A new and efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy

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Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is given a matrix continued-fraction representation whose coefficients can be obtained from the non-symmetric block-Lanczos method. The resulting algorithm allows for the calculation of the full spectrum of a system with a computational workload which is only a few times larger than that needed for static polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with the calculation of the spectrum of benzene, and prospects for its application to the large-scale calculation of optical spectra are discussed.