnetic orbitals of the two magnetic centers, the left panel corresponds to the magnetic orbital on Cu and the right panel to the VO site. The superposition of these two pictures in the middle defines the exchange pathway and can help us to decide upon the overlap between the two orbitals as they appear in the main equation of the Kahn–Briat model, see Eq. 4.9. Note, that this does not define a molecular orbital, it is merely a construction by superimposing the two magnetic orbitals. The product of the two functions is an odd function with respect to the xz-plane, and hence, integrating over the cartesian coordinates gives a zero overlap integral S of these two magnetic orbitals. When S is equal or close to zero, the first term in the Kahn–Briat equation determines the nature of the coupling. Therefore, the magnetic coupling in this Cu/V dimer is expected to be ferromagnetic, in line with the triplet ground state and singlet-triplet gap of approximately 100 cm observed experimentally [9].

In complexes with more than one unpaired electron on at least one of the magnetic sites, the overall magnetic coupling is the sum of the couplings along all exchange paths weighted by the product of the number of unpaired electrons on each magnetic center (the number of paths). To illustrate the potential of the Kahn–Briat model for predicting the nature of the magnetic coupling, we will focus on the trinuclear Cu complex schematically depicted in the upper part of Fig. 4.7 and discuss the effect of replacing the copper ion in the middle by other transition metals. The complex has approximate symmetry and the five 3d orbitals belong to the (2x), , and irreducible representations as shown in the lower part of the figure. The copper ions on the left and right sides of the complex with their electronic configuration have only one unpaired electron, which resides in the orbital of symmetry. When the magnetic center in the middle is also occupied by a Cu ion, the three magnetic orbitals are all of the same symmetry and hence there is a non-zero overlap leading to an antiferromagnetic coupling between the TM ions in the complex, in line with experiment [10].

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