Ortho-para conversion of endohedral water in the fullerene C$_{60}$ at cryogenic temperatures

Water displays the phenomenon of spin isomerism in which the two proton spins either couple to form a triplet (ortho water, $I=1$) or a singlet nuclear spin state (para water, $I=0$). Here we study the interconversion of para and ortho water. The exact mechanism of this process is still not fully understood. In order to minimize interactions between molecules we use a sample where a single H$_2$O is trapped in the C$_{60}$ molecular cage (H$_2$O@C$_{60}$) and H$_2$O@C$_{60}$ is crystallized. H$_2$O@C$_{60}$ has long-lived ortho state [Beduz et al., PNAS {\bf 109}, 12894 (2012)] and ortho-para conversion kinetics is non-exponential at LHeT [Mamone et al, J.Chem.Phys. {\bf 140}, 194306, (2014)]. We studied mixtures of H$_2$O@C$_{60}$, D$_2$O@C$_{60}$ and C$_{60}$ using IR absorption, NMR and dielectric measurements. We saw the speeding up of the interconversion with the growth of H$_2$O@C$_{60}$ concentration in C$_{60}$ or when D$_2$O@C$_{60}$ was added. At some temperatures the kinetics is exponential. Models are discussed in order to explain the $T$ and concentration dependence of ortho-para interconversion kinetics.