The electrical properties of self-assembled monolayers (SAMS) on a gold surface have been explored to address the relation between the conductance of a molecule and its electronic structure. We probe interfacial electron transfer processes, particularly those involving electroactive groups, of SAMS of thiolates on Au by using shear force-based scanning probe microscopy (SPM) combined with current-voltage (i-V) and current-distance (i-d) measurements. Peak-shaped i-V curves were obtained for the nitro- and amino-based SAMS studied here. Peak-shaped cathodic i-V curves for nitro-based SAMS were observed at negative potentials in both forward and reverse scans and were used to define the threshold tip bias, V-TH, for electric conduction. For a SAM of 2',5'-dinitro-4,4'-bis(phenylethynyl)-1-benzenethiolate, VIII, V-TH was nearly independent of the tip material [Ir, Pt, Ir-Pt (20-80%), Pd, Ni, Au, Ag, In]. For all of the SAMS studied, the current decreased exponentially with increasing distance, d, between tip and substrate. The exponential attenuation factors (beta values) were lower for the nitro-based SAMS studied here, as compared with alkylthiol-based SAMS. Both V-TH and beta of the nitro-based SAMS also depended strongly on the molecular headgroup on the end benzene ring addressed by the tip. Finally, we confirmed the "memory" effect observed for nitro-based SAMS. For mixed SAMS of VII and hexaclecanethiol, 1, the fraction of the charge collected in the negative tip bias region that can be read out at a positive tip bias on reverse scan (up to 38%) depended on the film composition and decreased with an increasing fraction of 1, suggesting that lateral electron hopping among molecules of VII occurs in the vicinity of the tip.