Ubiquitous Negative Electron Densities Discredit Smooth Energy Interpolation in Density Functional Theory

A unified theoretical framework for interpolating the energy and other molecular properties as a function of the number of electrons is presented. For any smooth interpolatory model of charge transfer, including the ubiquitous quadratic model, the electron density is always negative for some regions of space and some numbers of electrons. This has practical implications; e.g., we observe that parabolic interpolation predicts HF^+0.5 has an unphysical negative population on hydrogen for sufficiently compressed bonds. This suggests that the only sensible model for charge transfer, in most cases, is linear (zero-temperature grand canonical) interpolation.