Anisotropic spectra spin Hamiltonian

When the anisotropic spin Hamiltonian parameters g, and are obtained from the powder spectrum in the rigid limit, one can dehne the quantities... 

In order to analyze these data, the frequency shift of geffectivecan be calculated by averaging over all orientations the anisotropic shift derived from a static spin Hamiltonian [67]. This treatment is based on the assumptions that molecular motion neither changes the spin precession rate nor perturbs the states and, thus, that the center of gravity of the spectrum is invariant even in presence of some motional averaging. For the allowed 11/2) <-> <-l/2 transition under perturbation theory, with expressions valid up to the third order, this shift is given by [47] ... 

In the general case, both isotropic and anisotropic hyperfine interachons contribute to the experimental spectrum. The whole interaction is therefore dependent once again on orientation and must be expressed by a tensor. The effechve spin Hamiltonian for this more reahstic descriphon of a paramagnehc species in the solid state was given earher in Equahon 1.28. Nevertheless the A tensor may be split into its component isotropic and anisotropic parts as follows ... 

Unusual magnetic and electrical properties might also arise from quasi one-dimensional crystal structures of these compounds. The acceptor stacks /especially TCNQ/ may be either regular, i, e. with equally spaced molecules, or alternating when composed of diads, triads or tetrads. In the latter case some substances exhibit EPR spectrum characteristic of mobile, thermally activated triplet states /triplet excitons/, The spectrum may result from the excitation of two or more coupled TCNQ entities /6, 7/. The triplet character of the paramagnetic excitation is shown by the anisotropic two-lines EPR spectrum which results from a zero field splitting of the triplet levels being described by the spin Hamiltonian /8/j... 

An octahedral field leaves a T state lowest which is split by means of spin-orbit coupling. A Kramers doublet being lowest, the spectrum is usually isotropic with 5=. In a field of lower symmetry, the spectrum consists of six Kramers doublets and becomes highly anisotropic, although again S=j. The spectra are interpreted in terms of the spin Hamiltonian Eq. (16) using S=. ... 

In the columns for g and A, there is only one numerical value listed for each, whenever the spin Hamiltonian appears to be isotropic. Where an anisotropic (e.g. axial) spin Hamiltonian is applicable, the principal values of the g and A tensors are always preceeded by the appropriate symbols (e.g. g, gj or A,B). Due to space limitations, special inserts into the general table appear, whenever zero field splitting parameters are required in the description of the EPR spectrum. In this case, the parameters employed are specified in the headline to the insert, consistent with the appropriate spin Hamiltonian, e.g., D and E if the symmetry is lower than axial. 

In general, to describe the EPR spectrum in a motional regime, a procedure based on the solution of the stochastic Liouville equation should be used [49-52]. However, in low-viscosity media, a very fast molecular tumbling leads to an averaging of the anisotropic part of the spin Hamiltonian to zero, and the spectrum is composed of narrow Lorentzian lines, and is characterized by... 

In their early study of the ruby spectrum Sugano and Tanabe [44] attributed the zfs to the trigonal anisotropy of the spin-orbit coupling. In a simplified form the anisotropic s.o.c. hamiltonian may be written as ... 

Detailed calculations of the spinning sidebands in DAS spectra have been carried out using average Hamiltonian and irreducible tensor approaches (Sun et al. 1992). In DAS spectra the sideband intensities and their moments depend on the relative rotor phase between the two evolution periods. The sideband intensities additionally depend on the ratio of the time spent at each angle. The 2D O DAS spectrum of zeolite Sil-Y (Figure 3.22) shows three lines in the ratio 2 1 1 (Bull et al. 1998). Simulation of the anisotropic slices from the O 2D DAS spectrum for each peak allows extraction of xq and t] for each resonance. 

In an isotropic liquid the mean value of is zero and the quadrupole interaction contributes only to relaxation. In an anisotropic medium, on the other hand, the mean value of is no longer zero and a quadrupole splitting appears in the NMR spectrum. While the quadrupole hamiltonian in Eq. (7.3) may be evaluated in any coordinate system it is convenient to express the spin operators in a laboratory-fixed coordinate system and the electric field gradients in a principal axes coordinate system fixed at the nucleus. It is then suitable to rewrite the hamiltonian as... 

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