  We present a readily computable semi-analytic Layer Response Theory (LRT) for
analysis of cohesive energetics involving two-dimensional layers such as BN or
graphene. The theory approximates the Random Phase Approximation (RPA)
correlation energy. Its RPA character ensures that the energy has the correct
van der Waals asymptotics for well-separated layers, in contrast to simple
pairwise atom-atom theories which fail qualitatively for layers with zero
electronic energy gap. At the same time our theory is much less computationally
intensive than the full RPA energy. It also gives accurate correlation energies
near to the binding minimum, in contrast to Lifshitz-type theory. We apply our
LRT theory successfully to graphite and to BN, and to a graphene-BN
heterostructure.
