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We explore the merits of linear-response range-separated time-dependentdensity-functional theory (TDDFT) for the calculation of photoionizationspectra. We consider two variants of range-separated TDDFT, namely thetimedependent range-separated hybrid (TDRSH) scheme which uses a globalrange-separation parameter and the timedependent locally range-separated hybrid(TDLRSH) which uses a local range-separation parameter, and compare withstandard time-dependent local-density approximation (TDLDA) and time-dependentHartree-Fock (TDHF). We show how to calculate photoionization spectra withthese methods using the Sternheimer approach formulated in a nonorthogonalB-spline basis set with appropriate frequency-dependent boundary conditions. Weillustrate these methods on the photoionization spectrum of the Be atom,focusing in particular on the core resonances. Both the TDRSH and TDLRSHphotoionization spectra are found to constitute a large improvement over theTDLDA photoionization spectrum and a more modest improvement over the TDHFphotoionization spectrum.

Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom