Resonance integral modification

The modification of the QM resonance integrals to which the HO at hand is involved is somewhat more complex. It nevertheless uses the same (DCF) representation of the resonance integrals as previously ... 

In the case of the Type A rearrangement of 2,5-cyclohexadi-enones, simple one-electron computations of the Mul-liken-Wheland-Mann type were performed that involve iterative modification of resonance integrals. These led to results that were qualitatively similar to triplet configuration interaction computations carried out in parallel. The results are shown in Schemes 1.4a and 1.4b. 

The resonance integrals in the QM subsystem are also renormalized. In the DCF their modification can be expressed as ... 

The shape of the density of states reveals the peculiarities of the hybridization between anion and cation orbitals, which depend upon three parameters the values of the resonance integrals the coordination number of the surface atoms and the energy separation between the relevant atomic levels. In the absence of relaxation, rumpling or reconstructions, the resonance integrals have the same values as in the bulk. The surface atom coordination numbers and the level separation, on the other hand, are smaller than in the bulk and they decrease as the surface becomes more open. We will first discuss how these modifications are reflected in the gross features of the local densities of states at the surface and, more specifically, in their second moments. Then we will focus on the details of the band shapes and on the possible occurrence of localized states in the gap. 

The description of imaging experiments in reciprocal space is not restricted to k space, the Fourier conjugate space of physical space. The modification of the spin density by other parameters like resonance frequencies, coupling constants, relaxation times, etc., can be treated in a similar fashion [Miil4]. For the frequency-dependent spin density, the Fourier transformation with respect to 2 is already explicitly included in (5.4.7). Introduction of a Ti-dependent density would require the inclusion of another integration over T2 in (5.4.7) and lead to a Laplace transformation (cf. Section 4.4.1). 

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