  Temperature and quantum effects induce the structural complexity of condensed
hydrogen, and therefore they are expected to impact nontrivially the structures
of clathrate hydrides. Exemplified by clathrate calcium hydride, we show
through ab initio (path-integral) molecular dynamics simulations that these
effects are indeed pivotal at 100-200 GPa. The quantum equation of states
derived at 300 K suggests that the synthesized samples in previous experiments
were berthollide-like CaH$_{6-\delta}$, with the stoichiometric defect $\delta$
increasing smoothly during decompression. The change of composition provides an
explanation for the experimental observation of positive pressure dependence of
superconducting T$_c$ below 165 GPa. Furthermore, we find significant proton
diffusion in CaH$_{6-\delta}$ at 150-300 K, with the diffusion coefficient
reaching 10$^{-7}$ cm$^{2}$/s. This suggests a coexistence of superconductivity
and proton diffusion in clathrate hydrides. Our findings underline the
importance of temperature, quantum and defect effects to the understandings of
the structure and pertinent physics in high-T$_c$ superconducting clathrate
hydrides.
