Intermediate coupling effects

The crystal field parameters given in Tables 8.6 and 8.7 show an uneven variation with atomic number. The crystal field calculations are not of the same degree of reliability. In some cases, crystal field interactions between ion levels have been ignored. In other cases, the calculations included only levels derived from the ground multiplets while in some cases intermediate coupling effects have not been included. The validity of the data depends on whether all the available information has been used and the discrepancies are not due to incomplete treatment of the problem. 

Values of (r" ) are based primarily on theoretical calculations of the 4f wave functions, for example, those of Freeman and Watson (1962) and of Judd (1963). In table 18.5 are listed the values of (/ N /), (r ), and Hfs for the tripositive rare-earth ions. Strictly speaking, correction factors differing from unity by a few percent should be applied to these (/ M /) values [Bleaney (1972)] to take account of intermediate coupling effects which arise from the admixture into the ground state (L, S, J) wave function of states of different L, S, but the same /, by the spin-orbit interaction. A table of these values is included in Bleaney (1972). 

For mixtures of unlike ions (the usual case), the apparent diffusivity will be intermediate between these values because of the elec tric coupling effect. For a system with two counterions A and B, with charge z-a and z-b, Eqs. (16-73) and (16-74) reduce to ... 

As seen in Fig. 8 the experimentally determined magnetic moments at room temperature are in general much lower than the free ion values. To extract the contribution of orbital reduction, the influence of intermediate coupling, crystal field effects and j-j mixing must be considered. 

Intramolecular carbonylative cross-coupling involving enolizable GH-acidic fragments has been described by Negishi et al. In this case, trapping of acylpalladium intermediate is effected formally by enolate, either with carbon or oxygen center (Scheme 28). 

The foregoing has been concerned with the application of SERS to gain information on surface electronic coupling effects for simple adsorbed redox couples that are reversible in the electrochemical as well as chemical sense, that is, exhibit Nernstian potential-dependent responses on the electrochemical time scale. As noted in the Introduction, a major hoped-for application of SERS to electrochemical processes is to gain surface molecular information regarding the kinetics and mechanisms of multiple-step electrode reactions, including the identification of reactive surface intermediates. 

For C60, the coupling is in fact presumably in an intermediate coupling regime, so that all these effects should be taken into account and JT distortions could manifest themselves in a variety of ways. However, the previous classical treatment is very useful as a starting basis to get an intuitive idea of the situation and will be introduced now. The principle of the calculation is not fundamentally different than in the previous simple model, although symmetry considerations become more complicated as the number of modes involved increases, as well as their degeneracy. 

The relativistic effects of intermediate coupling are important in the case of superposition of spin-forbidden and spin-allowed transitions (chromium (III) in the cases when A 21B, most nickel (II), 03 of tetrahedral cobalt (II)) and in the cases of the 5d group (Re (IV), IrF etc.). 

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