Charge transfer, double and bond-breaking excitations with time-dependent density matrix functional theory

Time-dependent density functional theory (TDDFT) in its current adiabatic implementations exhibits three remarkable failures: (a) completely wrong behavior of the excited state surface along a bond-breaking coordinate; (b) lack of doubly excited configurations; (c) much too low charge transfer excitation energies. These TDDFT failure cases are all strikingly exhibited by prototype two-electron systems such as dissociating H2 and HeH+. We find for these systems with time-dependent density matrix functional theory that: (a) Within previously formulated simple adiabatic approximations, the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (b) An adiabatic approximation is formulated in which also the double excitations are fully accounted for.