The double-hybrid (DH) time-dependent density functional
theory
is extended to vertical ionization potentials (VIPs) and electron
affinities (VEAs). Utilizing the density fitting approximation, efficient
implementations are presented for the genuine DH ansatz relying on
the perturbative second-order correction, while an iterative analogue
is also elaborated using our second-order algebraic-diagrammatic construction
[ADC(2)]-based DH approach. The favorable computational requirements
of the present schemes are discussed in detail. The performance of
the recently proposed spin-component-scaled and spin-opposite-scaled
(SOS) range-separated (RS) and long-range corrected (LC) DH functionals
is comprehensively assessed, while popular hybrid and global DH approaches
are also discussed. For the benchmark calculations, up-to-date test
sets are selected with high-level coupled-cluster references. Our
results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the
most accurate and robust functional. This method consistently outperforms
the excellent SOS-ADC(2) approach for VIPs, although the results are
somewhat less satisfactory for VEAs. Among the genuine DH functionals,
the SOS-ωPBEPP86 approach is also recommended for describing
ionization processes, but its performance is even less reliable for
electron-attached states. In addition, surprisingly good results are
attained by the LC hybrid ωB97X-D functional, where the corresponding
occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs)
within the present formalism.