In recent years, intercalated and pillared graphitic systems have come under increasing scrutiny because of their potential for modern energy technologies. While traditional ab initio methods such as the local density approximation give accurate geometries for graphite, they are poorer at predicting physical 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 Dobson et al. Phys. Rev. Lett. 96, 073201 2006 as a starting point to show that the asymptotic C3D-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 C4D-4 power law for dispersion that has been widely used previously. The corrected power law and a calculated C3 coefficient is then applied to the semiempirical approach of Hasegawa and Nishidate HN Phys. Rev. B 70, 205431 2004 ; however, a meaningful result cannot be obtained in this approach. A modified, physically motivated semiempirical method adding some C4D-4 effects allows the HN method to be employed and gives an absolute increase of about 2%-3% to the predicted cohesive energy, while still maintaining the correct C3D-3 asymptotics.