Bleaney theory

In their subsequent analysis Baker and Bleaney (ibidem) decided to ignore the last term on the assumption that gdl 3b hv. Although this is a reasonable approximation for lanthanide and actinide integer-spin ions doped in single crystals, it is not usually an acceptable assumption for the broad-line spectra from metalloproteins. Furthermore, the assumption of a A-distribution around zero (i.e., D 0 but all other zero-field interaction parameters are zero) is equally untenable for biomolecules. Therefore, we go for a later extension of the theory, based on a full Equation 12.9 and on (A) 0, for application to metalloproteins (Hagen 1982b). 

Bleaney, B., Bowers, K.D., and Pryce, M.H.L. 1955. Paramagnetic resonance in dilute copper salts III. Theory, and evaluation of the nuclear electric quadrupole moments of 63Cu and 65Cu. Proceedings of the Royal Society of London A 228 166-174. 

Bleaney, M.F. (1976) Underconsumption Theories, London Lawrence and Wishart. 

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. 

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 ... 

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)... 

Bleaney, M. Underconsumption Theories. New York International Publishers 1977. 

References for the ENDOR experiment include the following A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, 2nd Ed. Oxford Press (Clarendon), Oxford, 1970 A. Carrington and A. D. McLachlin, Introduction to Magnetic Resonance with Applications to Chemistry and Chemical Physics. Harper Row, New York, 1967 N. M. Atherton, Electron Spin Resonance Theory and Applications. Halstead Press, New York, 1973 L. Kevan and L. D. Kispert, Electron Spin Double Resonance Spectroscopy. Wiley, New York, 1976 J. R. Pilbrow, Transition Ion Electron Paramagnetic Resonance. Oxford Univ. Press (Clarendon), Oxford, 1990. 

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. 

Fig. 7. Variation of the sub-lattice magnetization in the antiferromagnet GdV04 below = 2.4955(5)K. O from NMR frequency of V (J=i) (Bleaney et al. 1981c). Mossbauer data (Cook and Cashion 1979). — Molecular field theory.

In an NMR investigation of the spectrum in TmV04, Bleaney and Wells (1980) found that the frequency of oscillation of the RF circuit containing the crystal was a sensitive monitor of variations in the RF (adiabatic) magnetic susceptibility Zs-Below To, where the ground doublet is split by the distortion, is independent of a field applied along the c-axis, until this reaches the critical field B at which the Jahn-Teller distortion is reduced to zero. At this field Zs falls sharply, and the effect can be used to give a precise measurement of B. The results were fitted accurately to the relation b = B /Bo = tanh(b/f), where t - T/T ) = T/2.156 is the reduced temperature. This is the result expected from mean-field theory. In the distorted state below T, the presence of domains with principal axes [110] and [110] was confirmed by observation of two sets of anisotropic resonance curves (see fig. 13c), one set for (/ —i) and the other for the enhanced NMR of Tm (/ = i). 

Estimates of exchange int rals according to different measurement data depend critically on the g-values used for calculation of magnetic dipole-dipole interactions. The g-values calculated within the framework of the crystal field theories usually differ from the experimental results (EPR, magnetization) by up to 10%. This difference may be due to the covalency of lanthanide ion-ligand bonds (Abragam and Bleaney 1970) and to the vibronic reduction effects (Ham 1965). 

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). 

Condon, E.U., Shortley, G.H. TIte Theory of Atomic Spectra (Cambridge University Press 1953). Ballhausen, C.J. Introduction to Ligand Field Theory (McGraw-Hill Book Company, New York 1962). Bleaney, B., Stevens, K.W.H. Rept. Progr. Phys. 16 (1953) 108. 

The following paragraphs serve a dual purpose (a) to introduce, define and briefly discuss all those quantities which directly occur in the tables and (b) to provide a short introduction to the review literature on the EPR of transition metal compounds. For additional information on the theoretical and/or experimental aspects of the method, the literature listed in section 2.1.5.4 and section 2.1.5.5, respectively, may be useful. It should be observed that apart from the general references on EPR, viz. section 2.1.5.1, these sections inclusive of section 2.1.5.3 list only literature which has been published in the two years covered by this volume. Since the larger part of the basic theory of EPR was published before 1971, the reader might sometimes wish to consult the corresponding references in volumes II/2, II/8 and II/IO of the New Series. In addition, for transition metal compounds, the comprehensive volume of Abragam and Bleaney [1] should be consulted. An annual review on the EPR of transition metal compounds is now also available [29]. 

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. 

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