Alkanes
Aromatics
While it has been fashionable to build `first principles' theories of molecular wires (we have ourselves built a few of them), we now find that they are often rationalized by simple theories, at least semi-quantitatively. For instance, a Fermi's Golden Rule gives the broadening of the most delocalized (HOMO) levels by a featureless gold electrode to be about 100 meV. This predicts a maximum current of about 7 micro-Amps for a short benzene dithiol (BDT) molecule. The maximum current is the first thing to look at, as this is a closed shell result whose analytical formula is the same irrespective of the presence of correlation and scattering, such as electron-electron screening, phonons or Coulomb Blockade. This maximum current, for well studied single molecule junctions, agrees reasonably well with experiments. The well known early historic examples with smaller currents are now believed to involve multiple molecules with weak junctions between them.
The zero-bias conductance has attracted a lot of attention, mainly because the linear response conductivity (Kubo formula etc) occupies many-body physicists and provides ample opportunities to study correlation effects. This is also its bane, as the zero-bias conductivity of molecules gets complicated by more mundane effects such as metal-induced gap states from the contacts and image charge effects. It would serve well for theorists to get some perspective on the really important effects to keep in mind (I remember an ambitious theorist who included a large number of many-body diagrams in his calculation, but forgot about the dielectric constant of the surrounding solution medium! Similarly, the simple broadening chemistry at the molecule-contact interface, with possible shorts and vacuum layers, is probably of higher experimental relevance than other more profound effects). The measured conductances of BDT and xylyl dithiol (XDT) are typically 1000 to 10000 times smaller than the conductance quantum, which translates to a large barrier of around 1 eV (comparable to alkanes). This is a surprise, as typical LDA-DFT theories of BDT coupled to Au consistently produces smaller barriers around 0.1-0.5 V (the barrier is easily extracted by just taking a large cluster to extract the Fermi energy, and then identifying the molecular HOMO-LUMO levels simply by plotting their eigenfunctions or by projecting the density of states or transmission onto the molecular eigenstates).
The simplest explanation for this discrepancy is the fallacy of using LDA-DFT for extracting not total energies (geometries), but individual transport eigen-states through a Kohn-Sham calculation that does not necessarily yield the physical molecular quasi-particles. A reason for this discrepancy is the well-known `self-interaction error' in DFT. Simply put, an electron should not feel a Coulomb potential from itself, and excluding this correctly would require an orbital-dependent one-electron exchange-correlation potential not present in LDA-GGA approximations. Better approximations such as LDA+U should fix this. The absence of self-interaction correction causes LDA to overbind, and thus underestimate the barrier height, thus grossly over-estimating the zero-bias conductances. A proper theory of self-interaction corrected LDA-GGA would be interesting to try out, to see if this correctly predicts barriers near 1 eV.
MoleFETs
Initial excitement about molecular electronics often stemmed from the idea that molecular transistors may somehow trump silicon-based transistors. Understandably, the electrical engineering community treated this with lukewarm skepticism. What is relatively under-stated in the field is that molecular electronics is more about electronics than about the molecules! Coming from a theoretical physics background, the first thing I learned was how little I knew about the good old transistor! It is perhaps foolhardy to discuss MoleFETs as future transistors without first forming a really good idea on what a regular transistor should look like, what its performance parameters (DIBL, subthreshold swing, gain) are, what the issues are that plague regular transistors (short channel effects, tunneling, etc), and what steps have been taken over the decades to mitigate them. In short, in order to make an impact on the field, you must first do your homework! It is not sufficient that we can build a molecule and attach leads to it -- any more than we can hope to fly an airplane simply because we can build a runway and designate a take-off zone (read Feynman's incredible lecture on cargo-cult science! It's a lesson for every aspiring scientist).
Invariably therefore, simulated I-Vs of molecular transistors showed results that were much more modest than the grandiose pictures that often float around, and in fact, quite consistent with our understanding of all other transistors (FETs, ballistic FETs, SiNW and CNTFETs, MODFETs, etc). While a lot of effort still exists on finding the energy levels of a molecule, the fundamental driver behind FETs, the 3-D electrostatics, is usually the least discussed. It is easy to forget that the contacts are not infinite parallel plate capacitors (the resulting mundane electrostatics controls the entire property of a transistor!). Similarly, it is easy to forgot (but critical not to do so!) to include a gate oxide that would prevent charge from escaping directly into the gate! Anyway, once you put these in, especially a proper 3D Poisson electrostatics and a good description of the contacts into a model for a MoleFET, the two obvious things that our theory yields are in retrospect, quite expected: (1) the currents did not saturate, and (2) the currents responded poorly to the gate fields. In other words, the output impedance was low, as was the transconductance. The corresponding subthreshold swing was temperature independent and unacceptably high.
The low output impedance arose because the extreme size of a molecule meant that it was hard to put a gate close enough to effectively control its channel potential. Indeed, one of the biggest challenges with silicon electronics has been to effectively thin down the gate oxide -- typical transistors have oxides that are 40 times thinner than the channel, which makes it hard to build a gate close enough to the molecule. The molecule acts more like a two-terminal device controlled by source and drain capacitances, given poor saturating I-Vs. Furthermore, direct source-to-drain tunneling through the metal induced gap states in the contacts made it hard to turn off the transistor, reducing its transconductance and increasing its subthreshold swing. These features are consistent with the understanding of most engineers, but it was nice to have an atomistic theory that affirmed these concepts. Especially since a lot of theoretical treatments tend to ignore these effects, while experiments often bypass discussions on these and fail to quantify the degree of gateability of moleFETs. The few systematic experimental searches for moleFET action have so far agreed with this prediction of poor gateability.
Conformational MoleFETs
Molecular transistors must exploit properties unique to organic molecules, such as their conformational flexibility. Imagine a molecule whose parts can be rotated by coupling built-in charge dipoles with a transverse gate electric field. Turning a component away from conjugation would turn off the current. This has two significant advantages over electrostatic gating: (1) it exploits the directionality of the gate field over the drain -- since the gate field is perpendicular to the plane of the molecule, a built-in dipole would preferentially couple to it even if the gate sits far away. We are thus utilizing a vector property of the gate, namely that its field is in a different direction than that from the drain. (2) Physically moving the molecule away from the conducting path cuts off the current abruptly, giving a subthreshold swing that depends on the ratio of the dipole moment to the product of the electronic charge times the oxide thickness. In principle, this can be less than the textbook limit! (provided the dipole is large enough to circumvent thermal fluctuations). Most significantly, as we proved mathematically, the electronic and conformational gating components acted independently (owing to the large separation in their time scales), so that their subthreshold swings added in parallel . Thus, even if the conformational gating is slow enough that only a fraction of it is executed over the electronic transit time, it nonetheless serves to lower the intrinsic swing of the electronic degrees of freedom.
A good non-charge based transistor must thus exploit vector properties of the field such as dipoles or spins, and should use the non-charge based degrees of freedom as an additional cut-off filter to reduce the OFF current rather than enhancing the ON current. Furthermore, the electronic and non-electronic degrees should be oppositely correlated, and should be robust with respect to thermal fluctuations.