EvanCurtin

=Electron Flow Through Au|Dithiol|Au Junctions=

Introduction
In general, the process of electron transfer is applicable to everything from photosynthesis to electrode chemistry [1]. In the middle of the 20th century, the development of quantum mechanics had allowed for a means to study the behavior of electrons in varying types of environments. Simple electron exchanges in solution could be described for species which were comprised of ion-dipole bound heteroions by the 1950s [2]. This idea was quickly universalized to apply to general oxidation-reduction reactions [3]. Taking this one step further, the electron transfer at electrodes was reasonably well described from an ab initio theoretical perspective and agreed with experimental results [4]. While the Nobel prize in chemistry was awarded to Marcus for his work in describing this process, the field of electron transfer has since expanded in both breadth and depth [5].Recently, the demand for miniaturization of electronics has brought about a widespread interest in development of single molecule based electronic devices.

Au-Thiol Interface
One of the commonly used ways of creating an electronic junction is to use an organic dithiol as a bridge between gold electrodes. The sulfur atoms in the thiol allow for the molecule to bind to the gold. This bonding is accomplished in three different ways. The position of the sulfur atom in the gold lattice can be either directly on top of one of the gold atoms, above the midpoint between two gold atoms (commonly referred to as a “bridge” arrangement) or above the point equidistant from three gold atoms which form a triangle (referred to as "nested" figure 1).
 * Figure 1: ** Possible orientations of the sulfur-gold bond in organic bridge molecules. The strongest bond strengths is nested, followed by bridge, then on-top.

In the case where the sulfur atom is directly above a gold atom, the bonding interaction is predominately due to sigma type interactions, while in the other arrangements, the interaction is due mostly to pi type interactions of the gold and sulfur atomic orbitals [5]. The atoms in the second and third layers (and presumably any layers which lie beyond the first two) contribute little to the bonding of the gold to the sulfur atom. The bonding of the nested orientation is the strongest of the three, and can be explained by the fact that the sulfur atom’s orbitals can interact with each of the other gold atomic orbitals. However, in the other two cases, there is less overlap between the sulfur and multiple glold atoms. The nature and strength of this gold to sulfur bond is critical in the use of many organic molecules as bridges between two gold electrodes. Since the most simple sulfur containing organic compounds are the thiols, it is therefore reasonable to assume that a thiol would be a useful compound for this type of application. One must simply find a molecule which has two thiol functional groups, the simplest being alkanedithiols.

Since there is a thiol functional group on either end of the molecule, this allows the molecule to act as a bridge between the two gold electrodes. Thus, the use of dithiols as molecular current bridges can potentially allow for the creation of electronics on the single-molecule scale. However, in order to use such devices, the nature of these devices must first be understood. Since there is interest in using these molecules essentially as nanowires, it is of critical importance that the conductive properties of the molecules are understood. At its core, the conductive properties of a substance are related to electron transfer through the substance, as conductance is essentially a measurement of the ease with which an electron can pass through the substance. The electron transfer in some specific molecular junctions has been reasonably well described quantitatively by describing the current flow in terms of local contributions of substituent groups [6]. Furthermore, one can consider the conductance of a gold-molecule-gold junction to be the combination of the electron transfer properties of the molecule-gold junction and the electron transfer properties within the molecule itself.

When discussing the process of the transfer of electrons from the junction molecule to the metal surface, the ability of the molecule to stay attached to the metal is obviously of critical importance. After all, the ability of an electron to travel through the junction is heavily dependent on whether or not the molecule is actually attached to the metallic surface. In light of this, the binding of dithiols to the gold surface has been studied, and the breakdown of such a system has been shown to be caused by the detachment of gold atoms rather than the breaking of the molecule itself [7]. This was determined by investigating the amount of force that can be applied to the junction before it fails. The force required to break the molecular junction was determined to be 1.5 nN, which coincides with the force required to break an Au-Au bond[8].




 * Figure 2 [7]:** Illustration of the breakdown of a alkyldithiol. The force required to break the junction is exactly equivalent to the force required to remove a gold atom from a gold surface. Therefore the breaking of the junction can be said to be caused by removal of a gold atom from the gold surface.

These two independent conclusions that the breakage occurs between two gold atoms in dithiol linked junctions allows us to be reasonable confident that this is the true mechanism of degradation for such systems. With this understanding of the degradation mechanism of the junction, newer molecules can be designed which have improved stability and can be used more reliably in electronic applications. However, just because the molecular junction can bind to the gold electrode at either end, does not mean that the junction is useful. The conductive properties of the molecule as it attaches to the gold are just as important as the ability to attach to the gold surface.

Conductance of Dithiol-Gold Junctions
By using scanning tunneling microscopy approaches, the conductance of such molecular junctions can be measured experimentally. In the case where the molecule is a simple alkanedithiol, the conductance of the junction for a single molecule is independent of the solvent and constant over accessible temperatures, but is heavily dependent on electrode-molecule contact geometries [9]. The solvent independence of the conductance of the junction is expected to occur if the one thinks of the electrons moving through the molecule, as opposed to moving through the solvent. This is reasonable to expect if one assumes that it is more likely that an electron will move through chemical bonds than through free space. Indeed, the interaction of localized orbitals in a molecule can occur over long ranges (compared to the size of the orbital) through chemical bonds [10]. The dependence of the conductance on the contact geometries to the gold surface follows from a simple geometric argument. If the molecule is fixed to the gold in a certain orientation, this will have a significant impact on the shape and properties of the molecular orbitals of the molecule. This, in turn, effects the conductance.

While it is ostensibly quite obvious that the conformation of a molecule can influence the conductance of the overall junction, the relationship between the two is not inherently obvious. Luckily, this relationship has been investigated previously. The crucial part to consider in such metal-molecule-metal junctions is the fact that attachment to the gold electrode at either ends restricts the conformation of the molecule. Since isolated molecules are constantly rotating, vibrating and twisting, the sudden attachment to the gold at either end results in what is essentially a “snapshot” of the molecule in a random conformation. When the molecule is highly symmetric, this effect does not change the available conformations drastically. This can be visualized if one considers the molecule rotating around its central bond. In the case of higher symmetry, the various conformations are more similar to one another. Additionally, a higher degree of symmetry in a molecule will lower the rotational energy barrier between conformations, since the potential energy of the molecule will have a smaller periodicity. However, in the case of lower symmetry molecules, this “snapshot” can result in junctions with a wide range of conformation samples [11]. This is because the molecule becomes fixed in its position as it binds to the gold. The molecule will still rotate, but since the energy barriers will be greater in the lower symmetry case, it will not be able to sample the same amount of conformers as in the higher symmetry case. How does this translate into a change in conductance? The fact that the molecule is a different shape is a conceptually simple indication that the conductance will be different, and this is also in agreement with an argument from a molecular orbital perspective: the difference in conductance is influenced by the energies of the highest occupied molecular orbital at each respective conformation [12]. This is because the band gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital is dependent on the energies of the HOMO and LUMO. It is the size of this band gap which gives rise to varied conductance in different materials. For example, the band gap in a metal such as gold is significantly smaller than that of rubber, which results in a higher conductance in the metal. The energies of the highest occupied molecular orbital have been shown to be critically dependent on the dihedral angle along the backbone of molecules [13]. Thus, we have a relationship between the symmetry of the molecule and the variability in its conductance histogram.




 * Figure 3 [12]:** Conductance histograms of dithiols of biphenyl (A), dithiophene (B), a twisted bithiophene analog (C) and a flat bithiophene analog (D). The broad conductance range in B illustrates the wide variety of accessible conformers the molecule can assume in the junction. The molecules in C and D were essentially made in order to lock the orientations of the bithiopehene into a planar and twisted conformation. The C6H13 moeties in the T2-twist molecule (C) are n-hexyl groups ([12] - supporting information).

While Dell et al investigated the rotational barriers associated with bridged cyclic compounds, a related phenomenon exists for simpler alkanedithiol junctions. The conductance histograms for the series of alkanedithiols from lengths of 5 to 10 carbons showed 3 distinct peaks, corresponding to gauche defected chains as well as two types of all trans chains with two different bonds to the gold surface [14]. We therefore can see that the geometry and symmetry of the molecule binding the two electrodes together is important in a wide variety of systems.

The number of available conformations that a linking molecule can assume is partially dependent on the allowed angles that the carbon-sulfur bond can have with respect to the gold surface. However, there is a lack of sensitivity of the sulfur-gold bond to the orientation of the sulfur-carbon bond which results in a wide variety of conformations available to organic dithiols attached to the gold surface [15].




 * Figure 4 : ** The angle of the carbon-sulfur bond with respect to the gold surface has little impact on the strength of the sulfur-gold bond [15]. This was determined by application of density functional theory calculations to the thiol-gold contact.

Thus, the conformation of molecule bridging two gold electrodes together is really just dependent on the distance between the two gold surfaces and the molecule itself in addition to the geometric properties of the molecule itself, since the addition of the gold boundaries doesn’t really impose a restriction on the orientation of the carbon sulfur bond with respect to the gold surface (denoted in figure as theta). This is a convenient occurance, since this allows for a wider variety of molecules which can fit into a gap of a given size. This can be thought of in the following manner: one can imagine a case where the molecule could only fit into a junction if the C-S bond was at an extreme angle to the gold surface, due to simple geometric limitations. Since these angles still allow the sulfur to bind to the gold, this isn’t as much of a restriction as it could potentially be.

After considering how an organic molecule can be attached at either end to a gold electrode, the next step is considering how the electrons can travel from either gold electrode across the molecule into the other electrode. In the analogous classical case, electrons will travel through the wire connecting the two electrodes. This same process occurs in the single molecular case as well, as electrons can travel through the bonds in the molecule to get to the other side. However, as is usually the case in nanoscale systems, things can become more complicated. In classical mechanics, a particle can’t cross an energy barrier unless it has higher energy than the barrier. However, in small systems, there is a chance that a particle will pass through an energy barrier which has higher energy than the particle. This effect is known as tunneling.




 * Figure 5: ** The wave function of a particle is shown in red, with energy E. The energy of the barrier is greater than the energy of the particle, but even then the particle can move across.

In the quantum mechanical case, which certainly applies in single molecule electronics, there are two ways we can conceive of an electron passing through the wire. But which is the predominant means of current flow is not immediately apparent. As a general rule of thumb, the electrons will take the easiest path across the barrier. We can consider the electrons tunneling from one electrode to the other, with an energy barrier that depends on the molecule. The probability that the electron will tunnel thus depends on the molecule’s electronic properties as well as the distance between the two electrodes. When it comes to the electron going across the molecule, the impeding factor is the energy gap between the highest occupied molecular orbital and lowest unoccupied molecular orbital. When talking about extended systems, this difference is the band gap of the system. Indeed, it has been reported that in self-assembled monolayers, the main conduction mechanism is tunneling for monolayers with a large band gap [16]. The reduced probability that the electrons will travel across the molecule itself is a consequence of the high band gap energy, and as a result the predominant means for electron transfer from one electrode to the other is quantum tunneling.

However, in other cases, the rate of electron tunneling across a van der waals contact between the electrode and the hydrocarbon chain is inefficient compared to electron transfer along the carbon backbone [17]. This difference can occur because the energy gap between the HOMO and LUMO for molecules is clearly dependent on the molecule. For example, when a molecule is aromatic, the difference between these energy levels is decreased. This, in turn, causes the absorption of photons for the molecule to occur at lower energies, so that highly aromatic compounds generally absorb in the visible region. This same phenomena makes it easier for electrons to travel through the molecule, since they can be excited with lower amounts of energy. In extended aromatic systems, the conductance of the molecule has been shown to be highest when the aromaticity of the system is not disturbed, as the extended pi systems in such molecules allow for easier transfer of electrons through the molecule. [18]. For example, the highest conductive conformer of biphenyl and terphenyl occurs when the aromatic rings are coplanar [19]. This is because that one of the conditions for aromaticity is that the molecule is planar, which allows for adjacent p orbital overlap. Since the molecule’s conductance is highest when the molecule is planar, the conductance at low temperatures is decreased. This is because at low thermal energies, the conformation of the molecule is relatively fixed, and only a certain portion of the molecules will be in the highly conductive coplanar form, while at higher temperatures, the molecule is free to rotate and will be more highly conductive.

Conclusion
The development of electronic devices over the past century and a half or so has brought with it a colossal improvement in the efficiency of essentially everything that we do. Electronics have allowed for the development of computing, allow us to automate otherwise tedious tasks, and even provide us with more variety of entertainment. Thus the advancement of our understanding of electronics is of incredible interest. The current and recent trends in the area are to make everything as small as possible, as this allows for convenient usage of all of the devices we now take for granted in our daily life. In order to develop even smaller electronic devices, the properties of nanoscale conductors, transistors, and other electronic devices need to be understood. Advancements in our theoretical understanding of the electron transfer process, as well as improvements in our ability to make and characterize single molecule electronic junctions show great promise in this area for the future. It is now possible to characterize electronic properties such as voltage and conductance with a high degree of special resolution, which could allow for improved characterization of small scale electronics going forward [20]. Furthermore, the ability of organic dithiols to bind to gold make them interesting targets in the development of such electronics, as gold has long been known to be the preferred conductor in high performing electronics (whereas copper is used to lower cost in most cases). We have therefore investigated the properties which influence the conductance properties of gold-dithiol-gold single molecular junctions. Apparently, the conductance depends on many different factors such as temperature, geometry, aromaticity and distance between electrodes. While this large variety of parameters can serve to obfuscate our understanding of how this molecular junctions function, the variety of means through which we can potentially manipulate the conductance of these molecules gives us a way to customize molecules to perform the tasks we desire.