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The first KH theorem only speaks about the relation between the ground-state density and its external potential, while the second HK theorem refers to the relation of the ground-state density and the ground-state energy. Given a external potential, there is a ground-state density associated to it (1st HKT). That ground-state density can be used to calculate the ground-state energy (2nd HKT), as any other density will return a higher energy.
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