  The formation of precipitated zirconium (Zr) hydrides is closely related to
the hydrogen embrittlement problem for the cladding materials of pressured
water reactors (PWR). In this work, we systematically investigated the crystal
structures of zirconium hydride (ZrHx) with different hydrogen concentrations
(x = 0~2, atomic ratio) by combining the basin hopping algorithm with first
principles calculations. We conclude that the P3m1 {\zeta}-ZrH0.5 is
dynamically unstable, while a novel dynamically stable P3m1 ZrH0.5 structure
was discovered in the structure search. The stability of bistable P42/nnm
ZrH1.5 structures and I4/mmm ZrH2 structures are also revisited. We find that
the P42/nnm (c/a > 1) ZrH1.5 is dynamically unstable, while the I4/mmm (c/a =
1.57) ZrH2 is dynamically stable.The P42/nnm (c/a < 1) ZrH1.5 might be a key
intermediate phase for the transition of {\gamma}->{\delta}->{\epsilon} phases.
Additionally, by using the thermal dynamic simulations, we find that
{\delta}-ZrH1.5 is the most stable structure at high temperature while ZrH2 is
the most stable hydride at low temperature. Slow cooling process will promote
the formation of {\delta}-ZrH1.5, and fast cooling process will promote the
formation of {\gamma}-ZrH. These results may help to understand the phase
transitions of zirconium hydrides.
