  In recent years intercalated and pillared graphitic systems have come under
increasing scrutiny because of their potential for modern energy technologies.
While traditional \emph{ab initio} methods such as the LDA give accurate
geometries for graphite they are poorer at predicting physicial properties such
as cohesive energies and elastic constants perpendicular to the layers because
of the strong dependence on long-range dispersion forces. `Stretching' the
layers via pillars or intercalation further highlights these weaknesses. We use
the ideas developed by [J. F. Dobson et al, Phys. Rev. Lett. {\bf 96}, 073201
(2006)] as a starting point to show that the asymptotic $C_3 D^{-3}$ dependence
of the cohesive energy on layer spacing $D$ in bigraphene is universal to all
graphitic systems with evenly spaced layers. At spacings appropriate to
intercalates, this differs from and begins to dominate the $C_4 D^{-4}$ power
law for dispersion that has been widely used previously. The corrected power
law (and a calculated $C_3$ coefficient) is then unsuccesfully employed in the
semiempirical approach of [M. Hasegawa and K. Nishidate, Phys. Rev. B {\bf 70},
205431 (2004)] (HN). A modified, physicially motivated semiempirical method
including some $C_4 D^{-4}$ effects allows the HN method to be used
successfully and gives an absolute increase of about $2-3%$ to the predicted
cohesive energy, while still maintaining the correct $C_3 D^{-3}$ asymptotics.
