  Using density functional theory calculations, we have investigated the
structural, energetic, and electronic properties of ternary graphite
intercalation compounds (GICs) containing alkali atoms (AM) and normal
alkylamine molecules (nC$x$), denoted as AM-nC$x$-GICs (AM=Li, Na, K, $x$=1, 2,
3, 4). The orthorhombic unit cells have been used to build the models for
crystalline stage-I AM-nC$x$-GICs. By performing the variable cell relaxations
and the analysis of results, we have found that with the increase in the atomic
number of alkali atoms the layer separations decreases in contrast to AM-GICs,
while the bond lengths of alkali atoms with graphene layer and nitrogen atom of
alkylamine decreases. The formation and interlayer binding energies of
AM-nC3-GICs have been calculated, indicating the increase in stability from Li
to K. The calculated energy barriers for migration of alkali atoms suggest that
alkali cation with larger ionic radius diffuses in graphite more smoothly,
being similar to AM-GICs. The analysis of density of states, electronic density
differences, and atomic populations illustrates a mechanism how the insertion
of especially Na among alkali atoms into graphite with first stage can be made
easy by cointercalation with alkylamine, more extent of electronic charge
transfer is occurred from more electropositive alkali atom to carbon ring of
graphene layer, while alkylamine molecules interact strongly with graphene
layer through the hybridization of valence electron orbitals.
