Anisotropy term

The physical properties of metal nanoparticles are very size-dependent. This is clear for their magnetic properties, for which the shape anisotropy term is very important. This is also true for the optical properties of nanoparticles displaying plasmon bands in the visible range (Cu, Ag, Au) and for 111-V... 

For lanthanides other than Gd(III), the magnetic anisotropy still depends on the the local coordination environment it determines which crystal field anisotropy terms in Equation 7.2 are allowed by symmetry, the rest simply vanish. However,... 

The previous discussion refers mainly to diagonal anisotropy terms. 6° 0°, which only contain powers of Jz and are often dominant. Deviations from pure axial symmetry lead to non-zero off-diagonal terms with m 0. These terms mix... 

This equation shows that, at time t, each anisotropy term is weighted by a factor that depends on the relative contribution to the total fluorescence intensity at that time. This is surprising at first sight, but simply results from the definition used for the emission anisotropy, which is based on the practical measurement of the overall ly and I components. A noticeable consequence is that the emission anisotropy of a mixture may not decay monotonously, depending of the values of r, and Ti for each species. Thus, r(t) should be viewed as an apparent or a technical anisotropy because it does not reflect the overall orientation relaxation after photoselection, as in the case of a single population of fluorophores. 

This indicates that even in amorphous samples, in which the uniaxial Ki terms are expected to dominate due to the local distortions from cubic symmetry, there is still a significant contribution from the K4 cubic anisotropy terms. It is interesting to contrast this with the numerical simulations for a-TbFe2 which have shown that the fourth-order anisotropy eneigy per atom was an order of magnitude smaller than the second-order anisotropy energy per atom, albeit that the fourth-order term was of the same order of magnitude... 

The neighbor anisotropy term <7 of eq. (3.2) plays an important role in proton shielding, permitting, for example, a distinct differentiation between aromatic and olefinic protons due to the ring current effect. However, this contribution is small in 13C NMR (<2 ppm). A comparison of the methyl carbon shieldings in methylcyclohexene and toluene shows that the ring current effect often cannot be clearly separated from other shielding contributions ... 

Figure 20 shows a model of two coupled and generally nonequivalent magnetic nanodots or clusters. The dots total spins S and S can be written as S = N S0 and S = N S 0, where N and N are the respective numbers of magnetic atoms per dot. The Hamiltonian of the first dot contains the Zeeman energy - gjUojuBH S and the anisotropy term... 

All of these terms are written in the space-fixed axis system, with Z being the direction of the applied magnetic field, except for the last (the Zeeman anisotropy term), which is expressed in the molecule-fixed system. It is, of course, necessary to transform from space- to molecule-fixed axes in order to evaluate the matrix elements in a case (a) basis. 

The direction and magnitude of the shifts produced by lanthanide ions depends on their magnitude susceptibihty anisotropy terms. Because the unpaired electrons of the lanthanide ions are in 4f orbitals, and these are shielded by filled 5s and 5p orbitals, the magnetic terms are essentially independent of the ion s environment, and remain constant from complex to complex. In organic solvents such as chloroform, rare earths are found... 

The irreducible tensor product between two (spherical) vectors is defined in Eq. (37). An important feature of this Hamiltonian is that it explicitly describes the dependence of the coupling constants J, Am, and T, on the distance vectors rPP between the molecules and on the orientations phenomenological Hamiltonian (139). Another important difference with the latter is that the ad hoc single-particle spin anisotropy term BS2y, which probably stands implicitly for the magnetic dipole-dipole interactions, has been replaced by a two-body operator that correctly represents these interactions. The distance and orientational dependence of the coupling parameters J, A, , and Tm has been obtained as follows. 

The molecular spin-anisotropy term, the second term in Eq. (140), depends on the angle between the 02 spin momentum SP and the molecular axis. With respect to the global frame, this dependence can be expressed as in Eq. (140) with the second-rank tensor... 

For the prototype level (n,Jl,v, j, J)=(0,0,1,0,0T"of H2-, D2-and HD-Ar, the results of close coupling calculations for the partial and total predissociation widths are listed in Table V. Tests showed that the angular basis sets used to obtain these results were fully converged (25) they included diatom rotation states up to j 8 for v l and up to j" 10 for v -O. The absence of odd-j" dissociation products for H2- and D2-Ar merely reflects the fact that their potentials have no odd-j anisotropy terms. 

The discussions above have shown that the pseudocontact component of the isotropic shift in 1,1 -dialkyluranocenes is accurately given by the axially symmetric form of eq. 3 and thus, these systems can be used in evaluating both the assumptions employed in deriving, and the value of the anisotropy term (xn Xj[ ) used, by previous workers in factoring isotropic shifts in uranocenes. 

In the following discussion, all calculated shifts are derived assuming a temperature of 30°C. For numerical convenience, the anisotropy term Xu - Xj will be expressed in terms of y j2 - yj2. ... 

Reducing the magnitude of the calculated pseudocontact shifts requires smaller values of the anisotropy term X -Xj / which can only result if Xj O. This result provides independent confirmation of the same result of Fischer cited above. We noted also that both the electronic structure of uranocene proposed by Warren (63), assuming a Jz= 4 ground state, and a recent model proposed by Fischer (15), assuming a Jz=3 ground state, show that XjJLs non-zero, and less than X(j, at 30°C. 

Early attempts to factor the isotropic shifts in alkyl-uranocenes using eq. 9 were not completely successful because of failure to correctly assess the conformation of the substituent in solution and overestimation of the value of the anisotropy term jj-Xj (5,6,14). ... 

Another important result of this study is the confirmation of Fischer s demonstration that Xj is not equal to zero in uran-ocene. Early attempts to factor isotropic shifts in uranocene have generally assumed that Xj[=0, and leads to overestimation of the anisotropy term. A precise value of Xj is difficult to determine rigorously from analysis of available NMR data. We have found that y 2 - yj 2 = 12.5 BM2 leads to the best internal consistency factored isotropic shifts for a wide variety of 1,1 -dialkyluranocenes. Assuming yav2 = 5.76 BM2 and yjj - yj 2 = 12.5 BM2, at 30°C/ the corresponding values of y. 2 and yj2 are 14.09 and 1.59 BM2, respectively. This implies that Xj j/X L 8 uran ocene, a value substantilly larger than Fischer s ratio of X /Xj = 2.8 (15). 

All our attempts to observe Pt NMR signals from either PtCli " or cis-Pt( NH3)aCl2 bound to reduced cytochrome c or ribo-nuclease A (RNase) have so far failed. These platinum complexes are known to bind to the sulphur atoms of exposed methionines (residues 65 and 29 of Cyt c and RNase respectively) as shown by our previous H NMR studies on RNase (28) and those of Boswell et al on Cyt c (29) and x-ray crystallography. We assume therefore that the resonances are broadened beyond detection via chemical shift anisotropy relaxation. The restriction of Pt mobility on the protein will lead to a large increase in (see CSA equation above). The anisotropy term would also be expected to increase. Scalar coupling to N will also contribute to the increase in linewidths if nitrogen binding sites are involved. 

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