  Shockley surface states (SS) have attracted much attention due to their role
in various physical phenomena occurring at surfaces. It is also clear from
experiments that they can play an important role in electron transport.
However, accurate incorporation of surface states in $\textit{ab initio}$
quantum transport simulations remains still an unresolved problem. Here we go
beyond the state-of-the-art non-equilibrium Green's function formalism through
the evaluation of the self-energy in real-space, enabling electron transport
without using artificial periodic in-plane conditions. We demonstrate the
method on three representative examples based on Au(111): a clean surface, a
metallic nanocontact, and a single-molecule junction. We show that SS can
contribute more than 30\% of the electron transport near the Fermi energy. A
significant and robust transmission drop is observed at the SS band edge due to
quantum interference in both metallic and molecular junctions, in good
agreement with experimental measurements. The origin of this interference
phenomenon is attributed to the coupling between bulk and SS transport channels
and it is reproduced and understood by tight-binding model. Furthermore, our
method predicts much better quantized conductance for metallic nanocontacts.
