Reactivity indices and fluctuation formulas in density functional theory: Isomorphic ensembles and a new measure of local hardness

Abstract

Fluctuation formulas for the external potential v(r) are introduced in a modified Legendre-transformed representation of the density functional theory of electronic structure (isomorphic ensemble). A new (nuclear/geometric) reactivity index h(r), having the same status as the electronic Fukui function in the canonical ensemble, is thereby identified, h(r)=(1/N)[δμ/δσ(r)]N,T=(1/kT) [〈μ⋅v(r)〉−〈μ〉〈v(r)〉], where μ is the electronic chemical potential, σ is the shape factor of the electron density distribution, N is the number of electrons, 〈...〉 denotes the ensemble average of a quantity, and 〈v(r)〉 is the ensemble averaged external potential. This new local quantity is shown to be an inverse of the local softness, and to provide a useful definition of a local hardness.

Chemical reactivity indexes in density functional theory

“…61,62 The finite temperature ensemble description in DFT 63 has greatly helped to understand concepts such as hardness and softness, thanks to Parr and coworkers. 64,65 66 Relations connecting these functionś are given in subsequent sections.…”

Relations among several nuclear and electronic density functional reactivity indexes

“…13 has been recently discussed 8,9,14 and new definitions of nuclear/geometric reactivity indexes have been also put forward. [15][16][17] These studies 8 -12,14 -17 have reinforced the idea that a complete representation of the total chemical response to a given perturbation must involve the analysis of both electronic and nuclear reactivity descriptors. Because of the coupling between the electronic and nuclear responses to external perturbations, one can expect that relationships between nuclear and reactivity indexes exist.…”

Density Functional Theory Calculations of the Oxidative Dehydrogenation of Propane on the (010) Surface of V2O5†

“…36 Since the KohnSham orbitals 21 give the total ground-state electron density of the system, they also provide a measure of both the global and local chemical reactivity of the system. 22,27,[37][38][39][40][41][42] The Fukui functions (FF) and related hardness/softness characteristics constitute the major chemical descriptors of molecular species for open systems, in which the number of electrons is a continuous equilibrium variable. 22 In the frozen core approximation the FF represent the density of the relevant frontier molecular orbital involved in electron receiving (nucleophilic attack) or withdrawing (electrophilic attack) processes.…”