  We present a method capable of calculating elastic scanning tunneling
microscopy (STM) currents from localized atomic orbital density functional
theory (DFT). To overcome the poor accuracy of the localized orbital
description of the wave functions far away from the atoms, we propagate the
wave functions, using the total DFT potential. From the propagated wave
functions, the Bardeen's perturbative approach provides the tunneling current.
To illustrate the method we investigate carbon monoxide adsorbed on a Cu(111)
surface and recover the depression/protrusion observed experimentally with
normal/CO-functionalized STM tips. The theory furthermore allows us to discuss
the significance of $s$- and $p$-wave tips.
