Isotropic exchange constant

Intercentre distance determined from isotropic exchange constant given by the following equation = +JS-1S2. 

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. 

If b = 0, a = 1 the Ising model, if b = 1, a = 1 the isotropic Heisenberg model, and if b = 1, a = 0, the planar Heisenberg model or X-Y model is valid. In the following, the values of the exchange constants were calculated, or recalculated assuming a spin Hamiltonian of this form, instead of = - J 2 SjSi, occasionally used by certain au-... 

In Eq. (3-2), / is the value of the exchange integral between two electron spins (Si and S2) and the 1/2 term is put for convenience although it is not used in many textbooks. Eq. (3-3) is just the sum of spin Hamiltonian of one radical given by Eq. (2-22), but the nuclear Zeeman terms are omitted in Eq. (3-3) because their magnitude is much smaller than those of the electron Zeeman term and the HFC one. In Eq. (3-3), ga and gb are the isotropic g-values of two component radicals (radicals a and b) in a radical pair, respectively, and A, and A are the isotropic HFC constants with nuclear spins (/, and 4) in radicals a and b, respectively. 

Table 13. Calculated isotropic HFC constants, in MHz, of transition metal compounds and their dependence on the exchange-correlation functionals. Reproduced from 1155]...

Some magnetic parameters enter the matrix elements of the Hamiltonian concerned these are magnetogyric factors (g-factors, components of the g-tensors) and the coupling constants (components of the spin-spin coupling tensors D, in the case of an isotropic exchange abbreviated as J). 

From the temperature dependence of EPR spectral intensities over the range 9-18 K it is possible to estimate J, the isotropic exchange coupling constant for the irons of their spin-coupled centers This procedure yields J = 14 1 cm for uteroferrin and J = 11 1 cm for the splenic enzyme (taking the exchange Hamiltonian, Hex = + JSi S2). This low value for J has been corroborated by H NMR studies at room temperature for uteroferrin /. Recent studies of mixed-valence, spin-coupled Fe(ni)-Fe(III) model compounds for uteroferrin indicate that such low values for J are consistent with iron atoms joined by a p-hydroxo or p-phenoxo bridge . ... 

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