Bleaney’s theory

Studies on proton shifts in aqueous solutions of lanthanide perchlorates showed irregular sign variation of the shifts in the series and quite different from 170 shifts. This observation led to the idea that proton shifts are predominantly due to dipolar contributions. Further the proton shifts departed from Curie s law significantly [17]. The relative dipolar shifts and their temperature dependence can be predicted by Bleaney s theory [18]. For now Eu3+ and Sm3+ are not considered. 

Quantitative separation of the n contact and pseudocontact contributions to the lanthanide induced shifts (LIS) in aniline and m-and p-toluidines has been reported. (395, 396) The contact shift patterns are estimated from the rr-spin density distribution of the appropriate cation radical or from the Ni(acac)2 induced shifts. The separation of the shifts was checked by comparing the relative contact shift contribution with the <5 ) value of Golding and Halton (389) and the remaining pseudocontact contribution with the calculated values of Bleaney s theory. (380)... 

Obviously, the use of eq. (38.6), which considers only the first term in the expansion of the Boltzmann factors, with g-tensor components weighted by unequal populations of the corresponding levels is a contradiction in terms and as could be anticipated leads to erroneous results. It is thus clear that Bleaney s theory accounts satisfactorily for the dipolar shifts in lanthanide complexes, whereas the criticisms of this theory, Horrocks et al. (1973), seem to be not well founded. We wish to emphasize that the generalized treatment of Golding and Pyykko (1973) is of course more rigorous. 

The induced shifts of nuclei not directly adjacent to lanthanide ions have been known for many years to be predominantly dipolar in nature. However, a fully satisfactory theory to account for the variation in these induced shifts across the lanthanide series has been difficult to achieve. Theoretical treatments have been developed independently by Bleaney, (380) Golding and Pyykko, (381) and Horrocks et al. (382) Bleaney s approach involves the following power series expansion in temperature for the susceptibility anisotropy, assuming axial symmetry ... 

A large part of the theory of the effect of an external magnetic field on lanthanide ions in crystals was developed in the context of paramagnetic resonance (Bleaney and Stevens 1953). It is that field that bequeathed optical spectroscopists the spin Hamiltonian and its various elaborations. This is not to say that such devices have ever been taken much advantage of. After all, the perturbation Hamiltonian m-(L + 2S), where P is the Bohr magneton and H the applied magnetic field, is particularly simple to evaluate, since the quantum number S and L are used in defining all lanthanide states. 

The 4f electrons of the rare-earth ions are characterized by their total momentum J where J is in general a good quantum number, J=L+S. For a cubic crystal field (CF), group theory predicts that manifolds with J <2 are not split. The ground state hereby is a Fs doublet for y = 5, a F4 triplet for 7 = 1 or a Tg quartet for 7 =. The doublets Fs and Fy (7 > 2) can be described by spin Hamiltonians with 5=1 and have isotropic g-values (Abragam and Bleaney 1970). The Fg quartet can be described by a spin Hamiltonian with S=. Its peculiar magnetic properties are described in detail by Abragam and Bleaney (1970). 

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