  Motivated by recent experimental work, we use first-principles density
functional theory methods to conduct an extensive search for low enthalpy
structures of C$_6$Ca under pressure. As well as a range of buckled structures,
which are energetically competitive over an intermediate range of pressures, we
show that the high pressure system ($\gtrsim 18$ GPa) is unstable towards the
formation of a novel class of layered structures, with the most stable compound
involving carbon sheets containing five- and eight-membered rings. As well as
discussing the energetics of the different classes of low enthalpy structures,
we comment on the electronic structure of the high pressure compound and its
implications for superconductivity.
