Energetics of interlayer binding in graphite: The semiempirical approach revisited

We have developed a semiempirical method to obtain interlayer binding energy of graphite in the previous work [M. Hasegawa and K. Nishidate, Phys. Rev. B 70, 205431 (2004)]. In the present paper, we revisit this approach and develop an improved method, in which ab initio calculations based on the density functional theory (DFT) are also corrected through an empirical atom-atom van der Waals (vdW) interaction. The local density approximation (LDA) and generalized gradient approximation (GGA) are used in the DFT calculations. The parametrized damping function introduced to modify the asymptotic atom-atom vdW interaction is more flexible than the previous ones and covers a wider range of possibility in correcting for the approximate DFT calculations. The damping function is determined empirically by imposing the condition that the experimental interlayer spacing, in-plane lattice constant, and c-axis elastic constant are reproduced. We also require consistency between the LDA- and GGA-based methods (LDA+vdW, GGA+vdW) as the theoretically motivated necessary condition. The interlayer binding energy obtained by this method is 60.4 meV/atom at T=0 K. The result of similar to 54 meV/atom at room temperature corrected by the thermal effect is consistent with the most recent experiment, 52 +/- 5 eV/atom [R. Zacharia , Phys. Rev. B 69, 155406 (2004)]. The atom-atom vdW interaction obtained by the present semiempirical method favorably corrects for the overbinding and underbinding nature of the LDA and GGA, respectively, in the in-plane energetics of graphite. That interaction also provides a useful starting point for the studies of energetics of other graphitic systems such as fullerenes and carbon nanotubes.