We have studied the vibrational modes and their frequencies in both atomic and molecular phases of dense hydrogen to find the stable structures and evaluated the zero-point energies (ZPEs) and the effect on molecular dissociation. The most probable structure in the atomic phase is Cs IV whose vibrational modes have real frequencies over the whole Brillouin zone. And the structure in the molecular phase is very close to Cmca, whose vibrational modes with imaginary frequencies work as guides to the stable structure. Our estimates of the ZPE are very close to those of Kagan et al (Kagan Yu, Pushkarev V V and Kholas A 1977 Sov. Phys.-JETP 46 511). Adding the ZPE to the static energy, we estimated its effect on the pressure of the molecular dissociation. The reduction of the dissociation pressure due to the inclusion of the ZPE becomes over 100 GPa.