Conditions for the combination of Atomic Orbitals

Not every pair of atomic orbitals can combine into molecular orbitals — three conditions must ALL be satisfied first. First, the combining atomic orbitals must have COMPARABLE energies: for instance, a 1s orbital on one atom can combine with another atom's 1s orbital (same energy), but not with that atom's much higher-energy 2s orbital. Second, the combining atomic orbitals must share the SAME SYMMETRY about the molecular (internuclear) axis, conventionally taken as the z-axis: a 2s orbital, for example, can combine with another atom's $2p_z$ orbital (both are symmetric about the z-axis) but CANNOT combine with that atom's $2p_x$ or $2p_y$ orbital, because those are symmetric about a DIFFERENT axis, even though $2p_x$/$2p_y$ have the same energy as $2p_z$. Third, the combining atomic orbitals must overlap to the MAXIMUM extent possible — the greater the overlap, the greater the resulting electron density between the …