  The O(oxygen)-M(metal)-O(oxygen) molecule is a basic unit of high-temperature
superconducting cuprates and colossal magnetoresistance exhibiting manganates.
This molecule can be regarded either as an element of a linear chain or as an
ingredient of the corresponding cuprate or manganate lattice. The symmetry of
the unit being different in the two approaches, group theory imposes different
limitations on conceivable vibrational modes and atomic otbitals that control
its transport and optical properties. We now calculate the electron hopping
energies along Cu(P0-O(A) bonds, sites for nonlocal electron-vibrational mode
coupling. We find the electric transport along the O(A)-Cu(P)-O(A) molecule
dominated by scattering from bond polarons which is reflected in the two-branch
character of the temperature dependence of its electric resistance.
