  Where the doped holes reside in cuprate superconductors has crucial
implications for the understanding of the mechanism responsible for their high
temperature superconductivity. It has been generally assumed that doped holes
reside in hybridized Cu $d_{x^2-y^2}$ - O $p\sigma$ orbitals in the $CuO_2$
planes, based on results of density functional band structure calculations.
Instead, we propose that doped holes in the cuprates reside in O $p\pi$
orbitals in the plane, perpendicular to the $Cu-O$ bond, that are raised to the
Fermi energy through local orbital relaxation, that is not taken into account
in band structure calculations that place the bands associated with these
orbitals well below the Fermi energy. We use a dynamic Hubbard model to
incorporate the orbital relaxation degree of freedom and find in exact
diagonalization of a small $Cu_4O_4$ cluster that holes will go to the O $p\pi$
orbitals for relaxation energies comparable to what is expected from atomic
properties of oxygen anions. The bandwidth of this band becomes significantly
smaller than predicted by band structure calculations due to the orbital
relaxation effect. Within the theory of hole superconductivity the heavy hole
carriers in this almost full band will pair and drive the system
superconducting through lowering of their quantum kinetic energy.
