Field limit

From tire above equation it follows tliat in tire mean-field limit replica symmetry is not broken. This makes tire GLO model conceptually simpler to interirret tlian tire random bond heteropolymer model discussed in tire appendix. 

In molecular doped polymers the variance of the disorder potential that follows from a plot of In p versus T 2 is typically 0.1 eV, comprising contributions from the interaction of a charge carrier with induced as well as with permanent dipoles [64-66]. In molecules that suffer a major structural relaxation after removal or addition of an electron, the polaron contribution to the activation energy has to be taken into account in addition to the (temperature-dependent) disorder effect. In the weak-field limit it gives rise to an extra Boltzmann factor in the expression for p(T). More generally, Marcus-type rates may have to be invoked for the elementary jump process [67]. 

The approach we have adopted for the d configuration began from the so-called strong-field limit. This is to be contrasted to the weak-field scheme that we describe in Section 3.7. In the strong-field approach, we consider the crystal-field splitting of the d orbitals first, and then recognize the effects of interelectron repulsion. The opposite order is adopted in the weak-field scheme. Before studying this alternative approach, however, we must review a little of the theory of free-ion spectroscopy... 

Of course, in real systems, the relative contributions of Coulomb and crystal-field effects are such as to place chromophores somewhere inbetween the weak-and strong-field limits. In that case, a real Txg F) A2g transition is not a pure two-electron jump, so that some intensity is observed. 

Finally, we must remember that just as a d-d spectrum is not properly described at the strong-field limit - that is, without recognition of interelectron repulsion and the Coulomb operator - neither is a full account of the energies or number of charge-transfer bands provided by the present discussion. Just as a configuration... 

Once you know, or can guess, the field limits of your spectrum, setting the center field and sweep width values is not very difficult. The center field corresponds to the middle of the spectrum and a sufficiently large sweep width chosen so that all of the spectrum is recorded. 

The inequality S S S B is sometimes called the weak-field limit because the external magnetic field B of a typical X-band spectrometer is sufficiently weak for... 

INPUT g-values git linewidth r, frequency v, field limits INPUT stepwidth in solid angle dcosB, dip spectral points n NULL absorption-array... 

The zero-field spin Hamiltonian parameters, D and E, are assumed to be distributed according to a normal distribution with standard deviations oD and aE, which we will express as a percentage of the average values (D) and (E). -Strain itself is not expected to be of significance, because the shape of high-spin spectra in the weak-field limit is dominated by the zero-field interaction. 

Equation 12.3 is readily rewritten for any other half-integer spin. For integer spins we have one singulet (the ms = 0 level) and S doublets, but we do not bother writing down the modified equation, because spin counting for integer-spin systems in the weak-field limit is near-to-impossible (Hagen 2006). 

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