s-p mixing in a one-dimensional tight-binding chain ($H_{sp}(k)=2i{\beta }_{sp}\sin (ka)$)

Opposite parity of same-centre s orbitals and axial p orbitals makes their left and right nearest-neighbour hopping integrals opposite in sign. Their Bloch wave sum is consequently odd in wavevector and vanishes at the zone centre and boundary. Away from those points, orbital hybridization repels coupled levels and can produce an avoided crossing.