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 $\ell$-th degree Legendre polynomials $\tau_\ell$, and viscosity divided by temperature, $\eta/T$. Experiments on supercooled liquids are frequently performed to measure the SED relations, $\tau_{\ell}k_{\rm B}T/\eta$ 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 $\tau_\ell$ values exhibit a temperature dependence similar to that of $\eta/T$, whereas the lowest-order $\tau_\ell$ values are decoupled with $\eta/T$, 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.