title: When is the Fukui Function Not Normalized? The Danger of Inconsistent Energy Interpolation Models in Density Functional Theory.
abstract: When one defines the energy of a molecule with a noninteger number of electrons by interpolation of the energy values for integer-charged states, the interpolated electron density, Fukui function, and higher-order derivatives of the density are generally not normalized correctly. The necessary and sufficient condition for consistent energy interpolation models is that the corresponding interpolated electron density is correctly normalized to the number of electrons. A necessary, but not sufficient, condition for correct normalization is that the energy interpolant be a linear function of the reference energies. Consistent with this general rule, polynomial interpolation models and, in particular, the quadratic E vs N model popularized by Parr and Pearson, do give normalized densities and density derivatives. Interestingly, an interpolation model based on the square root of the electron number also satisfies the normalization constraints. We also derive consistent least-norm interpolation models. In contrast to these models, the popular rational and exponential forms for E vs N do not give normalized electron densities and density derivatives.
authors.affiliation: Department of Chemistry & Chemical Biology, McMaster University , Hamilton, L8S 4M1 Ontario, Canada.|Department of Inorganic and Physical Chemistry, Ghent University , Krijgslaan 281 (S3), 9000 Gent, Belgium.|Center for Molecular Modeling, Ghent University , Technologiepark 903, 9052 Zwijnaarde, Belgium.
authors.forename: Farnaz
authors.initials: F
authors.lastname: Heidar-Zadeh
authors.affiliation: Department of Chemistry & Chemical Biology, McMaster University , Hamilton, L8S 4M1 Ontario, Canada.|Laboratory of Computational and Theoretical Chemistry, Faculty of Chemistry, University of Havana , Havana, Cuba.
authors.forename: Ramón Alain
authors.initials: RA
authors.lastname: Miranda-Quintana
authors.affiliation: Center for Molecular Modeling, Ghent University , Technologiepark 903, 9052 Zwijnaarde, Belgium.
authors.forename: Toon
authors.initials: T
authors.lastname: Verstraelen
authors.affiliation: Department of Inorganic and Physical Chemistry, Ghent University , Krijgslaan 281 (S3), 9000 Gent, Belgium.
authors.forename: Patrick
authors.initials: P
authors.lastname: Bultinck
authors.affiliation: Department of Chemistry & Chemical Biology, McMaster University , Hamilton, L8S 4M1 Ontario, Canada.
authors.forename: Paul W
authors.initials: PW
authors.lastname: Ayers