Abstract
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 [Formula: see text]-th degree Legendre polynomials [Formula: see text], and viscosity divided by temperature, η/T. Experiments on supercooled liquids are frequently performed to measure the SED relations, [Formula: see text]k(B)T/η and D(t)[Formula: see text], 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 [Formula: see text] values exhibit a temperature dependence similar to that of η/T, whereas the lowest-order [Formula: see text] values are decoupled with η/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.