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In this paper we study nine neutral copper clusters through the theoretical characterization of their molecular structures, binding energy, electronic properties, and reactivity descriptors. Geometry optimization and vibrational analysis were performed using density functional theory calculations with a hybrid functional combined with effective core potentials. It is shown that reactivity descriptors combined with reactivity principles like the minimum polarizability and maximum hardness are operative for characterizing and rationalizing the electronic properties of copper clusters. [ABSTRACT FROM AUTHOR]