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Despite decades of study, several key aspects of the Al-H system remain the subject of considerable debate. In an effort to elucidate some of these unknowns, we perform a systematic study of this system using first-principles density-functional calculations. We show that generalized gradient approximation (GGA) calculations provide an accurate picture of energetics, phase stability and structure, diffusion, and defect binding in the Al-H system. A series of calculations for hydrides in the M-H systems (M= Al, Ba, Ca, K, Mg, La, Li, Na, Ni, Pd, Sc, Sr, Ti, V, and Y) also shows that the GGA calculations are a quantitatively accurate predictor of hydride formation energies. For Al-H, we find:(i) In agreement with experiment, the observed metastable hydride, AlH 3 is found to have a small, negative formation enthalpy at ambient conditions, but a strongly positive formation free energy.(ii) Linear response calculations of AlH 3 …