Quantum nuclear zero-point motions in solid H2 and D2 under pressure are investigated at 80 K up to 160 GPa by first-principles path-integral molecular dynamics calculations. Molecular orientations are well-defined in phase II of D2, while solid H2 exhibits large and very asymmetric angular quantum fluctuations in this phase, with possible rotation in the (bc) plane, making it difficult to associate a well-identified single classical structure. The mechanism for the transition to phase III is also described. Existing structural data support this microscopic interpretation.Keywords: hydrogen, deuterium, path-integral, quantum fluctuation, broken-symmetry phase Over the past 20 years, pressure-induced structural changes have been studied for most elements up to the 300 GPa range by a combination of synchrotron diamond anvil cell experiments and ab initio calculations. Although hydrogen has probably been the most extensively studied element under pressure, its crystalline structures above 10 GPa are still largely unknown. Experimental structural determination is hampered by hydrogen's weak x-ray scattering cross-section, and the use of neutron diffraction is equally, if not more, difficult. Theoretically, the difficulties stem from the fact that nuclear zero-point motions and exchange contributions can have important effects. Novel quantum many-body states of matter should be expected, such as the recently predicted superconducting/superfluid metallic state [1]. Understanding the phase diagram of hydrogen is thus an open challenge in modern condensed matter physics.The phase diagrams of solid hydrogen and deuterium have been extensively studied by Raman and infra-red vibrational spectroscopies. Phase boundaries have been determined for three phases [2][3][4]. The transition from phase I to II appears to be related to a quantum ordering of the molecules, whereas that from II to III is more likely a classical ordering [5]. A strong difference in pressure has been measured between the I-II boundary line of solids H 2 , HD and D 2 , whereas there is almost none for the II-III phase boundary. X-ray diffraction studies have shown that the mass centers of the molecules remain on an hcp lattice at the I-II and II-III transitions, indicating that these phases are differentiated by a molecular ordering on this lattice [6,7]. The nature of this ordering, however, is still unknown. Neutron diffraction data may rule out some theoretical predictions for phase II of D 2 but are insufficient for determination of the orientational order [6]. Numerous calculations using Density Functional Theory (DFT) have tried to examine structural changes in solid molecular hydrogen under pressure [8]. A very small energy difference between various candidate structures is obtained and the relative stability of these structures may be easily changed by including zero-point energy contributions. The most recent revision of the DFT phase diagram of hydrogen, including zero-point energy at the harmonic level, predicts the P 6 3 /m structure for phase...