Density-functional study of interplanar binding in graphite

Density-functional theory is applied to study the structural and elastic properties of the weak interplanar bonding in graphite. Using the Thomas-Fermi plus gradient approximation to the kinetic energy and taking the charge density to be a superposition of isolated C planes permit rapid computation of the graphite total energy as a function of plane separation. Values for the lattice constant, compressibility, cohesive energy, and phonon frequencies are obtained and are shown to be largely independent of the details of the in-plane C bonding. Agreement with experiment is qualitatively good, but quantitative discrepancies exist. It is argued that these discrepancies are not due to the charge-density approximation or to the Thomas-Fermi approach, but rather to the marginal applicability of the local density approximation to the exchange and correlation. We find that using a van der Waals point of view for the exchange and correlation does not quantitatively improve the theory; so some intermediate approach appears to be necessary.