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

Diverse fundamental properties in stage-n graphite alkali-intercalation compounds: anode materials of Li+-based batteries