  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.
