  Low-energy excitations of a single water molecule are studied when confined
within a nano-size cage formed by the ionic crystal lattice. Optical spectra
are measured of manganese doped beryl single crystal Mn:Be3Al2Si6O18, that
contains water molecules individually isolated in 0.51 nm diameter voids within
the crystal lattice. Two types of orientation are distinguished: water-I
molecules have their dipole moments aligned perpendicular to the c axis, and
dipole moments of water-II molecules are parallel to the c-axis. The optical
conductivity and permittivity spectra are recorded in terahertz and infrared
ranges, at frequencies from several wavenumbers up to 7000cm-1, at temperatures
from 5K to 300K and for two polarizations, when the electric vector E of the
radiation is parallel and perpendicular to the c-axis. Comparative experiments
on as-grown and on dehydrated samples allow to identify the conductivity and
permittivity spectra caused exclusively by water molecules. In the infrared
range well-known internal modes nu1, nu2 and nu3 of the H2O molecule are
observed for both polarizations, indicating the presence of water-I and
water-II molecules in the crystal. Spectra recorded below 1000cm-1 reveal a
rich set of highly anisotropic features in the low-energy response of H2O
molecule in a crystalline nanocage. While for E parallel to c only two
absorption peaks are detected, at 90cm-1 and 160cm-1, several absorption bands
are discovered for E perpendicular to c, each consisting of narrower
resonances. The bands are assigned to librational and translational vibrations
of water-I molecule that is weakly, via hydrogen bonds, coupled to the nanocage
walls. A model is presented that explains the fine structure of the bands by
splitting of the energy levels due to quantum tunneling between the minima in a
six-well potential relief felt by a molecule within the cage.
