When is the Fukui Function Not Normalized? The Danger of Inconsistent Energy Interpolation Models in Density Functional Theory

• DOI: 10.1021/acs.jctc.6b00494
• Publication Date: 2016-11-04T19:10:20Z
• Authors: Farnaz Heidar-Zadeh; Ramón Alain Miran...; Toon Verstraelen; Patrick Bultinck; Paul W. Ayers
• Keywords: Interpolation; Normalization

When one defines the energy of a molecule with noninteger number electrons by interpolation values for integer-charged states, interpolated electron density, Fukui function, and higher-order derivatives density are generally not normalized correctly. The necessary sufficient condition consistent models is that corresponding correctly to electrons. A necessary, but sufficient, correct normalization interpolant be linear function reference energies. Consistent this general rule, polynomial and, in particular, quadratic E vs N model popularized Parr Pearson, do give densities derivatives. Interestingly, an based on square root also satisfies constraints. We derive least-norm models. In contrast these models, popular rational exponential forms