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

TL;DR

This paper derives a universal long-range dispersion correction for layered graphite systems, improving semiempirical models by incorporating the correct asymptotic power law, leading to more accurate cohesive energy predictions.

Contribution

It introduces a corrected dispersion power law for graphitic systems and modifies existing semiempirical methods to include this correction, enhancing their accuracy.

Findings

The $C_3 D^{-3}$ dispersion dependence is universal for layered graphite.

The corrected power law improves cohesive energy estimates by 2-3%.

Modified semiempirical method successfully incorporates the new dispersion correction.

Abstract

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.