We present a detailed theory, implementation, and a benchmark study of a linear damped response time-dependent density functional theory (TDDFT) based on the relativistic four-component (4c) Dirac–Kohn–Sham formalism using the restricted kinetic balance condition for the small-component basis and a noncollinear exchange–correlation kernel. The damped response equations are solved by means of a multifrequency iterative subspace solver utilizing decomposition of the equations according to Hermitian and time-reversal symmetry. This partitioning leads to robust convergence, and the detailed algorithm of the solver for relativistic multicomponent wavefunctions is also presented. The solutions are then used to calculate the linear electric- and magnetic-dipole responses of molecular systems to an electric perturbation, leading to frequency-dependent dipole polarizabilities, electronic absorption, circular dichroism (ECD), and optical rotatory dispersion (ORD) spectra. The methodology has been implemented in the relativistic spectroscopy DFT program ReSpect, and its performance was assessed on a model series of dimethylchalcogeniranes, C4H8X (X = O, S, Se, Te, Po, Lv), and on larger transition metal complexes that had been studied experimentally, [M(phen)3]3+ (M = Fe, Ru, Os). These are the first 4c damped linear response TDDFT calculations of ECD and ORD presented in the literature.

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