The molecular dynamics technique is used to study the relative dynamics of tagged pairs of molecules and to derive the related translational density of states (DOS) of liquid water at 243, 273, and 373 K. The modes that compose the short-time dynamics of centers of mass are obtained. The dynamical quantities studied are characterized by a fast-time decay followed by a plateau whose height increases with the temperature and with the initial pair separation. The plateau is attributed to the nonharmonic motions and its height is related to the pair relative diffusion coefficient. An exponential relaxation is used to represent the way the system follows to reach the diffusive behavior; the derived relaxation times agree with those reported in the literature describing the fast translational dynamics. The frequencies of the other short-time modes are related to the main frequencies of the solid, while the mode damping is analyzed in terms of the damped harmonic oscillator model; it is found that the Gaussian damping gives a better fit to the DOS than the exponential one. The temperature evolution of the various modes is investigated and related to the microscopic pair dynamics. In particular, the modes at low frequencies (omega congruent to 50 cm(-1)) are absent in the vibrations along the hydrogen bond (longitudinal modes); they are present in the transverselike dynamics of other pair states. The temperature increase produces the intensity decrease of the 50-cm(-1) band and the pile-up of the DOS intensity towards zero frequency. The decay constants of these two effects have a different temperature dependence, which confirms the oxygen bending nature of the 50-cm(-1) band and its independence on the relaxational-like dynamics.