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

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 …