Excited electronic states of carotenoids: Time-dependent density-matrix-response algorithm

The response of the single-electron density matrix of a many-electron system to an external field is calculated using the time-dependent Hartree–Fock (TDHF) technique. A procedure for inverting the resulting nonlinear response functions to obtain an effective quantum multilevel system that has the same response is developed. The number of effective states is gradually increased as higher-order nonlinearities are computed. The complete set of intrastate and interstate density matrices and excited-state energies can be calculated. A favorable N-scaling of computational effort with size can be obtained making use of the localization of the optical transitions in real space.