Infrared spectroscopy of endohedral water in C$_{60}$
Infrared absorption spectroscopy study of endohedral water molecule in a solid mixture of H$_2$O@C$_{60}$ and C$_{60}$ was carried out at liquid helium temperature. From the evolution of the spectra during the ortho-para conversion process, the spectral lines were identified as para- and ortho-water transitions. Eight vibrational transitions with rotational side peaks were observed in the mid-infrared: $ω_1$, $ω_2$, $ω_3$, $2ω_1$, $2ω_2$, $ω_1 +ω_3$, $ω_2 +ω_3$, and $2ω_2+ω_3$. The vibrational frequencies $ω_2$ and 2$ω_2$ are lower by 1.6\% and the rest by 2.4\%, as compared to free \water/. A model consisting of a rovibrational Hamiltonian with the dipole and quadrupole moments of water interacting with the crystal field was used to fit the infrared absorption spectra. The electric quadrupole interaction with the crystal field lifts the degeneracy of the rotational levels. The finite amplitudes of the pure $v_1$ and $v_2$ vibrational transitions are consistent with the interaction of the water molecule dipole moment with a lattice-induced electric field. The permanent dipole moment of encapsulated \water/ is found to be $0.5\pm 0.1$ D as determined from the far-infrared rotational line intensities. The translational mode of the quantized center of mass motion of \water/ in the molecular cage of C$_{60}$ was observed at 110cm$^{-1}$ (13.6meV).