Extending the Runge-Gross Theorem for the Inclusion of Non-analytic Potentials and Densities

The Runge-Gross theorem reveals the existence of an invertible map between time-dependent (TD) electronic densities and external scalar potentials, provided the initial state of the system is fixed. This result provides solid footing to the TDDFT research field. The original version of the theorem, however, excluded potentials and densities that are not Taylor-expandable around the initial time of the propagation. This talk presents new developments that extend the theorem to include TD non-analytic potentials and densities. Relation with previous work, current limitations, and future directions are discussed.
Reference: J. Chem. Phys., 147, 134110.