On the Foundations of Chemical Reactivity Theory

Abstract

In formulating chemical-reactivity theory (CRT) so as to give it a deep foundation in density-functional theory (DFT), Parr, his collaborators, and subsequent workers have introduced reactivity indices as properties of isolated reactants, some of which are in apparent conflict with the underlying DFT. Indices which are first derivatives with respect to electron number are staircase functions of number, making electronegativity equalization problematic. Second derivative indices such as hardness vanish, putting hardness-based principles out of reach. By reformulating CRT within our partition theory, which provides an exact decomposition of a system into its component species, we resolve the conflict. We show that the reactivity of a species depends on its chemical context and define that context. We establish when electronegativity equalization holds and when it fails. We define a generalization of hardness, a hardness matrix containing the self-hardness of the individual species and the mutual hardnesses of the pairs of species of the system, and identify the physical origin of hardness. We introduce a corresponding generalization of the Fukui function as well as of the local and global softnesses and the softness kernel of the earlier formulation. We augment our previous formulation of the partition theory by introducing a model energy function and express the difference between the exact and the model forces on the nuclei in terms of the new reactivity indices. For simplicity, our presentation is limited to time-reversal invariant systems with vanishing spin density; it is straightforward to generalize the theory to finite spin density.

Partition Theory: A Very Simple Illustration

“…[2] and [3] is shown to hold in Section 7. Also in Section 7, the hardness [3] of the isolated H atom is calculated, shown to be nonzero, and correlated with the strength with which its electron is bound. Thus, despite the fact that the model is a caricature of the real system, meaningful features of the partition theory are indeed illustrated by it, as discussed in the concluding Section, 8.…”

“…In a series of recent papers [1][2][3], two of us have developed a rigorous method for dividing a complex system into its parts based on density-functional theory [4][5][6][7][8].…”

“…The underlying theory, partition-theory (PT), was used to construct a formulation of chemical reactivity theory (CRT) [3] which, for the first time, is consistent with the underlying density-functional theory [8,9] and is richer in structure than the preexisting CRT [10][11][12][13].…”

“…First the electron density of the whole system must be determined. Then, the densities of the parts must be determined simultaneously with v R , all of which is required to set the stage for the determination of mutual reactivities between parts, though certain self-reactivities can be determined for each species alone without reference to a larger system [3]. Accordingly, in the present paper, we develope the partition theory in detail for an extremely simple system to exhibit its main features explicitly.…”

Accurate Reference Data for the Nonadditive, Noninteracting Kinetic Energy in Covalent Bonds

“…These methods, such as subsystem density-functional theory [1,2] (subsystem-DFT) and partition density-functional theory [3][4][5] (PDFT) are based around a real space partitioning of the total density into fragments such that,…”