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

A theoretical and semiemprical correction to the long-range dispersion power law of stretched graphite