  Using first principles structure searching with density-functional theory
(DFT) we identify a novel $Fm\bar{3}m$ phase of Cu$_2$P and two low-lying
metastable structures, an $I\bar{4}3d$--Cu$_3$P phase, and a
$Cm$--Cu$_3$P$_{11}$ phase. The computed pair distribution function of the
novel $Cm$--Cu$_3$P$_{11}$ phase shows its structural similarity to the
experimentally identified $Cm$--Cu$_2$P$_7$ phase. The relative stability of
all Cu--P phases at finite temperatures is determined by calculating the Gibbs
free energy using vibrational effects from phonon modes at 0 K. From this, a
finite-temperature convex hull is created, on which $Fm\bar{3}m$--Cu$_2$P is
dynamically stable and the Cu$_{3-x}$P ($x < 1$) defect phase
$Cmc2_1$--Cu$_8$P$_3$ remains metastable (within 20 meV/atom of the convex
hull) across a temperature range from 0 K to 600 K. Both CuP$_2$ and Cu$_3$P
exhibit theoretical gravimetric capacities higher than contemporary graphite
anodes for Li-ion batteries; the predicted Cu$_2$P phase has a theoretical
gravimetric capacity of 508 mAh/g as a Li-ion battery electrode, greater than
both Cu$_3$P (363 mAh/g) and graphite (372 mAh/g). Cu$_2$P is also predicted to
be both non-magnetic and metallic, which should promote efficient electron
transfer in the anode. Cu$_2$P's favorable properties as a metallic,
high-capacity material suggest its use as a future conversion anode for Li-ion
batteries; with a volume expansion of 99% during complete cycling, Cu$_2$P
anodes could be more durable than other conversion anodes in the Cu--P system
with volume expansions greater than 150%.
