  The lithium-carbon binary system possesses a broad range of chemical
compounds, which exhibit fascinating chemical bonding characteristics that give
rise diverse and technologically important properties. While lithium carbides
with various compositions have been studied or suggested previously, the
crystal structures of these compounds are far from well understood. In this
work we present the first comprehensive survey of all ground state (GS)
structures of lithium carbides over a broad range of thermodynamic conditions,
using \textit{ab initio} density functional theory (DFT) crystal structure
searching methods. Thorough searches were performed for 29 stoichiometries
ranging from Li$_{12}$C to LiC$_{12}$ at 0 GPa as well as 40 GPa. Based on
formation enthalpies from optimized van der Waals density functional
calculations, three thermodynamically stable phases (Li$_4$C$_3$, Li$_2$C$_2$
and LiC$_{12}$) were identified at 0 GPa, and seven thermodynamically stable
phases (Li$_8$C, Li$_6$C, Li$_4$C, Li$_8$C$_3$, Li$_2$C, Li$_3$C$_4$, and
Li$_2$C$_3$) were predicted at 40 GPa. A rich diversity of carbon bonding,
including monomers, dimers, trimers, nanoribbons, sheets and frameworks, was
found within these structures, and the dimensionality of carbon connectivity
existing within each phase was observed to increase with increasing carbon
concentration. Of particular interest, we find that the well-known composition
LiC$_6$ is actually a metastable one. We also find a unique coexistence of
carbon monomers and dimers within the predicted thermodynamically stable phase
Li$_8$C$_3$, and different widths of carbon nanoribbons coexist in a metastable
phase of Li$_2$C$_2$ (\textit{Imm}2). Interesting mixed
\textit{sp}$^2$-\textit{sp}$^3$ carbon frameworks are predicted in metastable
phases with composition LiC$_6$.
