  Hydrogen-rich compounds have been extensively studied both theoretically and
experimentally in the quest for novel high-temperature superconductors. Reports
on sulfur-hydride attaining metallicity under pressure and exhibiting
superconductivity at temperatures as high as 200 K have spurred an intense
search for room-temperature superconductors in hydride materials. Recently,
compressed phosphine was reported to metallize at pressures above 45 GPa,
reaching a superconducting transition temperature (T$_{c}$) of 100 K at 200
GPa. However, neither the exact composition nor the crystal structure of the
superconducting phase have been conclusively determined. In this work the phase
diagram of PH$_n$ ($n=1,2,3,4,5,6$) was extensively explored by means of {\it
ab initio} crystal structure predictions using the Minima Hopping Method (MHM).
The results do not support the existence of thermodynamically stable PH$_n$
compounds, which exhibit a tendency for elemental decomposition at high
pressure even when vibrational contributions to the free energies are taken
into account. Although the lowest energy phases of PH$_{1,2,3}$ display
T$_{c}$'s comparable to experiments, it remains uncertain if the measured
values of T$_{c}$ can be fully attributed to a phase-pure compound of PH$_n$.
