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In analogy to the electrophilicity, we define potentialphilicity indicators that represent energetically favorable ways to change the external potential of a molecule at fixed electron number. Similarly, we define a potentialphobicity to represent the least favorable way to change the external potential of a molecule. The resulting indicators should be useful for describing how molecular geometries change and predicting favorable and unfavorable ways for a reagent to approach a molecule. The linear response function enters plays a very important role in this approach, analogous to the role of the hardness for the electrophilicity or the hardness kernel for the Fukui function. The mathematical properties of the response function and its implications for these reactivity indicators are discussed in depth. [ABSTRACT FROM AUTHOR]

Relationships between third-order reactivity indicators in the closed system [N, v(r)], open system [μ, v(r)], and density [ρ(r)] pictures are derived. Our method of derivation unifies and extends known results. Among the relationships is a link between the third-order response of the energy to changes in the density and the quadratic response of the density to changes in external potential. This provides a link between hyperpolarizability and the system’s sensitivity to changes in electron density. The dual descriptor is a unifying feature of many of the formulas we derive. [ABSTRACT FROM AUTHOR]