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Figure 1. Isovalue surfaces of A2n (p) for (a) tolane, 1, in the absence of an external field, (b) tolane thiolate, 2, in the absence of an external field, (c) tolane thiolate in an external field oriented in cooperation with the electron donation of sulfur (forward bias), and (d) tolane thiolate in an external field oriented in opposition to the electron donation of sulfur(reversebias). A2n (p) = -0.025 au everywhere on these surfaces, and A2n (p) < -0.025 au everywhere within these envelopes. The orientations ofthe molecules, and the momentum-space axes are as described in the "Getting Oriented" section.

Figure 1. Isovalue surfaces of A2n (p) for (a) tolane, 1, in the absence of an external field, (b) tolane thiolate, 2, in the absence of an external field, (c) tolane thiolate in an external field oriented in cooperation with the electron donation of sulfur (forward bias), and (d) tolane thiolate in an external field oriented in opposition to the electron donation of sulfur(reversebias). A2n (p) = -0.025 au everywhere on these surfaces, and A2n (p) < -0.025 au everywhere within these envelopes. The orientations ofthe molecules, and the momentum-space axes are as described in the "Getting Oriented" section.

Getting Oriented

Electrons with momentum parallel to the long axis in molecules 1,2 and 3 (which we define as the z -axis, and passes through the carbon atoms on each ring that are para to the bridging group) are located somewhere on the pz -axis in momentum-space, depending on their speed. In Figs. 1 and 2, the pz -axis is the one that appears to be coming out of the plane in these perspective renderings. Note that the electrons do not have to be on the z-axis, just possessing momentum that is parallel to it. They could be anywhere in coordinate-space. The x-axis in molecules 1,2 and 3 is defined to be perpendicular to the phenyl rings (which have a 0o dihedral angle in all of the conformations used to compute the images in Figs. 1 and 2). The px-axis is "horizontal" in Figs. 1 and 2, and passes through the centers of the pairs of irregularly shaped objects that appear as reflections of one another. The y -axis is thus coplanar with the phenyl rings, and in 1 and 2 it is prependicular to the triple bond. The py -axis is vertical in Figs. 1 and 2, and is in the plane of symmetry refered to above.

"Structure of Motion"

For tolane, 1, we find the lowest energy conformation to be that with a 0o dihedral angle between the phenyl rings (D2h symmetry), as was also reported by Seminario at al. using density functional methods.29 Interestingly, we found a very flat potential energy surface with respect to this torsional angle. There is no significant energy difference for the 45o conformation, and R(C=-C) is constant at 1.1882 A When the phenyl rings are orthogonal, the molecule is only 0.42 kcal/mol less stable, and R(C=-C) decreases very slightly to 1.1878 A We find that all conformations of tolane, 1, in the absence of an external electric field display nonlaminar slow electron dynamics (just the D2hconformation is shown in Fig. la). This is in contrast to the very laminar behavior of the slow electrons near the origin (A2n (p) << 0) for nearly all metal atoms in the periodic table,10 as well as diatomic and varyingly-shaped hexatomic clusters of Li and Na atoms.18 In general, systems that would commonly be described as "metallic", have to date been found to possess laminar slow electron dynamics, while systems that would commonly be described as "nonmetallic" have been found to possess nonlaminar slow electron dynamics.30 The key to this interpretation is that while electron-electron interactions are ubiquitous (both local and nonlocal), they are postulated to cause resistance only if the electrons are very close in momentum-space.10 We reiterate here the important, and surprising observation that even for monatomic systems, the element with A2n closest to zero at the origin, on a per electron basis, is silicon.10 Thus the slow electron dynamics of an isolated atom of silicon, in its ground state, presages a key property of the element in its bulk form. Furthermore, this information is extracted from just the density of the ground state. In Fig. la, regions of laminar electron flow are clearly seen at faster momenta (in the neighbor- hood of 0.5 au for all of the molecules studied in this work). We have not yet performed a topological analysis locating the extrema in A2n but we plan to do so. Although the A2n isolevel surface is not shown, this molecule can undergo a transition to laminar slow electron dynamics when an external electric field is turned "on". For tolane in an external electric field of 0.05 au (1 au =1 Eh(eao)-1 = 5.1422 x 1011 Vm-1), with a 0o dihedral angle, there is a qualitatively different topology of A2n near the origin. The fast concentrations seen in the absence of an external field shrink, but are still present, and a large brick-shaped concentration of charge appears at the origin. The new feature is similar in length to the cigar-shaped feature in Fig. 1c and has a similar orientation, but it is wider in the pz direction. In the presence of this field, the slow electrons are laminar, as in metallic systems. That is, this molecule behaves as a semiconducting wire , and is a prototype of what are termed "Tour wires4. We have not investigated the momentum-space properties of tolane at all fields up to 0.05 au, but at a field strength of 0.01 au there is no noticeable change from the surface shown in Fig. la.

As discussed above, for molecular electronics it is essential that some components be capable of restricting electron flow to a single direction when they are turned "on". A diode is a macroscopic electronic device that has this performance characteristic. By chemically modifying one end of a Tour wire, as shown in 2, we introduce asymmetry in the molecule and hence in its electron dynamics. Tolane thiolate, 2, is thus a prototype of a molecular rectifying diode. In fact, self-assembled monolayers of similar thiol-substituted Tour wires, between electrodes, have been shown to have such rectifying behavior.32 In this case, by substituting an electron donating group at one end, we might intuitively expect that electron flowfrom the substituted end towards the rest of the molecule would be enhanced somehow, or "pushed" as physical organic chemists imply with arrows. Indeed, we have found that in similar electric fields that induced a transition to laminar slow electron flow in the semiconducting wire above, we observe qualitatively different responses by the "molecular diode" 2, depending on the direction of the applied field. Fig. lb shows the structure of motion for the tolane thiolate ion in the absence of an applied field. The four "ear muffs" at the comers of the py = 0 plane are very similar to corresponding features in tolane. Directionally, these features correspond to diagonal motion in any plane that is parallel to the long axis and perpendicular to the phenyl rings, such as the % -planes of those bonds (four of them) in the rings that are parallel to the long axis. As in tolane, when a weak external electric field of 0.01 au is applied parallel to the long axis in either direction, there is no change in the structure of motion. When the field is oriented so that it pushes against the electron donation from sulfur, then the features (except the ear muffs) swell. Whereas there is virtually no change when the direction of the applied field cooperates with sulfur's electron pushing (surfaces not shown). This is in sharp contrast to what is observed in a stronger applied field of 0.025 au. Fig. 1c clearly shows a change in the structure of motion of the slow electrons when the applied field cooperates with electron donation from sulfur, while there is only further swelling of the "pancakes" for a field in the opposite direction (Fig. Id). Thus, the slow electron dynamics of tolane thiolate display rectifying behavior at a field strength of 0.025 au, since the onset of metallic character, A2n <0 at the origin, has a directional bias.

The characteristic behavior of a resonant tunneling diode (RTD) is "off,on,off", as the voltage across the device is swept from low to high.26 In macroscopic devices this is achieved by separating sources and sinks, each of which have discrete energy levels, by an insulating barrier that can be tunneled through. As the voltage is scanned, the energies of the states in the source rise, and those in the sink are lowered. Within the context of band theory, tunneling only occurs when the occupied states of the source have risen just the right amount so that they are in resonance with the virtual states of the sink. Further increase in the voltage disrupts this resonance, and the tunneling current shuts off. Within the context of molecular orbital theory, molecular analogues of such a device correspondingly achieve resonant tunneling via manipulation of the active, or frontier molecular orbital energy levels.27 Here, the molecular

Figure 2. Isovalue surfaces of A2n(p) for a diode-like molecule, 3, (a) field off, and (b) field on. A2n(p) = -0.025 au everywhere on these surfaces, and A2n (p) c -0.025 au everywhere within these envelopes. The orientation of the molecule, and the momentum-space axes are as described in the "Getting Oriented" section.

Figure 2. Isovalue surfaces of A2n(p) for a diode-like molecule, 3, (a) field off, and (b) field on. A2n(p) = -0.025 au everywhere on these surfaces, and A2n (p) c -0.025 au everywhere within these envelopes. The orientation of the molecule, and the momentum-space axes are as described in the "Getting Oriented" section.

orbitals are described as being localized on opposite sides of an insulating barrier, such as the ethylene bridge in 3, or other "island" that interupts the conjugation between the molecular "terminals". Molecule 3 is not a simple, or true RTD, in that it has an internal directional bias, and thus will admix rectifying behavior. True molecular RTD's have been successfully demonstrated to have "off,on,off" behavior.24 We have not completed our investigation of the slow electron dynamics of 3, but we report our observations for no field, and low field, since they present some interesting new features (Figs. 2a and 2b, respectively). Future work will complete the investigation of these devices. As before, we again observe a change in the structure of motion in the slow electron regime, from nonlaminar to laminar, indicating the onset of metallic behavior when the field is turned on. In this calculation the applied field is 0.05 au, in the- z direction (the applied field pushes the electrons from the cyano-bearing phenyl ring toward the methyl-substituted one). With the field on, the laminar domain near the origin is very similar in shape and orientation to those observed in the molecular wire and rectifying diode discussed above (in their "on" state). However, the laminar domains in the fast regime are qualitatively different from any other features reported so far. The "points" are particularly interesting. We also note that the internal bias of 3, due to the electron donating (CH3) and withdrawing (CN) groups, is in the opposite direction to this applied field bias. Yet, a transition to an "on" state is still observed. This might be an indication of a different physical mechanism underlying the transition in 3 as compared to 2, however we have not investigated the effect of field reversal on 3. Also, we have yet to determine whether or not further increase in field strength leads to another topological transition in A2n near the origin. Further investigation of the structure of motion in these molecular electronic devices will undoubtedly improve our understanding of the chemical control of electron transport.

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