  $\delta$-AlOOH is of significant crystallochemical interest due to a subtle
structural transition near 10 GPa from a $P2_1nm$ to a $Pnnm$ structure, the
nature and origin of hydrogen disorder, the symmetrization of the O-H$\cdots$O
hydrogen bond and their interplay. We perform a series of density functional
theory based simulations in combination with high-pressure nuclear magnetic
resonance experiments on $\delta$-AlOOH up to 40 GPa with the goal to better
characterize the hydrogen potential and therefore the nature of hydrogen
disorder. Simulations predict a phase transition in agreement with our nuclear
magnetic resonance experiments at $10-11$ GPa and hydrogen bond symmetrization
at $14.7$ GPa. Calculated hydrogen potentials do not show any double-well
character and there is no evidence for proton tunneling in our nuclear magnetic
resonance data.
