Liouville-space response theory in the self-consistent field approximation

We present a second-quantization based Liouville-space formulation of response theory for non-eigenstates of unperturbed Hamiltonian in the single-determinant self-consistent field framework, where we include a time-independent relaxation superoperator in the Liouville equation of motion. This density-based formulation uses quantities and concepts similar to those introduced in established wave function-based forms of approximate-state response theory, and we discuss how the wave function-based class of theory relates to the present more general treatment. We also discuss various aspects of the present methodology, including its opportunities and limitations/challenges, and outline future work.