  The diversified essential properties of the stage-n graphite
alkali-intercalation compounds are thoroughly explored by the first-principles
calculations. According to their main features, the lithium and non-lithium
materials might be quite different from each other in stacking configurations,
the intercalated alkali-atom concentrations, the free conduction electron
densities, and the atom-dominated & (carbon, alkali)-co-dominated energy bands.
The close relations between the alkali-doped metallic behaviors and the
geometric symmetries will be clarified through the interlayer atomic
interactions, in which the significant alkali-carbon chemical bondings are
fully examined from the atom- and orbital-decomposed van Hove singularities.
The blue shift of the Fermi level, the n-type doping, is clearly identified
from the low-energy features of the density of states. This study is able to
provide the partial information about anode of Li+-based battery. There are
certain important differences between AC$_6$/AC$_8$ and Li$_8$Si$_4$O$_{12}$.
