  Hydrogen hydrates present a rich phase diagram influenced by both pressure
and temperature, with the so-called C$_2$ phase emerging prominently above 2.5
GPa. In this phase, hydrogen molecules are densely packed within a cubic
ice-like lattice and the interaction with the surrounding water molecules
profoundly affects their quantum rotational dynamics. Herein, we delve into
this intricate interplay by directly solving the Schr\"{o}dinger's equation for
a quantum H$_2$ rotor in the C$_2$ crystal field at finite temperature,
generated through Density Functional Theory. Our calculations reveal a giant
energy splitting relative to the magnetic quantum number of $\pm$3.2 meV for
$l=1$. Employing inelastic neutron scattering, we experimentally measure the
energy levels of H$_2$ within the C$_2$ phase at 6.0 and 3.4 GPa and low
temperatures, finding remarkable agreement with our theoretical predictions.
These findings underscore the pivotal role of hydrogen--water interactions in
dictating the rotational behavior of the hydrogen molecules within the C$_2$
phase and indicate heightened induced-dipole interactions compared to other
hydrogen hydrates.
