Symmetry active definition

The following expressions of the transfer coefficient (symmetry factor) result from the quadratic activation-driving force relationship in equation (3.3) and from the definition of the intrinsic barrier in equation (3.4) ... 

As far as the definition of a as a measure of the symmetry of the activation barrier is concerned, as shown in Figure 15, let us focus on the apical region of the intersection between the free energy curves illustrated in Figure 14. 

This definition is because there are cases in which the Hamiltonian symmetry group has more elements (double) than the point symmetry group of the active center. Those cases deal with rare earth ions with half-integer J values for instance, the Nd + ion. They will be treated in Section 7.7. 

The g tensors and hyperfine constants of the paramagnetic centers observed in irradiated NH4Y zeolites after various activation treatments are given in Table VIII. Despite the abundance of experimental results, many of the structures proposed for these centers should be regarded as suggestive rather than definitive, as previously noted by Kasai and Bishop (264). Neither the axially symmetric g tensor of the V center associated with two aluminum atoms nor the isotropic g tensor of the V center associated with one aluminum atom reported by Vedrine et al. (266) is consistent with the symmetry of the respective models proposed above. 

The coupling terms and elastic energy terms must comply with standard symmetry rules, which require that each term in the free energy expansion transforms (in the group theoretical sense) as the identity representation, Lidentity- The order parameter, by definition, transforms as the active representation, Ractive- The rules for coupling terms are then as follows ... 

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