Excited State Densities from Time-Dependent Density Functional Response Theory

The idea to obtain electronic excited-state densities from TDDFT comes from the recognition that excited states are stationary points of the energy functional. This approach was explored two decades ago by Fillip Furche and coworkers. It becomes particularly relevant with the recent development of response-reformulated schemes for light-driven electron dynamics, which overcome challenging memory issues in the traditional real-time TDDFT approach. Instead, one requires high-quality linear-response properties of the driven system including excited-state densities. Using some well-defined approximations to excitation energy, we derive the expression for the excited-state density in real-space and compare its performance under exact-exchange and local-density approximations. We probe this approach on a range of one-dimentional systems including local and charge-transfer, and show the applicability to double-excitations which are beyond adiabatic approximation.