  We describe \ASTRA{} (AttoSecond TRAnsitions), a new close-coupling approach
to molecular ionization that uses many-body transition density matrices between
ionic states with arbitrary spin and symmetry, in combination with hybrid
integrals between Gaussian and numerical orbitals, to efficiently evaluate
photoionization observables. Within the transition-density-matrix approach, the
evaluation of inter-channel coupling is exact and does not depend on the size
of the configuration-interaction space of the ions. Thanks to these two crucial
features, \ASTRA{} opens the way to studying highly correlated and
comparatively large targets at a manageable computational cost. Here, \ASTRA{}
is used to predict the parameters of bound and autoionizing states of the boron
atom and of the N$_2$ molecule, as well as the total photoionization cross
section of boron, N$_2$, and formaldehyde, H$_2$CO. Our results are in
excellent agreement with theoretical and experimental values from the
literature.
