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We discuss the structural details and the ordering of hydrogen in LaH x for 2 x 3. To this end, we combine first-principles calculations with the cluster-expansion method. This approach allows us to follow the H occupation of the interstitial sites within the face-centered cubic matrix of La atoms. We find that LaH x clearly favors the fluorite structure at x = 2 and adds excess H atoms at the octahedral interstitial sites. The ground-state behavior of the system is discussed and is found in agreement with experimentally observed structures at compositions LaH 2.25 and LaH 2.50 ; an additional ground state at composition LaH 2.71 is predicted. The cluster expansion also permits an extensive scan of LaH x structures with two octahedral vacancies per unit cell. For energetically favorable configurations, this scan yields a vacancy percolation threshold at LaH 2.75 that possibly drives the concentration-dependent metal-insulator transition: The band gap calculated for isolated vacancy pairs disappears for percolating vacancy chains. This transition from metallic to insulating state is also experimentally observed near to the composition LaH 2.8 and gives rise to the "switchable mirror" phenomenon.

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