Unpaired f electrons

E—Electrons fill the orbitals individually before pairing. Unpaired f electrons = paramagnetic. 

Figure 7.14 (Upper) Different space groups and the types of coordination along the lanthanide series. (Middle) Plots of the SHG intensity along the type I and type II series as according to ionic radius and also (bottom) to the number of unpaired f electrons. Complexes with no unpaired f electrons are shown to follow a different trend (La, Y, Lu).

Ferromagnetic materials are those in which the magnetic moments align parallel to each other over considerable distances in the solid (Figure 12.3g). An intense external magnetic field is produced by this alignment. Ferromagnetism is associated with the transition elements, with unpaired d electrons, and the lanthanides and actinides with unpaired f electrons. 

Until about 1979, Th(IV) complexes of different types were the almost only f-element organometallies devoid of unpaired f-electrons that had been subjected to extensive H- and C-NMR studies [13]. As in the majority of cases the corresponding paramagnetic U(IV) complexes have also been studied, the reported NMR data on Th(IV) complexes provide, inter alia, an excellent basis for the evaluation of rather precise isotropic shifts of the homologous U(IV) complexes... 

Beware the assumption that this diagram, although correct, may be used to explain the properties of ions containing unpaired f electrons. The situation is more complicated, as will become evident in Chapter 11. 

Aeon is caused by contact interactions of unpaired f-electron spin density with the ligand, while Adip is due to the magnetic anisotropy of the molecule, where geometric factors are important. Normally the isotropic shift of the organolanthanide compounds is due mainly to the dipolar contribution (Adip) (or pseudo-contact contribution) as the contact contribution (Aeon) is very low because of the very contracted nature of the lanthanide f-orbitals. 

Shell structure, relativistic and electron correlation effects play an important role for the electronic structure of lanthanide and actinide systems. The importance and the magnitude of these effects have been examplified for the atoms Ce and Th, and the contributions of the Ce 4f and Th 5f shell to chemical bonding have been reviewed for the monoxides CeO and ThO, respectively. Currently quantitatively correct results for lanthanides and actinides can only be obtained from ab initio calculations for the easiest cases, e.g., small systems (atoms, diatomics containing one f element) with a possibly small number of unpaired f electrons and/or problems related only to configurations with the same f occupation number. In other cases ab initio quantum chemistry can at least help to interprete experimental findings. As an example organometallic cerium sandwich complexes such as cerocene were discussed, which may be considered to be molecular analogues of cerium(in)-based Kondo lattice systems. 

It may be helpful to explain the use of the terms rare earths and lanthanides throughout the text. By convenience, the term lanthanides refers to the elements La (Z = 57) to Lu (Z = 71). The term rare earths is commonly used for the lanthanides with inclusion of the elements Y (Z = 39) and Sc (Z = 21). Although one speaks often about rare-earth spectroscopy, the term lanthanide spectroscopy is preferable. The main objects of study in lanthanide spectroscopy are the trivalent lanthanide ions from Ce (4f ) to Yb3+ (4f ), since these ions have unpaired f electrons and can interact with ultraviolet, visible or near-infrared radiation. Divalent ions like Eu " " have gained less interest and will not be discussed here. The trivalent lanthanide ions La " (4f ) and Lu (4f ) are not spectroscopically active, because of an empty or filled 4f shell. The same is true for and Sc. Yttrium, lanthanum and to a lesser extent lutetium compounds are used as transparent host crystals in which other trivalent lanthanide ions can be doped. The trivalent lanthanide ions can readily substitute for Y, La " and Lu. Expressions like point group of the rare-earth site and the crystal field in rare-earth compounds are thus meaningful. 

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