  We present a second-order formulation of multi-reference algebraic
diagrammatic construction theory [Sokolov, A. Yu. J. Chem. Phys. 2018, 149,
204113] for simulating photoelectron spectra of strongly correlated systems
(MR-ADC(2)). The MR-ADC(2) method uses second-order multi-reference
perturbation theory (MRPT2) to efficiently obtain ionization energies and
intensities for many photoelectron transitions in a single computation. In
contrast to conventional MRPT2 methods, MR-ADC(2) provides information about
ionization of electrons in all orbitals (i.e., core and active) and allows to
compute transition intensities in straightforward and efficient way. Although
equations of MR-ADC(2) depend on four-particle reduced density matrices, we
demonstrate that computation of these large matrices can be completely avoided
without introducing any approximations. The resulting MR-ADC(2) implementation
has a lower computational scaling compared to conventional MRPT2 methods. We
present results of MR-ADC(2) for photoelectron spectra of small molecules,
carbon dimer, and equally-spaced hydrogen chains (H10 and H30) and outline
directions for future developments.
