  We present a study of the nearest--neighbor (nn) and next-nearest-neighbor
(nnn) exchange constants between magnetic Cu centers of the spin-Peierls
material CuGeO3. The dependence of these constants on the lattice parameters
(modified e.g. by variation of temperature, pressure or doping) is calculated.
Based on the observation that the bond angles are more susceptible than the
bond lengths we propose the so-called ''accordion'' model for the description
of the properties of CuGeO3. We show that the nn exchange constant in the CuO2
ribbon is very sensitive to the presence and position of the side group Ge with
respect to this ribbon. The angle between the two basic units the CuO2 ribbon
and the GeO3 zig-zag chain is, besides the Cu-O-Cu angle in the ribbon, one of
the principal lattice parameters determining the nn exchange in the c
direction. The microscopic calculations of different exchange constants and
their dependence on the lattice parameters are carried out using different
schemes (perturbation theory; exact diagonalization of Cu2O2 clusters; band
approach). The results compare favorable with experiment. The influence of Si
doping is also calculated, and the reasons of why it is so efficient in
suppressing the spin-Peierls phase are discussed. Thus the consistent
microscopic picture of the properties of CuGeO3 emerges.
