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Starting from the random phase approximation for the weakly coupled multibandtightly-bounded electron systems, we calculate the dielectric matrix in termsof intraband and interband transitions. The advantages of this representationwith respect to the usual plane-wave decomposition are pointed out. Theanalysis becomes particularly transparent in the long wavelength limit, afterperforming the multipole expansion of bare Coulomb matrix elements. Forillustration, the collective modes and the macroscopic dielectric function fora general cubic lattice are derived. It is shown that the dielectricinstability in conducting narrow band systems proceeds by a common softening ofone transverse and one longitudinal mode. Furthermore, the self-polarizationcorrections which appear in the macroscopic dielectric function for finite bandsystems, are identified as a combined effect of intra-atomic exchangeinteractions between electrons sitting in different orbitals and a finiteinter-atomic tunneling.Comment: 20 pages, LaTeX, no figure

The tight-binding approach to the dielectric response in the multiband systems