We performed static-lattice and dynamic-lattice diffusion Monte Carlo simulations of solid hydrogen candidate structures C2/c, Cmca-4, Cmca-12, and I4­1/amd from 350 to 800 GPa. The dynamic-lattice simulations treat electrons and protons on the same footing. This way we include anharmonic lattice vibration as well as electron-ion coupling without invoking the Born-Oppenheimer approximation. The relative enthalpies of the molecular structures were found to be in good agreement with previous quantum Monte Carlo studies. However, we find a higher transition pressure to the atomic phase. In addition to the equation of state, we extract plasma frequency from the static structure factor. We also calculate various lattice properties such as the bond length and orientation of the hydrogen molecules. Our calculations connect and extend previous quantum Monte Carlo datasets.