Ab Initio Density Functional Study on Negative Differential Resistance

Jan 12, 2008 - ... electron tunneling spectroscopy. Hisao Nakamura , Koich Yamashita , Alexandre. Rocha , Stefano Sanvito. Physical Review B 2008 78 (...
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J. Phys. Chem. C 2008, 112, 1685-1693

1685

Ab Initio Density Functional Study on Negative Differential Resistance in a Fused Furan Trimer Sabyasachi Sen and Swapan Chakrabarti* Department of Chemistry, UniVersity of Calcutta, 92, A.P.C. Ray Road, Kolkata 700 009, India ReceiVed: July 28, 2007; In Final Form: October 31, 2007

We investigate the electronic transport properties of a trimer unit of cis-polyacetylene and a fused furan trimer using the ab initio density functional technique. Within the density functional theory, the effect of finite bias is introduced through nonequilibrium Green’s functions. In the present study, both of the molecular systems have a thiol end group and they form a self-assembled monolayer on the Au (111) surface. The current-voltage characteristics of both the trimer unit of cis-polyacetylene and the fused furan trimer exhibit negative differential resistance over a certain range of bias voltage ((2.1 to (2.45 V), and it is quite evident from the plot of differential conductance versus voltage. A detailed analysis of the origin of negative differential resistance has been given by observing the shift in transmission resonance peak across the bias window with varying bias voltage. The origin of the transmission resonance peak at certain bias voltages has been described from a study of molecular projected self-consistent Hamiltonian states.

1. Introduction Electronic transport calculations through molecular and nanoelectronic devices are currently attracting much attention because of their potential applications in nanoscience and nanotechnology.1-8 The transport properties of a molecular wire cannot be described by the usual Boltzmann transport equation; rather, a complete description is needed considering quantum effects like quantum interference of electron waves, quantization of energy levels, and so forth. With the advent of experimental techniques like scanning tunneling microscopy (STM),7 break junction experiments,9 and so forth, there have been numerous experimental investigations on the quantum transport properties of various molecular systems. Small conjugated molecules, for example, phenyl-based derivatives, exhibit conducting behavior in break junction experiments. STM studies on the 1,4-benzenedithiolate7 molecular system report that the current-voltage (I-V) characteristic of a molecular wire is not ohomic in nature. Moreover, unusual I-V characteristics like negative differential resistance (NDR), highly nonlinear I-V relationship, current rectification, and switching behavior have been found in DNA,10 carbon nanotubes,11 and organic systems.12 In spite of all of these advancements, a detailed understanding of the physical mechanism underlying the quantum transport process in nanoscale devices remains one of the major challenges of modern nanoelectronics research. The recent advancement of the computational technique establishes the quantum chemistry approach as an important tool for the description of the quantum transport process in molecular systems. Using quantum chemistry, one can successfully design novel molecular systems with interesting transport features. Many theoretical works exist, where methods based on quantum chemistry have been used to explain the transport properties of molecular systems.2,13-18 Usually, the quantum transport properties of materials in the mesoscopic dimension is described by the Landauer theory.19 The theory relates the transmission * Corresponding author. E-mail: [email protected]. Fax: 9133-23519755.

probability of the electron with that of the current. Bu¨ttiker20 has given an extension of the Landauer theory19 in multiterminal molecular wire systems. A molecule or molecular chain attached to two bulk electrodes is a nonperiodic system. Because of the application of finite voltage, the system deviates from the equilibrium and the electrochemical potential at the moleculeelectrode contact gets changed. This nonequilibrium situation has been described mainly through semiempirical approaches.21 Other well-established theoretical methods like tight binding formalism and density functional theory (DFT) are also quite successful in describing the nonequilibrium situation. In one such investigation, Lang illustrated the NDR feature in conduction between two electrodes through two atomic dimers.22 Derosa and co-workers employed Green’s function technique and DFT to study quantum transport in molecular system of Aun-S-(p-C6H4)-S-Aun.23 The DFT technique was also employed by Xue and co-workers to explain the transport characteristics of a phenyldithiolate molecule bridging two gold electrodes.24 In their investigation, the molecule was described self-consistently and electrodes semiempirically. Seminario et al.25 used DFT combined with molecular dynamics simulations to explain the conductance of the thiotolane monolayer. The present study is aimed at searching the NDR behavior of novel molecular systems. The issue of NDR in molecular electronic devices has been addressed in a large number of communications. Reed and co-workers8 observed the NDR feature in 2′-amino-4-ethynylphenyl-4′-ethynylphenyl-5′-nitro1-benzenethiolate. They predicted that the molecules with the NDR feature could be used for data storage purposes because they can switch between high and low current states. Chen et al.26 reported NDR behavior in molecules containing a nitroamine redox center. In their investigation, the NDR feature was attributed to the voltage-induced redox reaction, that is, on the change in the charge distribution in the wire and on conformational changes. A quantum chemical study of Karzazi et al.27 described NDR behavior in polyphenylene-based molecular wires incorporating saturated spacers. They conjectured that resonant tunneling originating from shifting of the molecular

10.1021/jp075979q CCC: $40.75 © 2008 American Chemical Society Published on Web 01/12/2008

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Figure 1. Structure of the two-probe system of the fused furan trimer self-assembled on the Au (111) surface. The thiol-ended fused furan trimer together with two surface gold layers in the left and right electrodes are included in the self-consistent calculation, while the remainder of the gold electrodes are atoms described by employing bulk Hamiltonian parameters and self-energies on Au in the electrode region.

Figure 2. Current-voltage (I-V) characteristic of the two-probe systems of the trimer unit of cis-polyacetylene and the fused furan trimer self-assembled on the Au (111) surface.

energy level by an external electric field might lead to NDR. The explanation of NDR behavior in a molecular device composed of donor and acceptor moieties offered by Lakshmi et al.28 is also quite remarkable. From their simple two-level model calculations, they concluded that the NDR behavior appears because of the bias-driven electronic structure change from one class of insulating phase to another through an exceedingly delocalized conducting phase. The quantum transport properties of a chain molecule were investigated by Emberly et al.29 In their tight binding formalism, they concluded that a saturation in net current through a molecular wire creates a charge density wave and, as a consequence, weakening of some molecular bonds take place. At a specific level of bond weakening, the current through the molecular wire decreases with the increase in bias, which in turn is responsible for the NDR behavior of the system. Tight binding formalism was also employed by Le´onard et al.30 to explain the NDR feature in nanotube devices. Besides this, several other explanations exist, such as the effect of charging,31-33 reduction of the acceptor moiety,34 and so forth. Albeit there have been a lot of theoretical as well as experimental investigations pursued on NDR materials, the

Figure 3. Differential conductance against voltage (dI/dV-V) curve of the two-probe systems of the trimer unit of cis-polyacetylene and the fused furan trimer self-assembled on the Au (111) surface.

number of molecular systems having the NDR feature are very limited. In this work, we demonstrate the NDR feature in molecular systems of the trimer unit of cis-polyacetylene and a fused furan trimer. All of the calculations have been performed through the ab initio nonequilibrium Green’s functions (NEGF) technique combined with DFT.2,35,36 2. Computational Details The geometries of the trimer unit of cis-polyacetylene and the fused furan trimer have been optimized through GAUSSIAN 03 suite of programs37 using the B3LYP38,39 type hybrid exchange-correlation functional and the 6-31+G(d, p) basis set. Optimized structures form self-assembled monolayer on the Au (111) surface with a thiol end group. In these structures, the C-S (thiol end group) distance is found to be 1.76 Å, whereas the measured S-Au distance is 2.39 Å. To calculate quantum transport properties, we follow the method of Brandbyge et al.40 Within this method, the electronic current has been estimated by considering the Kohn-Sham wave function as an authentic single-particle wave function. Consequently, even with the use of commonly used exchange correlation functionals, the nonequilibrium situation of electrons

Negative Differential Resistance

J. Phys. Chem. C, Vol. 112, No. 5, 2008 1687 In the present theoretical work, the region of interest is two semi-infinite electrodes (L and R) coupled via the contact (C) region (molecule or molecular chain in a particular calculation; here the trimer unit of cis-polyacetylene or the fused furan trimer). The atoms in two semi-infinite electrodes (L and R) are contributed by semi-infinite bulk electrodes, which interact with the atoms of contact (C) region. The Hamiltonian along with the density matrix are assumed to converge to bulk values in the region of semi-infinite bulk electrodes. The distinction from the bulk values of the Hamiltonian, density matrix and overlap matrix appears only in the C, C-L, and C-R regions. Thus, the system under consideration reduces to the finite L-C-R element of the infinite system. The density matrix is achieved from a series of Green’s-function matrices. In the present work, the Green’s-function matrix is obtained by inverting the finite matrix corresponding to the L-C-R part. With the use of NEGF formalism, the current (I) through the system becomes

I(V) ) G0 Figure 4. Zero bias transmission spectra of the two-probe systems of the trimer unit of cis-polyacetylene and the fused furan trimer selfassembled on the Au (111) surface.

∫-∞f∞ d[nF( - µL) nF( - µR)] Tr[ΓL() G†() ΓR() G()] (1)

where G is the retarded Green’s function of the coupled system, ΓR() ) i[ΣR() - Σ†R()]/2, and ΓL() ) i[ΣL() - Σ†L()]/2. Self-energies, describing the coupling of the L and R regions to the rest of the semi-infinite electrodes are ΣL and ΣR, respectively. It is noteworthy that G0 ) 2e2/h is called the conductance quantum and µL and µR are the electrochemical potential of the left and right electrode, respectively. Furthermore, in eq 1, V represents the applied bias with eV ) µL µR. If the left-to-right transmission amplitude matrix t() is expressed as

t() ) [ΓR()]1/2G()[ΓL()]1/2

(2)

then eq 1 results in the Landauer-Bu¨ttiker formula44 for the conductance σ ) I/V; that is

σ(V) ) G0/V{

∫-∞f∞ d[nF( - µL) nF( - µR)]}Tr[t†() t()] (3)

Figure 5. Zero bias DOS of the two-probe systems of the trimer unit of cis-polyacetylene and the fused furan trimer self-assembled on the Au (111) surface.

due to a current flow has been described satisfactorily.40 Earlier, Stokbro et al.35 noticed that zero bias transmission spectrum of di-thiol-benzene does not change appreciably because of a change in the DFT functional from the local density approximation (LDA) to the generalized-gradient approximation (GGA). Moreover, the use of the GGA functional in quantum transport calculations takes enormous computational time. Keeping these facts in mind, the whole set of calculations of the present work have been performed using the double-ζ polarized (DZP) basis function at the LDA level of theory. Under LDA, we took up Perdew-Zunger parametrization41 of the correlation energy of a nonspin-polarized homogeneous electron gas as calculated by the Ceperly-Alder technique.42 Apart from the exchangecorrelation potential, the other effective DFT potentials used in the calculations are the Hartree potential and pseudopotential. The norm-conserving Troullier-Martins pseudopotentials have been used for the core electrons of the system.43

Using the abovementioned methodology, the current-voltage (I-V) characteristics have been estimated through the ATK 2.0.445 computational technique. 3. Results and Discussion The model systems chosen for the present investigation are the trimer units of cis-polyacetylene and a fused furan trimer. Figure 1 describes the two-probe configuration of the fused furan trimer self-assembled on the Au (111) surface with a thiol end group. Polyacetylene has two geometric isomers, namely, cisand trans-polyacetylene. Although the structure of transpolyacetylene is thermodynamically stable, it has been observed that in presence of heteroatoms (sulfur, nitrogen, oxygen, carbonyl group, CdC(CN)2, etc.), the cis isomer forms a thermally stable fused five-membered ring system. Such a structure is not uncommon. Lambert and co-workers46,47 have already provided experimental justification of such structures. The fused furan trimer may be achieved by the inclusion of oxygen as a heteroatom to the trimer unit of cis-polyacetylene, and all quantum transport calculations have been performed on these systems.

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Figure 6. Transmission spectra of the two-probe systems of the fused furan trimer and the trimer unit of cis-polyacetylene self-assembled on the Au (111) surface, at positive bias voltages of 0.0, 0.4, 1.0, 1.6, and 2.0 V, respectively. Pink lines indicate the bias window. A positive bias corresponds to the electron current from the left to the right electrode.

Figure 7. Transmission spectra of the two-probe systems of the fused furan trimer and the trimer unit of cis-polyacetylene self-assembled on the Au (111) surface, at positive bias voltages of 2.0, 2.1, 2.3, 2.4, and 2.6 V, respectively. Pink lines indicate the bias window. A positive bias corresponds to the electron current from the left to the right electrode.

The trimer unit cis-polyacetylene has a quantum well-like configuration. We focus primarily on the electronic transport through such a quantum well-like structure under a nonequilibrium situation. Furthermore, we also focus on the modification of the I-V characteristic because of the addition of a heteroatom (oxygen) to the cis conformation. Figure 2 depicts the I-V characteristic of the trimer unit of cis-polyacetylene and the fused furan trimer. In the I-V characteristic curve, the voltage has been varied from -2.8 to +2.8 V. It is quite clear from Figure 2 that initially the current through both molecular structures increases with the increases in external voltage for both positive and negative bias. The increase in current due to the variation in voltage is observed up to (2.0 V. Beyond (2.0 V, there is a rapid decrease in current with the increase in bias voltage (shaded region in Figure 2) in both molecular systems. This decrease in current due to an increase in voltage is the manifestation of the NDR feature. NDR behavior is quite prominent up to a bias voltage of (2.45 V. It is also clear from Figure 2 that above (2.5 V the NDR feature is completely lost and the current through the two-probe system again increases

with an increase in voltage. All of these observations are supported by the pertinent variation of differential conductance (dI/dV) against V. Relevant variations are presented in Figure 3. A close look at Figures 2 and 3 reveals that the reduction of current is greater in the case of the fused furan trimer. Thus, the magnitude of the NDR character in the fused furan trimer is superior to its pristine analog. In the present context, it is worth mentioning that the NDR feature in the polyacetylene system (trans-polyacetylene) has been reported by Emberly et al. already.29 In the present study, we observe that the NDR feature is also present in the cis-configuration and the addition of a heteroatom (oxygen) to the cis conformation improves its NDR feature. From Figure 3, it is quite evident that in either sample the dI/dV against V graph is not perfectly symmetric about zero voltage. This asymmetric nature is more prominent in the case of the fused furan trimer. The mechanically controlled break junction experiment of Reichert and co-workers48 has already established that contact asymmetry may cause asymmetry in I-V characteristics even in a perfectly symmetric molecule. An

Negative Differential Resistance asymmetric I-V with a symmetric molecule may be due to several factors such as the different electrode surface, inclusion of an additional atom, and so forth. Earlier, Zahid et al.49 provided theoretical justification of the observed asymmetry in the I-V characteristics of a spatially symmetric molecule [9,10-bis((2-para-mercaptophenyl)-ethinyl)-anthracene]. From their self-consistent model for molecular conduction, they conjectured that unequal coupling of the molecules with the surface atoms of the electrodes can result in an asymmetric I-V relation through asymmetric charging. In this work, the observed asymmetry in the dI/dV against V curve may be due to the small asymmetry in the optimized structures of the molecular systems (see the Supporting Information). In Figure 1, the flow of current from the left to the right electrode corresponds to positive bias and that from the right to the left electrode corresponds to negative bias. Although asymmetry in the molecular structure is not properly noticeable from Figure 1, the presence of small asymmetry can be captured if we look at the coordinates of the molecules, surface atoms, and electrodes (presented in the Supporting Information). As a result, current through the molecular structure will be different in either direction. In a recent work, Zhou and co-workers2 discussed the NDR behavior of HCOO-C6H4-(CH2)n sandwiched between two aluminum electrodes. They studied the transmission spectra obtained at different biases to explain the NDR behavior in their model system. The Landauer-Bu¨ttiker formula states that the current (I) is directly dependent on the transmission coefficient. In view of this, Zhou et al.2 emphasized the shift in the transmission resonance peak across the bias window to explain the NDR behavior and rectifying nature of I-V characteristics. To shed light on the NDR behavior in the fused furan trimer, we have also monitored the shift in the transmission resonance peak across the bias window at different bias voltages. Primarily, we compared the zero bias transmission spectra of both samples. Figure 4 demonstrates such a variation. The transmission spectra of both samples are quite similar except for an additional transmission peak around 1.6 eV in the case of the trimer unit of cis-polyacetylene. Besides this, we also analyzed density of states (DOS) of both the molecular systems obtained at zero bias voltage. Figure 5 describes such a variation. Similar to the transmission spectra, the zero bias density of states of both systems are quite comparable except for an additional peak at around 1.6 eV. The transmission spectra obtained at the positive bias voltages of 0.0, 0.4, 1.0, 1.6, and 2.0 V are presented in Figure 6. It is evident from Figure 6 that in the case of both molecular systems with the increase in positive bias voltage from 0.0 V the contribution of the transmission resonance peak into the bias window increases gradually. Consequently, the current through the two-probe systems increases. A similar analysis on the transmission spectra corresponding to positive bias voltages of 2.0, 2.1, 2.3, 2.4, and 2.6 V reveals a gradual reduction of the transmission resonance peak within the bias window above 2.0 V (Figure 7). As a result, current through the molecular systems diminishes with the increase in positive bias voltage above 2.0 V and below 2.5 V. Thus, within this positive bias range both of the two-probe systems would exhibit NDR character. At relatively higher positive bias voltage, contributions from other resonance peaks enter into the bias window. Consequently, the current through both of the twoprobe systems increases. In Figure 7, the resonance peak at -1.3 eV results in an overall increase of current at the positive bias voltage of 2.6 V. As a result, the NDR feature disappears at this positive bias voltage. A closer look at Figure 7 manifests that in the case of the trimer unit of cis-polyacetylene at higher

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Figure 8. Transmission spectra of the two-probe systems of the fused furan trimer and the trimer unit of cis-polyacetylene self-assembled on the Au (111) surface, at negative bias voltages of -2.0, -2.1, -2.3, -2.4, and -2.6 V, respectively. Pink lines indicate the bias window. A negative bias corresponds to the electron current from the right to the left electrode.

positive bias voltages contribution form additional transmission resonance peak enters into bias window. As a result, the reduction in current is relatively greater in the fused furan trimer than that in the trimer unit of cis-polyacetylene (Figures 2 and 3). The transmission spectra corresponding to negative bias voltages of -2.0, -2.1, -2.3, -2.4, and -2.6 V are presented in Figure 8. Similar to Figure 7, a gradual reduction in the transmission resonance peak within the bias window is observed as the negative bias voltage is increased beyond -2.0 V. As a result, the NDR feature is apparent over the negative bias voltage above -2.0 V and below -2.5 V. At and above the negative bias voltage of -2.6 V, the NDR feature disappears because of the insertion of additional resonance peaks within the bias window. To describe the observed behavior of transmission spectra, we employ an effective method where the self-consistent Hamiltonian of the molecular junction is projected onto the molecule and the molecular projected self-consistent Hamiltonian (MPSH) matrix is diagonalized. Related MPSH states are

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Figure 9. Molecular projected self-consistent Hamiltonian (MPSH) states of the two-probe system of the fused furan trimer self-assembled on the Au (111) surface, contributing to the bias window at bias voltages of 0.0, 2.3, 2.4, and 2.6 V, respectively. A positive bias corresponds to the electron current from the left to the right electrode.

the eigenstates of the molecular system placed in a two-probe environment. Staykov et al.6 employed the MPSH study in the explanation of the electrical rectifying properties of a singlemolecule nanowire of type donor-π-bridge-acceptor. The theoretical work of Staykov et al.6 illustrates that MPSH states localized on any one of the electrodes will not contribute to the transmission spectra, and complete delocalization of MPSH states across the scattering region will make a contribution to the transmission spectra. We first consider the MPSH states of the fused furan trimer. Figure 9 presents a comparative study of MPSH states contributing to the bias window within the bias voltages of 0.0, 2.3, 2.4, and 2.6 V. Although there is a complete delocalization of MPSH states 237, 228, and 227 at zero bias voltage, respective MPSH states are completely localized at 2.3 and 2.4 V. This feature clearly indicates that MPSH states 237, 228, and 227 will result in transmission peaks at zero bias voltage only and the same will be absent at 2.3 and 2.4 V. Thus, there will be a reduction in current at 2.3 and 2.4 V. From Figure 9, it is also evident that MPSH states 237, 228, and 227 are

also localized at 2.6 V but contribution from MPSH state 213 will again result in an increase of current through the molecular system. When these MPSH states are compared with that of the trimer unit of cis-polyacetylene, it is observed that similar to the fused furan trimer certain MPSH states (229, 222, and 219) are completely delocalized only at zero bias voltage. Consequently, transmission peaks will be absent at 2.3 and 2.4 V and current through the molecular system would diminish at these voltages. At the bias voltage of 2.6 V, MPSH states 229, 222, and 219 are completely localized and delocalization is noticed at the MPSH state 214; as a result, current through the two-probe system again increases. This indicates the absence of the NDR feature at the bias voltage of 2.6 V. One of the interesting aspects of the present investigation is the enhancement of the NDR feature due to the addition of a heteroatom (oxygen) to the cis-polyacetylene moiety. This feature is attributed to the presence of an additional transmission peak in the trimer unit of cis-polyacetylene. In Figure 11, we present an MPSH analysis corresponding to this additional

Negative Differential Resistance

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Figure 10. Molecular projected self-consistent Hamiltonian (MPSH) states of the two-probe system of the trimer unit of cis-polyacetylene selfassembled on the Au (111) surface, contributing to the bias window at bias voltages of 0.0, 2.3, 2.4, and 2.6 V, respectively. A positive bias corresponds to the electron current from the left to the right electrode.

transmission peak. Figure 11 reveals that although MPSH states corresponding to this transmission peak in the trimer unit of cis-polyacetylene are completely delocalized, the MPSH states in the fused furan trimer do not exhibit any delocalization. As a result, the magnitude of the NDR feature will be smaller in the trimer unit of cis-polyacetylne than that in the fused furan trimer. Because the additional transmission peak of the trimer unit of cis-polyacetylene plays a crucial role in determining the NDR behavior, we investigated the nature of the state associated with this transmission peak. At zero bias voltage, this peak corresponds to the MPSH state 237 having an energy eigenvalue of 1.61 eV. From Figure S2 of the Supporting Information, it is evident that this state is completely delocalized and can contribute to additional current if it enters into the bias window. In addition, we also perform a population analysis on the trimer unit of cis-polyacetylene. Our analysis suggests that the state (at 1.61 eV) corresponding to an additional peak in the DOS

spectrum of the trimer unit of cis-polyacetylene is contributed mainly by pz orbitals of carbon atoms having delocalized π character and surprisingly this particular state (at 1.61 eV) is absent in the fused furan trimer. It is also interesting that before entering into the NDR region, the current passing through the fused furan trimer is larger than that of the trimer unit of cis-polyacetylene. This feature is prominent at the bias voltages of (1.8 and (2.0 V (Figure 2). The transmission spectra of Figure 6 illustrates that at these bias voltages ((1.8 and (2.0 V) the additional transmission peak of the trimer unit of cis-polyacetylene does not contribute to the bias window. Moreover, examinations of the MPSH states of both of the molecular systems contributing to the bias window at 1.8 and 2.0 V indicate that these states are more delocalized in the fused furan trimer and are quite evident from Figures S3 and S4 of the Supporting Information. Finally, as a result of the above two factors, the current flowing through the fused

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Figure 11. Comparison of molecular projected self-consistent Hamiltonian (MPSH) states contributing to the additional transmission peak in the two-probe system of the trimer unit of cis-polyacetylene self-assembled on the Au (111) surface (at 1.61 eV at the bias voltage of 0.0 V, at 1.42 eV at the bias voltage of 2.3 V, at 1.38 eV at the bias voltage of 2.4 V, and at 1.39 eV at the bias voltage of 2.6 V) and corresponding MPSH states in the two-probe system of the fused furan trimer self-assembled on the Au (111) surface. A positive bias corresponds to the electron current from the left to the right electrode.

furan trimer is significantly larger than that of the trimer unit of cis-polyacetylene at 1.8 and 2.0 V. 4. Conclusions In the present theoretical work, we report that the NDR behavior appearing in the trimer unit of cis-polyacetylene can be improved significantly if heteroatoms (oxygen) are added to the cis configuration. The ab initio nonequilibrium Green’s function technique has been used to evaluate the related quantum transport properties. In both samples, the NDR behavior is observed over a certain range of applied bias voltage ((2.1 to (2.45 V, Figure 2). This is further verified from a variation of dI/dV against V. The observed NDR behavior has been explained by looking at the shift in transmission resonance peak across the bias window with varying bias voltage. We provide a

molecular origin of the observed transmission spectra through an analysis of MPSH states contributing to the bias window at specific bias voltages. Evaluation of the quantum transport properties emphasizing the NDR behavior of some other fused heterocycles is in progress, and those results will be communicated elsewhere. Acknowledgment. At the very outset, we convey our deepest gratitude to Atomistix Inc. for allowing us to use ATK 2.0.4 for the electronic transport calculations. The financial support from DST, Govt. of India (under the FIST program) to purchase the GAUSSIAN 03 program is gratefully acknowledged. S.S. acknowledges Prof. A. Guha, Director, JIS College of Engineering. S.S. also thanks P. Seal for providing necessary computational help.

Negative Differential Resistance Supporting Information Available: Atomic coordinates (in Å) of both the two-probe system of the fused furan trimer and the trimer unit of cis-polyacetylene and a selected view of the contact region of the two-probe configuration of the fused furan trimer. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Zhang, C.; Du, M. H.; Cheng, H. P.; Zhang, X. G.; Roitberg, A. E.; Krause, J. L. Phys. ReV. Lett. 2004, 92, 158301. (2) Zhou, Y-h.; Zheng, X-h.; Xu, Y.; Zeng, Z. Y. J. Chem. Phys. 2006, 125, 244701. (3) Bauschlicher, C. W., Jr.; Lawson, J. W. Phys. ReV. B 2007, 75, 115406. (4) Koch, J.; Raikh, M. E.; von Oppen, F. Phys. ReV. Lett. 2006, 96, 056803. (5) Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge University Press: Cambridge, 1995. (6) Staykov, A.; Nozaki, D.; Yoshizawa, K. J. Phys. Chem. C 2007, 111, 11699. (7) Reed, M. A.; Zhou, C.; Muller, C. J.; Burgin, T. P.; Tour, J. M. Science 1997, 278, 252. (8) Reed, M. A.; Chen, J.; Rawlett, A. M.; Price, D. W.; Tour, J. M. Appl. Phys. Lett. 2001, 78, 3735. (9) Halbritter, A.; Csonka, Sz.; Mihaly, G.; Jurdik, E.; Kolesnychenko, O. Y.; Shklyarevskii, O. I.; Speller, S.; van Kempen, H. Phys. ReV. B 2003, 68, 035417. (10) Roche, S. Phys. ReV. Lett. 2003, 91, 108101. (11) Andriotis, A. N.; Menon, M.; Srivastava, D.; Chernozatonskii, L. Phys. ReV. Lett. 2001, 87, 066802. (12) Emberly, E. G.; Kirczenow, G. Phys. ReV. Lett. 2003, 91, 188301. (13) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Phys. ReV. Lett. 2000, 84, 979. (14) Ness, H.; Fisher, A. J. Phys. ReV. Lett. 1999, 83, 452. (15) Emberly, E. G.; Kirczenow, G. Phys. ReV. B 2000, 62, 10 451. (16) Hall, L. E.; Reimers, J. R.; Hush, N. S.; Silverbrook, K. J. Chem. Phys. 2000, 112, 1510. (17) Emberly, E. G.; Kirczenow, G. J. Appl. Phys. 2000, 88, 5280. (18) Emberly, E. G.; Kirczenow, G. Phys. ReV. B 1998, 58, 10911. (19) (a) Landauer, R. IBM J. Res. DeV. 1957, 1, 223. (b) Landauer, R. Phys. Lett. 1981, 85A, 91. (20) Bu¨ttiker, M. Phys. ReV. Lett. 1986, 57, 1761. (21) Emberly, E. G.; Kirczenow, G. Phys. ReV. B 2001, 64, 235412. (22) Lang, N. D. Phys. ReV. B 1997, 55, 9364. (23) Derosa, P. A.; Seminario, J. M. J. Phys. Chem. B 2001, 105, 471. (24) Xue, Y.; Datta, S.; Ratner, M. A. J. Chem. Phys. 2001, 115, 4292. (25) Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 1998, 120, 3970. (26) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550.

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