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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. [ABSTRACT FROM AUTHOR]

The energy barriers for the cis–trans isomerization are obtained for a sample of push–pull compounds. The appropriate trend in the values for the barriers is obtained after an instability treatment of the restricted Kohn–Sham solution. At the instability zone, some compounds exhibit a singlet open-shell configuration. The width of the instability region around the transition state is characterized in an asymmetric push–pull compound. These results show that the instabilities in the twisted configuration of double bonds are mainly related to spin symmetry effects rather than to the molecular symmetry. For the open-shell singlet, an ensemble model is used to compute the electronic properties. The singlet–triplet energy gap along the rotation coordinate is qualitatively described by the use of spin potential and hardness. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A previously derived [J. Chem. Phys. 103, 7645 (1995)] general variational principle, for determining the hardness (or band gap) of electronic systems, is applied to π-electron systems by a straightforward simple parameterization of the hardness kernel. For conjugated polyenes and annulenes, the hardness (band gaps) are essentially the same as (although no identical with) those predicted by the Hückel method. In contrast with the Hückel method, one need not assume that the total electronic energy is a sum of one-electron energies. Comparisons are made with Nalewajski’s Charge Sensitivity Analysis. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The Fukui function for a neutral atom is expressed as its LDA approximation plus a one-parameter gradient correction, and the resultant formula is numerically tested. Expressing hardness as a density functional involving this Fukui function, global hardness values are determined for several atoms. Estimates also are made of the covalent radii of neutral atoms. Calculated Fukui functions exhibit characteristics similar to those reported in the literature. Calculated hardnesses compare favorably with experimental values, and predicted covalent radii are in agreement with existing theoretical values and experimental data. No information other than the electron densities of the neutral species enter in the calculations. An exact nuclear cusp condition on the Fukui function is derived. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The exchange energy density functional of an N electron atom is approximated by a combination of the Dirac and the Fermi–Amaldi approximations. The unknown coefficients of the combination are estimated by requiring that the sum of the Coulombic and exchange energies vanish when evaluated with the exact one-electron density. Evaluating the present functional with the Hartree–Fock densities of 1785 atoms and ions, and comparing the resulting exchange energies with the corresponding Hartree–Fock values gave an average error of 2%. The functional derivative has the correct long-range behavior, and leads to an Euler–Lagrange equation whose solutions gave energies which were in very good agreement with the Hartree–Fock values. [ABSTRACT FROM AUTHOR]