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Based on the relationship between average local ionization energy I ̄ (r) and average local electron affinity A ̄ (r) with the electronic Fukui functions, i.e., f−(r) and f+(r), respectively, in this paper, we establish a connection between nuclear and electronic Fukui functions beyond frontier molecular orbitals. As a consequence of this connection, we obtain expressions of average nuclear Fukui functions interpreted as a variation of average nucleophilicity or electrophilicity (weighted by the electronic orbital Fukui functions) with respect to nuclear displacements, which goes beyond the highest occupied molecular orbital/or lowest unoccupied molecular orbital consideration. Furthermore, from this connection and considering the frontier molecular orbital approximation, we derive expressions of nuclear Fukui functions in terms of the atom-condensed electronic Fukui functions, which imply a locality in the chemical reactivity and could be used to study the variation of local nucleophilicity or electrophilicity with respect to nuclear displacements. Finally, this new way to interpret the nuclear Fukui function could be useful in the future to study the chemical reactivity related to molecular vibrations, internal rotations, bond dissociation, chemical reaction along the model of reaction coordinate, and so on. [ABSTRACT FROM AUTHOR]

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]