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 l-th degree Legendre polynomials tau(l), and viscosity divided by temperature, eta/T. Experiments on supercooled liquids are frequently performed to measure the SED relations, tau(l)k(B)T/eta and D-t tau(l),where D-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(l) values exhibit a temperature dependence similar to that of eta/T, whereas the lowest-order tau(l) values are decoupled with eta/T, but are coupled with the translational diffusion constant D-t. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.