  Starting from the random phase approximation for the weakly coupled multiband
tightly-bounded electron systems, we calculate the dielectric matrix in terms
of intraband and interband transitions. The advantages of this representation
with respect to the usual plane-wave decomposition are pointed out. The
analysis becomes particularly transparent in the long wavelength limit, after
performing the multipole expansion of bare Coulomb matrix elements. For
illustration, the collective modes and the macroscopic dielectric function for
a general cubic lattice are derived. It is shown that the dielectric
instability in conducting narrow band systems proceeds by a common softening of
one transverse and one longitudinal mode. Furthermore, the self-polarization
corrections which appear in the macroscopic dielectric function for finite band
systems, are identified as a combined effect of intra-atomic exchange
interactions between electrons sitting in different orbitals and a finite
inter-atomic tunneling.
