Free-ion states

The assumption of a large crystal-field interaction for Pu5+ spectra makes it necessary to conclude that while certain aspects of earlier free-ion estimates (37) are valid, the "assignment" of free-ion states to observed absorption bands was premature. Much of the structure must be due to crystal-field components of many free-ion groups that overlap in energy or to vibronic satellites similar to those encountered in CS2UCI6 (33). Thus, while the present computations would agree with earlier work in interpreting the levels observed in... 

When a lanthanide ion is placed in a ligand environment with symmetry lower than spherical, the energies of its partly filled 4f orbitals are split by the electrostatic field of the ligand. The result is a splitting of the 2/ + 1 degeneracy of the free ion states (see Figure 1.2). 

This notion of occasional ion hops, apparently at random, forms the basis of random walk theory which is widely used to provide a semi-quantitative analysis or description of ionic conductivity (Goodenough, 1983 see Chapter 3 for a more detailed treatment of conduction). There is very little evidence in most solid electrolytes that the ions are instead able to move around without thermal activation in a true liquid-like motion. Nor is there much evidence of a free-ion state in which a particular ion can be activated to a state in which it is completely free to move, i.e. there appears to be no ionic equivalent of free or nearly free electron motion. 

The luminescence of Yb " in the near UV and visible is due to 4/ -4/ 5d transitions. The energy level scheme of the Af Sd configuration of Yb in crystals is complicated due to the simultaneous action of the crystal field and spin-orbit coupling on the free ion states. The lowest energetic excited states, arising from the free ion level, have and Eu symmetry. About 2,000-3,000 above these levels there are levels from the state. Only transitions between the ground state ( Ai ) and states with Ti symmetry are symmetry allowed. 

The most important free ion states are ground level and excited level. In an octahedral field, the level splits into the A2 groimd state and the excited T2 and states. The spin allowed transitions that could therefore be used to populate the excited states directly correspond to A2 T2 and... 

As stated in an earlier paragraph, the sharp emission and absorption lines observed in the trivalent rare earths correspond to/->/transitions, that is, between free ion states of the same parity. Since the electric-dipole operator has odd parity,/->/matrix elements of it are identically zero in the free ion. On the other hand, however, because the magnetic-dipole operator has even parity, its matrix elements may connect states of the same parity. It is also easily shown that electric quadrupole, and other higher multipole transitions are possible. 

Since a chemical environment does not normally interact directly with electron spins, the spin multiplicity of a state is unaffected by the splitting and the split states will have the same multiplicity as the parent free ion state. The quantum number J also remains unaltered. For this reason, multiplicities and J values are left out in Table 12-5.1. 

For a d1 ion in a tetrahedral environment, exactly the same procedure can be carried out. The free ion states will be the same as in the octahedral case. The type of states produced from a particular free-ion... 

The second part of Bethe s paper describes a method by which the magnitudes of the splittings of the free-ion states may be calculated, assuming... 

There are, however, many cases of interest in which we may want to determine the splitting of a state that is well characterized by its total angular momentum, J. This will in fact be the only thing of importance in the very heavy elements, for example, the rare earth ions, where states of particular L cannot be used since the various free-ion states of different J are already separated by much greater energies than the crystal field splitting energies. 

Figure 27 Splitting of a free-ion state into 27+1 components by a magnetic field (a) for J even, (b) for J odd (i) for the first-order Zeeman effect (ii) including the second-order Zeeman effect...

Mah et al. demonstrated the effect of counterions on the cationic polymerization of styrene [35-37]. The radiation-induced polymerization is much more sensitive to impurities than the catalytic polymerization, as the former involves the cationic species in a free ion state. Thus, one can expect, in the presence of stable anions, the promotion of the cationic polymerization because of the ion-pair formation between the dimer cation and the counterion. The effect was... 

Fig. 17. Electron configurations of di- and tri-valent iron and cobalt in the free ion state and in the cyanide complexes (Pauling).

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