Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory

Abstract

Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used "average of degenerate states approximation" for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases.

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Sin (n = 12–20) clusters

“…This approximation will be used in this work. Additionally, in those cases where the frontier orbitals are degenerate, an average over the set of degenerate orbitals has been used [38][39][40][41] In our proposal, in contrast with the classical condensation schemes [42,43] (i.e., by means of atomic charges), the molecular space is partitioned into Fukui basins, which in turn are characterized by attractors at position k, according to the topological analysis of the gradient field of the Fukui function. Not only does this scheme avoid some ambiguities related with others (such as basis set dependence), [44][45][46] but it also provides regions of chemical interest that are not necessarily nuclear positions, which enrich the regioselectivity analysis.…”

An explicit approach to conceptual density functional theory descriptors of arbitrary order

“…(15) we assume that none of the reference states used to parameterize the model has spatially degenerate ground states. [38,39] Derivatives of the density with respect to N and  define the local reactivity indicators of conceptual DFT. The first derivative with respect to N is the Fukui function, [40][41][42] …”

Analysis of molecular and (di)atomic dual-descriptor functions and matrices

“…Provided that the system has no degenerate states, δ E δ v(r) N corresponds to ρ (r), the electron density function of the molecule. In case of degenerate states, the density to be used derives from degenerate perturbation theory [7][8][9] . Provided non-degenerate states, some trivial manipulations reveal that the dual descriptor is actually the N-derivative of the Fukui function f (r) [10][11][12] :…”