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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]

This paper supersedes previous theoretical approaches to conceptual DFT because it provides a unified and systematic approach to all of the commonly considered formulations of conceptual DFT, and even provides the essential mathematical framework for new formulations. Global, local, and nonlocal chemical reactivity indicators associated with the “closed-system representation” ([Nα,Nβ,να(r),νβ(r)]) of spin-polarized density functional theory (SP-DFT) are derived. The links between these indicators and the ones associated with the “open-system representation” ([μα,μβ,να(r),νβ(r)]) are derived, including the spin-resolved Berkowitz–Parr identity. The Legendre transform to the “density representation” ([ρα(r),ρβ(r)]) is performed, and the spin-resolved Harbola–Chattaraj–Cedillo–Parr identities linking the density representation to the closed-system and open-system representations are derived. Taken together, these results provide the framework for understanding chemical reactions from both the electron-following perspective (using either the closed-system or the open-system representation) and electron-preceding perspective (density representation). A powerful matrix-vector notation is developed; with this notation, identities in conceptual DFT become universal. Specifically, this notation allows the fundamental identities in conventional (spin-free) conceptual DFT, the [Nα,Nβ] representation, and the [N=Nα+Nβ,NS=Nα-Nβ] representation to be written in exactly the same forms. In cases where spin transfer and electron transfer are coupled (e.g., radical+molecule reactions), we believe that the [Nα,Nβ] representation may be more useful than the more common [N,NS] representation. [ABSTRACT FROM AUTHOR]

The relaxation of the Pauli principle associated with density scaling is examined. Scaling the density has been investigated in the development of density functional computational methods with higher accuracy. Scaling the density by ρ(r)ζ=ρ(r)/ζ reduces the number of electrons to M=N/ζ when ζ>1. The minimum kinetic energy of the scaled density, Ts[ρ/ζ], can be scaled back to the N-electron system by multiplying the M-electron Kohn-Sham-type occupation numbers by ζ to produce Tζ[ρ]. This relaxes the Pauli principle when the orbital occupation numbers are greater than 1 in the N-electron system. The effects of antisymmetry on solutions to the Kohn-Sham equations are examined for Ne and the Be isoelectronic series. The changes in Tζ[ρ] and the exchange energy Exζ[ρ] when ζ is varied show that these two quantities are inextricably linked. [ABSTRACT FROM AUTHOR]

Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb’s Legendre transform ansatz to the generalized Hohenberg-Kohn functional not only solves the υ-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the v- and N-representability problems based on the constrained search formalism. [ABSTRACT FROM AUTHOR]

The hard/soft-acid/base (HSAB) principle indicates that hard acids prefer binding to hard bases (often forming bonds with substantial ionic character) while soft acids prefer binding to soft bases (often forming bonds with substantial covalent character). Though the HSAB principle is a foundational concept of the modern theory of acids and bases, the theoretical underpinnings of the HSAB principle remain murky. This paper examines the exchange reaction, wherein two molecules, one the product of reacting a hard acid and a soft base and the other the product of reacting a soft acid with a hard base, exchange substituents to form the preferred hard–hard and soft–soft product. A simple derivation shows that this reaction is exothermic, proving the validity of the HSAB principle. The analysis leads to the simple and conceptually appealing conclusion that the HSAB principle is a driven by simple electron transfer effects. [ABSTRACT FROM AUTHOR]