  Despite several first principles studies, the relative stability of BN
polymorphs remains controversial. The stable polymorph varies between the cubic
(c-BN) and hexagonal (h-BN) depending on the van der Waals (vdW) dispersion
approximation used. These studies are unable to explain the main experimental
results, c-BN is stable, the relative stability order and the large energy
difference between h-BN and c-BN (greater than 150 meV/formula unit). In this
study, we introduce contributions from electron-phonon interactions (EPI) to
the total energy of BN polymorphs. This clearly establishes c-BN is the stable
polymorph irrespective of the vdW approximation. Only by including EPI
contributions do the ab initio results match, for the first time, the main
experimental results mentioned above. The EPI contribution to the total energy
is strongly sensitive to chemical bonding (approximately twice in $sp^2$-bonded
layered over $sp^3$-bonded polymorphs) and to crystal structure. The crucial
role of EPI contributions is seen in $sp^2$-bonded layered BN polymorphs where
it is greater than the vdW contribution. Given that h-BN is a prototype layered
material, in bulk or 2D form, our results have a broader relevance, that is,
including EPI correction, along with vdW approximation, is vital for the study
of energetics in layered materials.
