We investigate the energy relaxation of intermolecular motions in liquid water at temperatures ranging from 220 K to 300 K and in ice at 220 K using molecular dynamics simulations. We employ the recently developed frequency resolved transient kinetic energy analysis, which provides detailed information on energy relaxation in condensed phases like two-color pump-probe spectroscopy. It is shown that the energy cascading in liquid water is characterized by four processes. The temperature dependences of the earlier three processes, the rotational-rotational, rotational-translational, and translational-translational energy transfers, are explained in terms of the density of states of the intermolecular motions. The last process is the slow energy transfer arising from the transitions between potential energy basins caused by the excitation of the low frequency translational motion. This process is absent in ice because the hydrogen bond network rearrangement, which accompanies the interbasin transitions in liquid water, cannot take place in the solid phase. We find that the last process in supercooled water is well approximated by a stretched exponential function. The stretching parameter, β, decreases from 1 to 0.72 with decreasing temperature. This result indicates that the dynamics of liquid water becomes heterogeneous at lower temperatures.

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