  The renormalization of the band structure at zero temperature due to
electron-phonon coupling is investigated in diamond, BN, LiF and MgO crystals.
We implement a dynamical scheme to compute the frequency-dependent self-energy
and the resulting quasiparticle electronic structure. Our calculations reveal
the presence of a satellite band below the Fermi level of LiF and MgO. We show
that the renormalization factor (Z), which is neglected in the adiabatic
approximation, can reduce the zero-point renormalization (ZPR) by as much as
40%. Anharmonic effects in the renormalized eigenvalues at finite atomic
displacements are explored with the frozen-phonon method. We use a
non-perturbative expression for the ZPR, going beyond the Allen-Heine-Cardona
theory. Our results indicate that high-order electron-phonon coupling terms
contribute significantly to the zero-point renormalization for certain
materials.
