Self-consistent charge densities, band structures, and staging energies of graphite intercalation compounds

A model, self-consistent band structure is calculated for a thin film of $n$ graphite layers bounded by two, partially ionized intercalant layers for stages $n=2-8\mathrm{}$. The quantum mechanics of the electrons in the graphite layers is modeled using a variant of the three-dimensional linear combination of atomic orbitals Hamiltonian whose parameters have been determined for pure graphite. The effects of the nonhomogeneous distribution of electrons in the $n$ layers (screening) are taken into account by adding a self-consistently determined layer-potential term to the tight-binding Hamiltonian. The layer charge densities, potentials, and total energies are presented for $n=2-8\mathrm{}$ along with representative band structures for charge transfer per intercalant ($f$) of $f=1\mathrm{} \mathrm{and} \frac{1}{4}$ (referred to ${\mathrm{C}}_{12n}X$). The stage dependence of the total energy in this model is related to the stage dependence of the chemical potential (intercalant vapor pressure) in an intercalation reaction. Comparison of theory and experiment indicates the significance of the electronic energy in stabilizing the high-stage structures.