The fundamental equations to describe the change from one ground-state to another, in the framework of density functional theory, are used to analyze a set of hardness and softness functions that are hierarchized as non-local, local and global quantities. Through these definitions it is shown that under conditions of constant chemical potential, the interaction between two chemical systems evolves towards a state of maximum hardness, and that soft-soft, and hard-hard interactions are energetically favored. It is also shown that to a good approximation, the ground-state energy of a system decreases when its hardness increases. Possible applications of these principles are briefly discussed.
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