The δ-AlOOH can transport water into the deep mantle along cold subducting slab geotherm.We investigate the hydrogen-bond symmetrization behavior of δ-AlOOH under the relevant pressure-temperature condition of the lower mantle using ab initio molecular dynamics (MD).The static symmetrization pressure of 30.0 GPa can be reduced to 17.0GPa at 300 K by finite-temperature (T) statistics,closer to the experimental observation of ～10.0GPa.The symmetrization pressure obtained by MD simulation is related to T by P (GPa) =13.9 (GPa) +0.01 (GPa/K) × T (K).We conclude that δ-AlOOH in the lower mantle exists with symmetric hydrogen bond from its birthplace,or someplace slightly deeper,to the core-mantle boundary (CMB) along cold subducting slab geotherm.The bulk modulus decreases with T and increases anomalously upon symmetrization:K0 (GPa) =181 (GPa)-0.013 (GPa/K) × T (K) for δ-AlOOH with asymmetric hydrogen bond,and K0 (GPa) =216 (GPa)-0.013 (GPa/K) × T (K) for δ-AlOOH with symmetric hydrogen bond.Our results provide an important insight into the existent form and properties of δ-AlOOH in the lower mantle.