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The host–guest structure of scandium is described as being built of two penetrating substructures with the incommensurate periods of the channels along the c axis. We present the ideal commensurate value of 4/3 in Sc-II using ab initio calculations. We reveal that the 3cH and 4cG structures do interpenetrate and combine to the commensurate value of 4/3 of Sc-II at a pressure of 70 GPa. Ab initio molecular dynamics confirms the stability of the commensurate value 4/3 of the host–guest structure at 300 K and 72 GPa. The pressure-induced structural phase transitions in scandium under high pressure up to 200 GPa are investigated. We use ab initio random structure searching to predict the crystal structure of Sc-III: it is the tetragonal structure with space group P41212. Our calculations show that superconductivity arises in the P41212 structure. This high pressure structure is not only a superconducting phase but also has been reported for the first time in this group of elements.

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