Further electronic effects on nuclear relaxation

1 The effect of g anisotropy and of the splitting of the S manifold at zero magnetic field 

The electronic term which is the first term in the Hamiltonian written in Eq. (3.13) and used to derive the Solomon and Bloembergen equations (Eqs. (3.16), (3.17), (3.19), (3.20), (3.26), (3.27)) may be inappropriate in many cases, since the electron energy levels may be strongly affected by the presence of ZFS or hyperfine coupling with the metal nucleus. Therefore, the electron static Hamiltonian to be solved to find the cos values, i.e. all electron energy transitions, and their probabilities, will be, in general, 

Let us discuss first the case in which only the first term is present. In the Solomon and Bloembeigen equations for / , (i = 1, 2) there is the cos parameter at the denominator of a Lorentzian function. Up to now cos has been taken equal to that of the free electron. However, in the presence of orbital contributions, the Zeeman splitting of the Ms levels changes its value and cos equals xs / o or (g/h)pBBo- When g is anisotropic (see Fig. 1.16), the value of cos is different from that of the free electron and is orientation dependent. The principal consequence is that another parameter (at least) is needed, i.e. the 0 angle between the metal-nucleus vector and the z direction of the g tensor (see Section 1.4). A second consequence is that the cos fluctuations in solution must be taken into account when integrating over all the orientations. Appropriate equations for nuclear relaxation have been derived for both the cases in which rotation is faster [40,41] or slower [42,43] than the electronic relaxation time. In practical cases, the deviations from the Solomon profile are within 10-20% (see for example Fig. 3.14). 

In any case, the presence of ZFS may cause the occurrence of a further dispersion in the plot of relaxation rate as a function of proton Larmor frequency, corresponding to the transition from the dominant ZFS limit to the dominant Zeeman limit6 (Fig. 3.15). 

Another mechanism to provide splitting of the S manifold is the hyperfine coupling between the unpaired electron and the metal nucleus. For example, at zero magnetic field an S = Vi / = V2 system gives two sets of levels of degeneracy 3 and 1, separated by A (see Appendix III) where A is the metal-nucleus-unpaired-electron hyperfine coupling. The effect of this splitting is 

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