  $\delta$-AlOOH ($\delta$) is a high-pressure hydrous phase that participates
in the deep geological water cycle. At 0 GPa, $\delta$ has asymmetric hydrogen
bonds (H-bonds). Under pressure, it exhibits H-bond disordering, tunneling, and
finally, H-bond symmetrization at ~18 GPa. This study investigates these 300 K
pressure-induced state changes in $\delta$ with ab initio calculations. H-bond
disordering in $\delta$ was modeled using supercell multi-configuration
quasiharmonic calculations. We examine: (a) energy barriers for proton jumps,
(b) the pressure dependence of phonon frequencies, (c) 300 K compressibility,
(d) neutron diffraction pattern anomalies, and (e) compare ab initio bond
lengths with measured ones. Such thorough and systematic comparisons indicate
that: (a) proton "disorder" has a restricted meaning when applied to $\delta$.
Nevertheless, H-bonds are disordered between 0 and 8 GPa, and a gradual change
in H-bond configuration results in enhanced compressibility. (b) several
structural and vibrational anomalies at ~8 GPa are consistent with the
disappearance of a particular (HOC-12) H-bond configuration and its change into
another one (HOC-11*). (c) between 8-11 GPa, H-bond configuration (HOC-11*) is
generally ordered, at least in short- to mid-range scale. (d) between 11.5-18
GPa, H-bond lengths approach a critical value that impedes compression,
resulting in decreased compressibility. In this pressure range, especially
approaching H-bond symmetrization at ~18 GPa, anharmonicity and tunneling
should play an essential role in the proton dynamics. Further simulations
accounting for these effects are desirable to clarify the protons' state in
this pressure range.
