  Scanning tunneling spectroscopy (STS) allows to image single molecules
decoupled from the supporting substrate. The obtained images are routinely
interpreted as the square moduli of molecular orbitals, dressed by the
mean-field electron-electron interaction. Here we demonstrate that the effect
of electron correlation beyond mean field qualitatively alters the uncorrelated
STS images. Our evidence is based on the ab-initio many-body calculation of STS
images of planar molecules with metal centers. We find that many-body
correlations alter significantly the image spectral weight close to the metal
center of the molecules. This change is large enough to be accessed
experimentally, surviving to molecule-substrate interactions.
