  We explore theoretically the scanning tunneling microscopy of single
molecules on substrates using a framework of two local probes. This framework
is appropriate for studying electron flow in tip/molecule/substrate systems
where a thin insulating layer between the molecule and a conducting substrate
transmits electrons non-uniformly and thus confines electron transmission
between the molecule and substrate laterally to a nanoscale region
significantly smaller in size than the molecule. The tip-molecule coupling and
molecule-substrate coupling are treated on the same footing, as local probes to
the molecule, with electron flow modelled using the Lippmann-Schwinger Green
function scattering technique. STM images are simulated for various positions
of the stationary (substrate) probe below a Zn(II)-etioporphyrin I molecule. We
find that these images have a strong dependence on the substrate probe
position, indicating that electron flow can depend strongly on both tip
position and the location of the dominant molecule-substrate coupling.
Differences in the STM images are explained in terms of the molecular orbitals
that mediate electron flow in each case. Recent experimental results, showing
STM topographs of Zn(II)-etioporphyrin I on alumina/NiAl(110) to be strongly
dependent on which individual molecule on the substrate is being probed, are
explained using this model. A further experimental test of the model is also
proposed.
