Extended Data Fig. 5: Rotational dynamics of monolayer hexatic water.

(a) 1st order orientational autocorrelation function of the hexatic phase at 3 GPa from 340 to 400 K calculated as C₁(t) = 〈P₁[v(0) ⋅ v(t)]〉 > where, v(t) is the orientation of the O–H bond at time t, and P₁ is the Legendre polynomial of degree one. (b) Temperature dependence of the 1st order orientational relaxation time, computed as the time integral of C₁(t), for the O–H molecular axis of the hexatic phase at 3 GPa. The relaxation time at 340 K is around seven times smaller than that of room temperature liquid water, indicating facile rotation of water molecules in the hexatic-like phase. (c) The vibrational density of states across the flat-rhombic (up to 320 K) to the hexatic-like phase transition (beyond 340 K) as calculated by the Fourier transform of the velocity autocorrelation function. The flat-rhombic phase is characterized by two distinct vibrational bands for hydrogen bonded and dangling O–H bonds, and clear features for the librational modes. On the other hand, the rotations in the hexatic-like phase merge the two stretching bands into a doublet, and smear out the fine structure of the librational band.