  In the past decade, photoemission orbital tomography (POT) has evolved into a
powerful tool to investigate the electronic structure of organic molecules
adsorbed on (metallic) surfaces. By measuring the angular distribution of
photoelectrons as a function of binding energy and making use of the
momentum-space signature of molecular orbitals, POT leads to an
orbital-resolved picture of the electronic density of states at the
organic/metal interface. In this combined experimental and theoretical work, we
apply POT to the prototypical organic $\pi$-conjugated molecule bisanthene
(C$_{28}$H$_{14}$) which forms a highly oriented monolayer on a Cu(110)
surface. Experimentally, we identify an unprecedented number of 13 $\pi$ and 12
$\sigma$ orbitals of bisanthene and measure their respective binding energies
and spectral lineshapes at the bisanthene/Cu(110) interface. Theoretically, we
perform density functional calculations for this interface employing four
widely used exchange-correlation functionals from the families of the
generalized gradient approximations as well as global and range-separated
hybrid functionals. By analyzing the electronic structure in terms of
orbital-projected density of states, we arrive at a detailed orbital-by-orbital
assessment of theory vs. experiment. This allows us to benchmark the
performance of the investigated functionals with regards to their capability of
accounting for the orbital energy alignment at organic/metal interfaces.
