  In density functional theory (DFT) based total energy studies, the van der
Waals (vdW) and zero-point vibrational energy (ZPVE) correction terms are
included to obtain energy differences between polymorphs. We propose and
compute a new correction term to the total energy, due to electron-phonon
interactions (EPI). We rely on Allen's general formalism, which goes beyond the
Quasi-Harmonic Approximation (QHA), to include the free energy contributions
due to quasiparticle interactions. We show that, for semiconductors and
insulators, the EPI contributions to the free energies of electrons and phonons
are the corresponding zero-point energy contributions. Using an approximate
version of Allen's formalism in combination with the Allen-Heine theory for EPI
corrections, we calculate the zero-point EPI corrections to the total energy
for cubic and hexagonal polytypes of Carbon, Silicon and Silicon Carbide. The
EPI corrections alter the energy differences between polytypes. In SiC
polytypes, the EPI correction term is more sensitive to crystal structure than
the vdW and ZPVE terms and is thus essential in determining their energy
differences. It clearly establishes that the cubic SiC-3C is metastable and
hexagonal SiC-4H is the stable polytype. Our results are consistent with the
experimental results of Kleykamp. Our study enables the inclusion of EPI
corrections as a separate term in the free energy expression. This opens the
way to go beyond the QHA by including the contribution of EPI on all
thermodynamic properties.
