Spin-Hamiltonian parameters asymmetry

Fig. 20 Spin-Hamiltonian projection (level-6) of magnetic parameters on tetragonal distortion of Ti(III) complexes. D is the asymmetry parameter - gray area white surface -exact multiplet splitting...

Fig. 95 Spin-Hamiltonian projection (level-6) of magnetic parameters on tetragonal distortion of high-spin/intermediate- and weak-field Co(II) complexes. D relates to the energy gap for the compressed bipyramid, and refers to the asymmetry parameter for the elongated one light surface - exact multiplet splitting gray area - spin Hamiltonian projection. Note the graphs for the g-components and TIP have interchanged axes...

As an example of how to determine the electronic ground state of a low-spin iron(lll) compound, we present work on the ferric low-spin heme complex [TPPFe(NH2PzH)2]Cl, which has been shown to have a (dxy) (dxz, dj, ) electronic ground state. The field-dependent Mossbauer spectra of [TPP Fe(NH2PzH)2]Cl displayed in Fignre 12 are well reproduced by simulations, which yield 5 =0.25mms , AEq = ( )2.50imns, an asymmetry parameter rj = —3, and an anisotropic A tensor of" / nMn = (-47.6, 6.7, 18.3)T. The g values necessary for the 5" = 1 /2 spin Hamiltonian (g z = 2.39, gyy = 2.28, and gxx = L87) have been taken from a combined EPR and electron spin echo envelope modulation spectroscopy ESEEM analysis. 

The detailed structure of the Mossbauer and ESR spectra for the iron transport compounds can be described in terms of a spin Hamiltonian with effective spin S= 5/2 for the high spin ferric ion. These parameters can give information about the site symmetry of the iron. Since there is no orbital angular momentum in the 6S state, the effective spin is the same as the real spin of the iron ion. There is spherical symmetry in the 6S state to first order, but spin-orbit coupling to excited (non-spherical) orbital states gives rise to asymmetries about the iron site which are reflected in the spin Hamiltonian. The general form of the spin Hamiltonian which we will use here is a quantum mechanical operator which acts on the electronic states ms> and nuclear states mf>. 

A rather complete Mossbauer study of the 57Fe complexed by deferoxamine has been done by Bock and Lang (38) and their results are in excellent agreement with a model spin Hamiltonian in which the coupling constants have the values D=0.5 cm-1, A = 77/3 =0.46, Aex = 1.474 mm/sec, P =—0.30 mm/sec (or AEq =0.77 mm/sec in absence of magnetic interactions). The asymmetry parameter A = /3> 1/3 merely means that the principal distortion axis is in the y-direction instead of the z-direction for the axis system assumed for the spin Hamiltonian. We will use an axis system in which 0 < X < 1 and D >0 so that we can compare with other molecules. Some of the data and the fitted curves show the typical features associated with these iron transport compounds. 

Figure 8 Mossbauer spectrum of a frozen aqueous solution of [ Fe +]-ferrioxamine B (12mM) employing BSA (lOOmM) as a dilutant to minimize spin-spin relaxation. The solid line represents a simulation based on a spin Hamiltonian line width = 0.35 mm s zero-field splitting, D = 1.2 cm E rhombicity parameter, E/D = 0.33 8 = 0.52mms A q = —0.84mms asymmetry parameter, rj = and isotropic hyperfine coupling tensor Axx/gN/XN = Ayy/gNMN = Azz/gx/XN = —22.1 T. The simulation does not completely fit the experimental data. This discrepancy is caused by relaxation effects that are not dealt with in the spin Hamiltonian simulation...

The last three terms of the spin Hamiltonian shape the Mossbauer spectrum because they describe the interaction of the nucleus with the atom, the solid and the external magnetic field. The term I - A - S describes the magnetic interaction between the nucleus and the atom. This acts through components of the atomic spin which are determined by the Boltzmann population of the spin Hamiltonian states shown in Figure 4.2. Thus the first three terms of the spin Hamiltonian act to determine values for the components of S that are used in the magnetic interaction that shapes the Mossbauer spectrum. The mechanisms involved in this nucleus-atom interaction I A S will be discussed in detail in the next section. The quadrupole interaction term represents the interaction of the nuclear quadrupole moment with the EFG produced by the atom and the lattice. The principal component of the EFG is V — d Vldz (V is the electric potential at the nucleus) and the asymmetry parameter =... 

As mentioned in Section 3.1, phase biaxiality may be described by a set of microscopic order parameters when the mesogen is a rigid uniaxial particle, where a and (5 refer to the space-fixed axes x y z). Biaxial nematics [3.31], some smectic phases, like smectic C, and certain discotic phases [3.32] exhibit phase biaxiality. The order parameters 5, , and 5, , are different in these phases. NMR may be used to detect phase biaxiality through measurement of a non-zero motionally induced asymmetry parameter in nuclear spin interactions such as dipole-dipole and electric quadrupole interactions. To see how exists in biaxial mesophases, the previous discussion on motional averaging of spin Hamiltonian is gen-... 

There is a general statement [17] that spin-orbit interaction in ID systems with Aharonov-Bohm geometry produces additional reduction factors in the Fourier expansion of thermodynamic or transport quantities. This statement holds for spin-orbit Hamiltonians for which the transfer matrix is factorized into spin-orbit and spatial parts. In a pure ID case the spin-orbit interaction is represented by the Hamiltonian //= a so)pxaz, which is the product of spin-dependent and spatial operators, and thus it satisfies the above described requirements. However, as was shown by direct calculation in Ref. [4], spin-orbit interaction of electrons in ID quantum wires formed in 2DEG by an in-plane confinement potential can not be reduced to the Hamiltonian H s. Instead, a violation of left-right symmetry of ID electron transport, characterized by a dispersion asymmetry parameter Aa, appears. We show now that in quantum wires with broken chiral symmetry the spin-orbit interaction enhances persistent current. 

Henceforth the term t) will be taken to refer exclusively to the asymmetry parameter in the quadrupole interaction). The energy equation for the quadrupole interaction can be transformed into a form that makes it compatible with the other Hamiltonians above by substituting spatial operators with spin operators using the Wigner-Eckart theorem (Slichter 1990) which after some manipulation gives the quadrupole Hamiltonian in the PAS of this interaction... 

In quadrupolar nuclei, the situation differs notably the quadrupolar interaction only affects spins with I>% and is created by electric field gradient resulting from the asymmetry of charge distribution around the nucleus of interest. The quadrupolar interaction is characterized by the nuclear quadrupolar coupling constant Cq (from 0 in symmetrical environments to tens or hundreds of MHz) and an asymmetry parameter T]q. NMR spectra are usually recorded when Cq Vl the Larmor frequency of the quadrupolar spin. In such a case, the NMR spectrum can easily be simulated First, the first-order quadrupolar Hamiltonian, which is the quadrupolar interaction Hamiltonian truncated by the Larmor frequency, has to be taken into account. The first-order quadrupolar interaction (or the zeroth-order term in perturbation theory) is an inhomogeneous interaction and is modulated by MAS and does not affect symmetrical transition —m +m. Therefore, in half-integer spins, the single-quantum central transition (CT, i.e., —1/2 +1/2) is not affected by the first-order quadrupolar inter-... 

NH2 Radical. The NH2 radical Is an asymmetric top with the asymmetry parameter k = (2 B-A-C)/(A-C)= -0.38 (axes b C2, c molecular plane). An increase of the rotational quantum number N leads to a change from prolate- to oblate-top behavior. The rotational constants A, B, and C, the centrifugal distortion constants Ak, A k, A, 5k, and 5, and the spin-rotational coupling constants Ag, Bg, and Cg, for the vibrational ground and excited states are listed in Table 10, p. 182. The rotational Hamiltonian used for fitting the spectroscopic data is a combination of the A-reduced asymmetric rotor Hrot [1] and the spin-rotation Hamiltonian figR [2] ... 

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