Interface models for matching either w-BN or h-BN layers to an Si(001) substrate, are considered. Aligning the [2 - 1 - 10] direction of h-BN (or equivalently the [- 1 - 120] direction in w-BN) along [1 - 10] of the Si(001), chemical saturation of interface bonds can be achieved. For h-BN, orientations of the basal plane parallel and perpendicular to the surface are both considered. The total energy of atomic clusters constructed to represent these models, are calculated using the AMl quantum chemical Hamiltonian, and atomic geometries optimised allowing full symmetric relaxation of interface atoms. Only the perpendicular h-BN basal plane model is found to be energetically favourable compared to earlier calculations for cubic boron nitride.