  A probability density function describing the angular evolution of a
fixed-length atom-atom vector as a L\'{e}vy rotor is derived containing just
two dynamical parameters: the L\'{e}vy parameter $\alpha$ and a rotational time
constant $\tau$. A L\'{e}vy parameter $\alpha\!<\!2$ signals anomalous
(non-Brownian) motion. A molecular dynamics simulation of water at 298\,K
validates the probability density function for the intra-molecular $^1$H--$^1$H
dynamics of water. The rotational dynamics of water is found to be
approximately Brownian at sub-picosecond time intervals but becomes
increasingly anomalous at longer times due to hydrogen-bond breaking and
reforming. The rotational time constant lies in the range $8 \! < \! \tau \! <
\! 11$\,ps. The L\'{e}vy rotor model is used to estimate the intra-molecular
contribution to the longitudinal nuclear-magnetic-resonance relaxation rate
$R_{1,{\rm intra}}$ due to dipolar $^1$H--$^1$H interactions. It is found that
$R_{1,{\rm intra}}$ contributes $65\,\pm 7$\% to the overall relaxation rate of
water at room temperature.
