This paper examines charge transport by tunneling across a series of electrically (insulating molecules with the structure HS(CH 2 ) 4 CONH(CH 2 ) 2 R) in the form of selfassembled monolayers (SAMs), supported on silver. The molecules examined were studied experimentally by Yoon et al. (Angew. Chem. Int. Ed., 51, 4658−4661, 2012), using junctions of the structure AgS(CH 2 ) 4 CONH(CH 2 ) 2 R//Ga 2 O 3 /EGaIn. The tail group R had approximately the same length for all molecules, but a range of different structures. Changing the R entity over a range of different structures (aliphatic to aromatic) does not influence the conductance significantly. To rationalize this surprising result, we investigate transport through these SAMs theoretically, using both full quantum methods and a generic, independent-electron tight-binding toy model. We find that the frontier orbitals HOMO, HOMO-1, HOMO-2 and HOMO-3, have similar structures for all of the different R-groups, and that the HOMO, which is largely responsible for the transport in these molecules, is always strongly localized on the thiol group. The relative insensitivity of the current density to the structure of the R group is due not only to these similar frontier orbitals but also to a combination of energy levels (ε) and tunneling amplitudes (t), which lead to similar conductance for different tail groups, i.e. the large difference between ε's in conjugated and saturated groups is compensated by tunneling amplitudes inside the tail group. In addition, the coupling of the tail group to the alkane chain is much weaker for conjugated groups than for saturated ones. Conductance change in these molecules is not influenced by the broadening of the molecular levels connected to the left and right electrodes, since in all these molecules the effective coupling to the silver substrate is the same, whereas the other effective couplings are determined by the weak connection to the oxide Ga 2 O 3 layer. All these factors combine to produce currents largely insensitive to the R group.An estimation of the attenuation constant, β, of the simplified Simmons equation obtained using these methods is β = 1.1 per CH 2 group, in good agreement with observed results. Our analysis sketches the potential landscapes across which tunneling occurs, and suggests that it will be difficult to change rates of tunneling by simple changes 2 in molecular structure. This work indicates that significant control over SAMs largely composed of nominally insulating groups may be possible when tail groups are used that are significantly larger than those used in the experiments of Yoon et al. 13