Evolutionary structure searches predict three new phases of iodine polyhydrides stable under pressure. Insulating P1-H5I, consisting of zigzag chains of HI (delta+)and H2(delta-) molecules, is stable between 30-90 GPa. Cmcm-H2I and P6/mmm-H4I are found on the 100, 150 and 200 GPa convex hulls. These two phases are good metals, even at 1 atm, because they consist of monoatomic lattices of iodine. At 100 GPa the Tc of H2I and H4I are estimated to be 7.8 and 17.5 K, respectively. The increase in Tc relative to elemental iodine results from a larger omega-log from the light mass of hydrogen, and an enhanced lambda from modes containing H/I and H/H vibrations.
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