Dramatic changes in electronic structure revealed by fractionally charged nuclei

Discontinuous changes in the electronic structure upon infinitesimal changes to the Hamiltonian are demonstrated. Remarkably, these are revealed in one and two electron molecular systems if the realm of the nuclear charge is extended to be fractional. Dramatic changes in the electron density from full configuration interaction are observed in real space illustrating key intricacies of electronic structure including the transfer, hopping and removal of electrons. Physically, this is due to the particle nature of electrons and manifests itself theoretically as a diverging linear density response function or an energy derivative discontinuity that occurs at constant number of electrons. This is essential to correctly describe real physical processes, from chemical reactions to electron transport and metal-insulator transitions. The dramatic errors of DFT are seen in real space as this physics is missing from currently used approximations and poses a great challenge for the development of new electronic structure methods.