  Scanning tunneling microscopy (STM) has been a fundamental tool to
characterize many-body effects in condensed matter systems, from extended
solids to quantum dots. STM of molecules decoupled from the supporting
conductive substrate has the potential to extend STM characterization of many
body effects to the molecular world as well. In this article, we describe a
many-body tunneling theory for molecules decoupled from the STM substrate, and
we report on the use of standard quantum chemical methods to calculate the
quantities necessary to provide the 'correlated' STM molecular image. The
developed approach has been applied to eighteen different molecules, to explore
the effects of their chemical nature and of their substituents, as well as to
verify the possible contribution by transition metal centers. Whereas the bulk
of calculations have been performed with CISD because of the computational
cost, some tests have been also performed with the more accurate CCSD method to
quantify the importance of the computational level on many-body STM images. We
have found that correlation induces a remarkable squeezing of the images, and
that correlated images are not derived from Hartree-Fock HOMO or LUMO alone,
but include contributions from other orbitals as well. Although correlation
effects are too small to be resolved by present STM experiments for the studied
molecules, our results provide hints for seeking out other species with larger,
and possibly experimentally detectable, correlation effects.
