The authors study the renormalization of hopping integrals between localized and delocalized levels due to a Coulomb interaction between these two types of levels. They 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.
 

Physical Review B, 40 4160-3, 1989.