We study the renormalization of hopping integrals between localized and delocalized levels due to a Coulomb interaction between these two types of levels. We find that the renormalization enhances the effective hopping matrix elements, due to effects of the type that enhance x-ray spectra at the threshold. This effect tends to make the hopping integrals appear larger for thermodynamic properties than for spectroscopic properties.
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Gunnarsson et al. (1989) studied this question.
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