Spurious violation of the Stokes-Einstein-Debye relation in supercooled water

The theories of Brownian motion, the Debye rotational diffusion model, and hydrodynamics together provide us with the Stokes–Einstein–Debye (SED) relation between the rotational relaxation time of the $\mathrm{\ell }$-th degree Legendre polynomials ${\tau }_{\mathrm{\ell }}$, and viscosity divided by temperature, $\eta \mathrm{/}T$. Experiments on supercooled liquids are frequently performed to measure the SED relations, ${\tau }_{\mathrm{\ell }}{k}_{\mathrm{B}}T\mathrm{/}\eta$ and $D_{\rm t}\tau_{\ell}$,where$D_{\rm t}$ is the translational diffusion constant. However, the SED relations break down, and its molecular origin remains elusive. Here, we assess the validity of the SED relations in TIP4P/2005 supercooled water using molecular dynamics simulations. Specifically, we demonstrate that the higher-order ${\tau }_{\mathrm{\ell }}$ values exhibit a temperature dependence similar to that of $\eta \mathrm{/}T$, whereas the lowest-order ${\tau }_{\mathrm{\ell }}$ values are decoupled with $\eta \mathrm{/}T$, but are coupled with the translational diffusion constant. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.