In pursuit of negative Fukui functions: molecules with very small band gaps.

A justification for the likely presence of negative Fukui functions in molecules with small band gaps is given, and a computational study performed to check whether molecules with small band gaps have negative Fukui functions to a chemically significant extent is reported. While regions with negative Fukui functions were observed, significantly negative values for the atom-condensed Fukui functions were not observed.

In pursuit of negative Fukui functions: examples where the highest occupied molecular orbital fails to dominate the chemical reactivity.

In our quest to explore molecules with chemically significant regions where the Fukui function is negative, we explored reactions where the frontier orbital that indicates the sites for electrophilic attack is not the highest occupied molecular orbital. The highest occupied molecular orbital (HOMO) controls the location of the regions where the Fukui function is negative, supporting the postulate that negative values of the Fukui function are associated with orbital relaxation effects and nodal surfaces of the frontier orbitals. Significant negative values for the condensed Fukui function, however, were not observed.

Symmetric Nonlocal Weighted Density Approximations from the Exchange-Correlation Hole of the Uniform Electron Gas.

Nonlocal exchange-correlation energy functionals are constructed using the accurate model exchange-correlation hole for the uniform electron gas developed by Gori-Giorgi and Perdew. The exchange-correlation hole is constrained to be symmetric and normalized, so the resulting functionals can be viewed as symmetrized versions of the weighted density approximation; we call them two-point weighted density approximations. Even without optimization of parameters or functional forms, the exchange-correlation energies for small molecules are competitive with those of the best generalized gradient approximation functionals. Two-point weighted density approximations seem to be an interesting new direction for functional development. A more general version of the conditions that define the energy for fractional electron number and fractional spin are presented. These "generalized flat-planes" conditions are closely linked to the normalization of the spin-resolved exchange-correlation hole at noninteger electron number. This and many other properties of the exact exchange-correlation functional can be imposed straightforwardly and directly in symmetrized weighted density approximation.