Band-Structure Trend in Hole-Doped Cuprates and Correlation with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">c</mml:mi><mml:mi/><mml:mi>max</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

By calculation and analysis of the bare conduction bands in a large number of hole-doped high-temperature superconductors, we have identified the range of the intralayer hopping as the essential, material-dependent parameter. It is controlled by the energy of the axial orbital, a hybrid between Cu 4s, apical-oxygen 2p(z), and farther orbitals. Materials with higher T(c max) have larger hopping ranges and axial orbitals more localized in the CuO2 layers.