The total energy is the most fundamental quantity in ab initio studies. To include electron-phonon interaction (EPI) contribution to the total energy, we have recast Allen's equation, for the case of semiconductors and insulators. This equivalent expression can be computed using available software, leading to more accurate total energy. We calculate the total energies and their differences for carbon-diamond and carbon-hexagonal polytypes. For ab initio investigations on crystalline materials, the accepted norm is to compute important quantities only for the primitive unit cell because per-atom quantities are independent of unit cell size. Our results, unexpectedly, show that the per-atom total energy (EPI included) depends on the unit cell size and violates the unit cell independence. For example, it differs for carbon-diamond by 1 eV/atom between the primitive cell and supercells. We observe that reliable energy differences between polytypes are obtained when, instead of primitive cells, supercells with identical number of atoms are used. A crucial inference of general validity is that any equation which contains a partial Fan-Migdal self-energy term violates the unit cell independence. Further theoretical studies are needed to establish if the total energy (EPI included) is an exception or can be reconciled with the unit cell independence.