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We explore theoretically the scanning tunneling microscopy of singlemolecules on substrates using a framework of two local probes. This frameworkis appropriate for studying electron flow in tip/molecule/substrate systemswhere a thin insulating layer between the molecule and a conducting substratetransmits electrons non-uniformly and thus confines electron transmissionbetween the molecule and substrate laterally to a nanoscale regionsignificantly smaller in size than the molecule. The tip-molecule coupling andmolecule-substrate coupling are treated on the same footing, as local probes tothe molecule, with electron flow modelled using the Lippmann-Schwinger Greenfunction scattering technique. STM images are simulated for various positionsof the stationary (substrate) probe below a Zn(II)-etioporphyrin I molecule. Wefind that these images have a strong dependence on the substrate probeposition, indicating that electron flow can depend strongly on both tipposition and the location of the dominant molecule-substrate coupling.Differences in the STM images are explained in terms of the molecular orbitalsthat mediate electron flow in each case. Recent experimental results, showingSTM topographs of Zn(II)-etioporphyrin I on alumina/NiAl(110) to be stronglydependent on which individual molecule on the substrate is being probed, areexplained using this model. A further experimental test of the model is alsoproposed.Comment: Physical Review B, in pres

Two-probe theory of scanning tunneling microscopy of single molecules: Zn(II)-etioporphyrin on alumina