Exchange isotropic

Isoselectivity rule, 238 Isotropic exchange (see Exchange reactions)... 

Let us now consider the metallic regime, following the discussion of [18]. For nuclei coupled to a mobile system of independent electrons by an isotropic exchange interaction of the form A l S, where I is the nuclear spin and S the electron s spin, the Knight shift can be written as... 

Equation 7.1 utilizes exchange coefficients to predict steady-state BCFs and ATswS, and the model assumptions include a uniform lipid phase enclosed in a non-interactive membrane. The model shows that the magnitude of a BMO s BCF or an SPMD s Ksvj is affected by variations in ku and/or ke, unless both constants rise or fall proportionally. In the case of SPMDs, Huckins et al. (1993,2002a) have shown that the uptake and release process is essentially isotropic for HOCs. When residue exchange is isotropic, AfswS will remain relatively constant even when exposure conditions affect SPMD ku and ke values. This is not always the case for BMOs, yet isotropic exchange is a fundamental assumption of EP theory. 

Recent studies of the 180 isotropic exchange of [V 0028]6 and the orthovanadate ion, [V04] 3 , have shown slow kinetic exchange (fy2> minutes to hours) and have proven the identity of discrete decavanadate ions in solution. 

In subunit R2 of ribonucleotide reductase there is a tyrosyl radical (Y ) in close proximity to a di-iron cluster.100 In the protein from E. coli the EPR signal from Y can be observed up to room temperature. However, in the protein from yeast the Y signal broadens above 15 K and is not observable above about 60 K. Saturation recovery measurements at 140 GHz showed that at 60 K the spin-lattice relaxation rates for the Y signal in the yeast protein were about 2 orders of magnitude faster than for the E. coli protein. The temperature dependence of the relaxation enhancement was consistent with the activation energy for the first excited state of the di-iron cluster, so the relaxation enhancement was attributed to interaction with the di-iron cluster. Relaxation enhancements measured at 140 GHz showed little orientation dependence so the enhancement was assigned to isotropic exchange, which is different from the orientation-dependent dipolar interaction observed for the E. coli protein.100... 

The coefficients a and b (see Table 3.2) take into account the restrictions in spin dimensionality. For a = b= 1, the Heisenberg model with isotropic exchange interaction and isotropic susceptibility results. The combination of a = 1 and b = 0 yields the strictly anisotropic Ising model, in which the orientation of the spins is restricted to the z-axis. Consequently, the susceptibility is strongly orientation dependent and one needs to differentiate between x" in the direction of the z-axis ( easy axis ) and x perpendicular to z. The molar susceptibilities are then related as... 

What is the coimection between the HDW exchange interaction of eqnation (27) and the complexities of an ion in a crystal field The isotropic exchange Hamiltonian is always correct since it is a direct conseqnence of the Panli Exclusion Principle. However, a modified form of the exchange interaction is frequently nsed to describe those cases in which the individnal moments are no longer isotropic. 

The symmetry-adapted vibrations A Qai = Q ) and doubly degenerate E type Qex = Qx, Qej = Qy) of an equilateral triangular unit are shown in Fig. 1 along with the molecular coordinate system. The vibronic interaction arises mainly from the modulation of the isotropic exchange interactions by the molecular displacements and can be expressed as ... 

This result proves to be valid for all MV — d" pairs with n < 4, provided that the spin core is defined as an ion without extra electron. It is also valid for n > 4 but in such case the spin core must be defined as an ion without extra hole. The ferromagnetic effect of the double exchange is illustrated by Fig. 7. Along with the double exchange, the isotropic exchange interaction plays an important role in MV clusters. This interaction is described by the HDVV spin Hamiltonian ... 

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