Quasiparticle density-matrix representation of nonlinear time-dependent density-functional response functions

The time-dependent density-functional (TDDFT) equations may be written either for the Kohn-Sham orbitals in Hilbert space or for the single-electron density matrix in Liouville space. A collective-oscillator, quasiparticle, representation of the density response of many-electron systems which explicitly reveals the relevant electronic coherence sizes is developed using the Liouville-space representation of adiabatic TDDFT. Closed expressions for the nonlinear density-density response are derived, eliminating the need to solve nonlinear integral equations, as required in the Hilbert-space formulation of the response.