  A detailed Linear Combination of Atomic Orbitals (LCAO) tight-binding model
is developed for the layered High-Temperature Superconductor cuprates. The band
structure of these materials is described using a sigma-band Hamiltonian
employing Cu4s, Cu3d_x^2-y^2, O2p_x and O2p_y atomic orbitals. The Fermi level
and the shape of the resulting Fermi surface are fitted to recent Angle
Resolved Photon Emission Spectroscopy (ARPES) data to realistically determine
the dispersion in the conduction band. Electron-electron interactions and,
ultimately, Cooper pairing is obtained by introducing a Heitler-London,
two-electron exchange between adjacent orbitals within the CuO_2 plane.
Finally, using the LCAO wavefunctions determined by the band structure fit, the
Bardeen-Cooper-Schrieffer type kernel is derived for interatomic exchange.
