Using high resolution inelastic neutron scattering measurements of the phonon density of states of ice, two separate molecular optic bands at about 28 and 37 meV for ice Ih-and ice Ic have been observed, which is the direct result of the very high flux of pulsed neutron source and excellent energy resolution of the inelastic instruments on ISIS at the Rutherford-Appleton Laboratory. In order to reproduce the measured phonon density of states, a new lattice dynamic model has been proposed that two interaction strengths among the H bonds in ice Ih (and ice Ic) associated with the proton configurations have to be assumed. These two force constants are randomly distributed in the network of ice, having a ratio of almost 1:2. This model is capable of reproducing almost every aspect of the measured spectra, the two molecular peaks in 28 and 37 meV in particular and may provide insight into the complex nature of H bonding in ice and water. The large differences in the force constants between the strong and weak H bonds in a disordered ice structure as required by the model would affect the physical and chemical properties of ice and water and could have broader implications. In this paper, we illustrate a complete measurement for all possible recovered high-pressure forms of ice, including ice I, II, IX, V, VI, VII, VIII, and high-/low-density amorphous ice. These measurements demonstrate that the two well-separated molecular bands are associated with the local configurations configurations of protons, which have quite different interaction strengths.