Control of Electron Transport by Manipulating the Conjugated

J. Phys. Chem. C 2007, 111, 15397-15403

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Control of Electron Transport by Manipulating the Conjugated Framework Sang Uck Lee,* Rodion V. Belosludov, Hiroshi Mizuseki, and Yoshiyuki Kawazoe Institute for Materials Research, Tohoku UniVersity, Sendai, 980-8577, Japan ReceiVed: June 4, 2007; In Final Form: July 26, 2007

We present a systematic analysis of molecular level alignments and electron transport characteristics based on the nonequilibrium Green’s function (NEGF) approach combined with density functional theory (DFT) for six conjugated molecules (PTP, CPTP, NiPTP, CoPTP4, CoPTP5, and FePTP) containing different types of conjugated frameworks. The conjugated molecules are classified into three groups according to the incorporated component into the conjugated framework where group I, group II, and group III contain antiaromatic, nonaromatic, and aromatic units, respectively. The results show that the combining of non- and antiaromatic components increases the conductance due to the close alignment of the HOMO level relative to the Fermi level. Consequently, the order of current follows the manner of group I > group II > group III ([NiPTP > CoPTP4 > CPTP] > [CoPTP5 > FePTP] > [PTP]). The important feature emerging from this work is that the distinct response of each group to molecule-contact coupling and applied bias voltage causes distinguishable features of electron transport characteristics and these factors may give an insight into the design of new nanoscale molecular electronic devices.

1. Introduction Recently, electron transport in nanoscale systems has received particular interest due to the significant progress of nanotechnology, facilitated by the advent of the technologically motivated field of molecular electronics,1-4 the advancement of techniques for characterizing and manipulating individual molecules,5-8 and the availability of first-principles methods to describe electron tunneling through atomic chains or single molecules.9-18 The theoretical methods are usually based on density functional theory (DFT) in combination with the nonequilibrium Green’s function formalism (NEGF).19 Despite the fact that useful devices can be realized on the basis of individual molecules, it is essential to have a thorough understanding of the electron transport processes at the molecular level, and this understanding can eventually give an insight into the design of new molecular scale electronic devices. It has become clear through many studies20-26 that electron transport characteristics are influenced by the intrinsic properties of molecules, including their length, conformation, energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and the alignment of molecular levels relative to the Fermi level of the metal contact. It has been demonstrated that the conductance of molecules can be controlled by the position of individual molecular levels.22 Therefore, the determination of factors controlling the alignment of molecular levels relative to the Fermi level of the metal contact becomes a key role in the design and operation of future molecular scale devices. To date, delocalized orbital networks in conjugated molecules have been proposed as the ideal design for molecular wires. Many experimental and theoretical groups have investigated various conjugated all-organic molecules27-33 and have attempted to control the electron transport through the modification of chemical functions34-38 of the conjugated framework. * Address correspondence to this author. E-mail: [email protected]. Phone: +81-22-215-2054. Fax: +81-22-215-2052.

For example, in benzene derivatives the addition of electrondonating substituents (methoxy or methyl groups) increases conductance while the addition of electron-withdrawing substituents (chlorine or cyano groups) decreases conductance, which indicates the influence of the alignment of molecular levels relative to the Fermi level of the metal contact.26 In addition, a metallocene-based organometallic unit can be incorporated into a conjugated framework,39-42 and in the case of a ferrocene moiety it has been shown that the rate of electron transfer through the resulting framework can rival that through an all-organic conjugated system.40 To understand how to control the electron transport through a conjugated framework, we have performed a systematic analysis of molecular level alignments and electron transport characteristics for several conjugated molecules having distinct conjugated frameworks. Starting from the p-terphenyl structure, composed only from the aromatic components, the central moiety has been substituted by an antiaromatic (C4H4) and a nonaromatic (C5H5) ring. Cyclobutadiene and metallocene molecules, (η4-C4H4)2Ni, (η4-C4H4)Co(η5-C5H5), and (η5-C5H5)2Fe, are used as substituents. All studied structures have been classified into three groups such as antiaromatic (group I), nonaromatic (group II), and aromatic (group III). Considering a delocalized orbital network in the conjugated system, both aromatic and antiaromatic molecules contain an uninterrupted π-electron cloud allowing the electrons to flow easily around the molecule despite the different chemical and physical properties of the molecules. Therefore, it is of interest to compare the electron transport characteristics of the conjugated molecules containing the distinct conjugated framework. 2. Theoretical Formula and Computational Details For the “contact-device-contact” open system, the coupling between the device and metal contacts plays a crucial role in electron transport. The nonequilibrium Green’s function (NEGF) formalism43 has been proved to be a powerful approach for studying the electron transport phenomena in nanodevices and

10.1021/jp074294n CCC: $37.00 © 2007 American Chemical Society Published on Web 10/03/2007

15398 J. Phys. Chem. C, Vol. 111, No. 42, 2007 provides a link between electron transport, first-principles electronic structure theory, and qualitative molecular orbital theory. This approach allows us to separate the “contactdevice-contact” open system into a physically interesting “device” subspace and a “contact” subspace such that the computation can be focused on the device part incorporating the effects of the outside world (“contact”) through appropriately defined self-energy matrices and standard quantum chemistry techniques can be employed in the analysis of the electronic structure of a finite-sized device subspace. However, the NEGF method based on density functional theory (DFT) includes approximations in describing the non-Hermitian self-energy and Green’s function, using the real DFT exchange-correlation potential and an incomplete basis set.44,45 In this paper, the contacts and the devices are described by using the LanL2DZ basis set46,47 incorporating relativistic core pseudopotentials because the LanL2DZ basis set provides a good description of the contact surface density of states around the Fermi level.48 And the self-consistent potential is calculated by using DFT with Becke-3 exchange49 and Perdew-Wang 91 correlation50 because the B3PW91 functional has been proven to be suitable for metal-organic complexes in several studies.51-53 The contact part is treated via a one-time calculation of the surface Green’s function (SGF) of the contacts including their atomicity and crystalline symmetry. The SGF of the gold contact is obtained recursively for a periodic lattice by the decimation process.54 Ideally, an infinite cluster should be used to obtain the Fock and overlap matrices obeying crystalline symmetry. For practical reasons, we used a finite cluster model consisting of 43 gold atoms (Au12-Au19-Au12) arranged in a FCC(111) geometry. Therefore, the correct crystalline symmetry should be imposed to the obtained Fock and overlap matrices of the Au43 cluster, enforcing which makes the Fock and overlap matrices Hermitian.12 In this place, the relatively delocalized d-functions of the LanL2DZ basis should be accounted for to accurately obtain the SGF, because the d-functions bring about non-Hermitian Fock matrices. Hence, we followed Damle’s approach;12 the Fock matrix (especially off-diagonal components) is adapted to the well-known Hu¨ckel principle. And then, we define two Fourier components, nearest-neighbor in-plane (FakB and SakB) and out-of-plane (FbkB and SbkB) using the extracted Fock (Fmn) and overlap (Smn) matrices from the Au43 cluster

∑n Fmn exp[-ikB(br m - br n)] FbkB ) ∑ Fmn exp[-ik B(b rm - b r n)] n SakB ) ∑ Smn exp[-ik B(b rm - b r n)] n SbkB ) ∑ Smn exp[-ik B(b rm - b r n)] n FakB )

where m is an arbitary gold atom, and n involves a sum over m and all its nearest neighbors, with coordinate b rn. We then define in-plane and out-of-plane couplings R and β for gold and recursively solve for the SGF in B k space.

RBk ) (E + i0 + )SakB - FakB,

βBk ) (E + i0 + )SbkB - FbkB

gBk -1 ) RBk - βBk gBk βBk + Finally, we obtain the real space Au(111) SGF matrix by adding the independent B k contributions.

Lee et al.

gmn )

1 N

∑Bk gBk exp[ikB(br m - br n)]

For every molecule bonded to Au(111) thereafter, we extract a coupling matrix (τ) between the molecule (device part) and Au(111) surface (contact part) using the Gaussian03 program,55 and couple with the above SGF matrix (g) to get the self-energy matrix (Σ) using following equation.

Σi ) τigiτi+

(i ) 1, 2)

We then self-consistently combine the NEGF formalism for transport under bias with a supplemented Fock matrix (Fd) of device to obtain a density matrix (F) at the B3PW91/LanL2DZ level of theory, which we thereafter feed back to the Gaussian03 self-consistent field loop. This process continues until the density matrix converges. The NEGF equations are

Gd ) (E+Sd - Fd - Σ1 - Σ2)-1 F)

1 2π

∫-∞∞ [f1GdΓ1G+d + f2GΓ2G+d ] dE

Here E+ denotes the energy plus an infinitesimal imaginary part (usually 10-5 or 10-6), and Sd, Fd, and Σ1,2 are the overlap, Fock, and self-energy of the contacts matrices, respectively. The broadening functions, Γ1,2 ) i[Σ1,2 - Σ+ 1,2], which denote the finite lifetime of the electron, are the anti-Hermitian components of the self-energy. The f1,2 are the Fermi functions with electrochemical potential µ1,2

(

f1,2(E) ) 1 + exp

[

])

E - µ1,2 kBT

-1

An applied bias leads to two different contact chemical potentials, µ1,2 ) Ef - eV/2. The converged density matrix (F) is used to obtain the total number as well as the spatial distribution of electrons by using

N ) trace(FS) n(b) r )

Fmnφm(b)φ r n(b) r ∑ m,n

where φm,n(r b) represent molecular basis functions. The converged density matrix may also be used to obtain the terminal current.43 For coherent transport,56 we can simplify the calculation of the current by using the transmission formalism where the transmission function43

T(E) ) trace[Γ1GΓ2G+] is used to calculate the terminal current

I ) (2e/h)

∫-∞∞ dET(E)(f1(E) - f2(E))

In this process, we define the device part as an “extended molecule” including the molecule itself and a few surface metal atoms in order to account for the charge and potential perturbations of the metal surface caused by molecular adsorption. It has been recognized that the influence extends only over a finite region into the metal surface due to metallic screening in the electrodes and the charges imaged on the metallic contact from the molecule also reside on a few surface metal atoms close to the molecule.11,12 Therefore, the effects induced by molecular adsorption can be taken into account in the self-consistent calculation if a few surface metal atoms are included as part of the device. In addition, the charge densities on the atoms at the device edge are inaccurate because the device and contact basis

Control of Electron Transport

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Figure 1. Schematic of a molecule connected to two semi-infinite gold contacts. Six gold atoms closest to the end sulfur atoms on each electrode are included in the “extended molecule”.

Figure 3. I-V curves of p-terphenyl (PTP) and cyclobutadiene substituted p-terphenyl (CPTP). CPTP_S and CPTP_T denote singlet and triplet states, respectively. Up or down indicates the spin state.

Figure 2. Structures of (a) p-terphenyl (PTP) and its derivatives (be). The substituents are (b) C4H4 (CPTP), (c) (η4-C4H4)2Ni (NiPTP), (d) (η4-C4H4)Co(η5-C5H5) (CoPTP4 and CoPTP5), and (e) (η5-C5H5)2Fe (FePTP).

functions are not orthogonal to each other. Therefore, it is desirable to define the “extended molecule” as the device so as to allow an accurate calculation of the molecular charge. Accordingly, we define an “extended molecule” including the molecule itself and six nearest-neighbor gold atoms on each metal surface. Previous literature states that three gold atoms are adequate as part of the device.9 The “contact-devicecontact” system is shown in Figure 1. 3. Results and Discussion Conjugated Frameworks and Contact Configurations. Figure 2 shows the investigated core molecules composed of two side phenyl rings and one central ring (C6H6-central ringC6H6). To provide three groups of conjugated framework (C6H6-C4H4-C6H6, C6H6-C5H5-C6H6, and C6H6-C6H6C6H6), we vary the central ring: (a) C6H6 (PTP), (b) C4H4(CPTP), (c) (η4-C4H4)2Ni (NiPTP), (d) (η4-C4H4)Co(η5-C5H5)

(CoPTP4 and CoPTP5), and (e) (η5-C5H5)2Fe (FePTP). The central rings are parallel with neighboring phenyl rings, except for PTP, which has 43° torsion angle.57 In (c), (d), and (e), we chose well-known metallocene molecules that are stable in a singlet neutral state. When metallocene molecules are combined with two side phenyl rings, an acetylene group is used as a linker to avoid steric hindrance between neighboring phenyl rings. For the (η4-C4H4)Co(η5-C5H5), two different conjugated frameworks (C6H6-C4H4-C6H6 and C6H6-C5H5-C6H6) are available according to which ring of the (η4-C4H4)Co(η5-C5H5) is combined with the two side phenyl rings (CoPTP4 is with C4H4 and CoPTP5 is with C5H5). In this work, we use the same hollow contact configuration, where all core molecules are anchored with a thiol group to the gold contact in a hollow position, as seen in Figure 1, [AuS-phenyl-[core molecule]-phenyl-S-Au]. However, we recognized that hollow and optimized contact configurations provide similar transport characteristics in a previous investigation regarding the effect of contact configurations, where we used a “phenyl dithiol” molecule containing the same contact structure, [Au-S-phenyl-], as we used in this work, [AuS-phenyl-[core molecule]-phenyl-S-Au] (Supporting Information). Therefore it is reasonable to use the same hollow contact configuration (180° of contact angle and 1.90 Å of end sulfur-surface distances)58 for all core molecules instead of the optimized contact configuration, tilted bridge (42° of contact angle and 1.97 Å of end sulfur-surface distances). In addition, the effect induced by a different contact configuration can be diminished in this work because all core molecules have the same side phenyl rings (C6H6-central ring-C6H6). The geometries of the adsorbed molecules are taken to be the same as the singlet geometry of the free molecule optimized at the B3PW91/6-31G* level. Effects of Aromatic and Antiaromatic Components. First, we have investigated two molecules containing either aromatic or antiaromatic component in their conjugated framework. One is the p-terphenyl (PTP) molecule constructed by all aromatic components (C6H6-C6H6-C6H6) and the other is the cyclobutadiene substituted PTP (CPTP) molecule containing an antiaromatic component at the center of the framework (C6H6C4H4-C6H6). Current-voltage (I-V) characteristics of two PTP and CPTP are shown in Figure 3. Because the energy difference between singlet and triplet states of CPTP is small (0.07 eV), we have investigated the I-V characteristics in the singlet (CPTP_S, closed shell singlet) and triplet (CPTP_T) spin states.

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Figure 4. Energy level diagrams of the isolated extended model (upper) and the coupled extended model (lower) and equilibrium transmission curves, T(E,V)0), with the partial density of state (PDOS) described with respect to the molecule (PTP or CPTP) and Au atoms: (a) p-terphenyl (PTP) and (b) singlet cyclobutadiene substituted p-terphenyl (CPTP). The vertical red lines represent the energy levels of the coupled model. The red and blue arrows show the shift of the HOMO and LUMO levels between isolated and coupled models. The change of molecular orbitals from isolated to coupled extended model is shown in the inset.

For bias voltages below 2.0 V, the current through CPTP_S is higher than the current through PTP. This difference is about 1 order of magnitude for bias voltages below 1.0 V and more than three times above the 1.0 V bias voltages. Another interesting feature, shown in Figure 3, is that each spin component carries a different amount of current when the bias voltage is applied in the triplet state. At 0.0 V < V < 1.5 V applied bias voltages, the current is carried dominantly by the spin down electron and the spin up electron carries less than 1 µA. Also, the current carried by the spin down electron is much larger than the total current of spin up and spin down in the singlet state. From the viewpoint of applications, it is attractive that the molecule can transport each spin component with different weights. For example, if the magnetization axis of the molecule is fixed by an external magnetic field, and if the spin flip does not occur during the transmission, the assumed molecule is considered to be used as a spin filter or a spin valve.18,27,41 Such distinguishable I-V characteristics of CPTP in comparison to PTP arise from the distinctive response of molecular levels with respect to the perturbation induced by moleculecontact coupling. Figure 4 shows the molecular level alignment analysis of PTP and CPTP with equilibrium transmission curves, T(E,V)0), partial density of state (PDOS), and energy level diagrams, using the isolated extended model and the coupled extended model. The PDOS is described with respect to a molecule (PTP or CPTP) and Au atoms. The molecular levels at the isolated extended model are obtained by the Roothaan equation, FC ) SCλ , and the position of the levels of the coupled extended model come from the singular points of the Green’s function, (F + Σ 1 + Σ 2)C ) SCλ . The effect of

molecule-contact coupling is included by self-energy matrices (Σ1,2), which causes shifting and broadening of molecular levels. From the T(E,V)0) curves in Figure 4, we find that the Fermi level lies closer to the HOMO level than to the LUMO level for both molecules. Accordingly, the conductance is due to electron transmission through the occupied molecular states rather than the unoccupied molecular states for both molecules. The T(E,V)0) and PDOS of Au atoms (red line) show that there is no contribution to transmission from the metal-induced gap states (MIGS) arising from the hybridization of the gold surface states and molecular states located on the HOMO-LUMO gap and the PDOS of Au atoms (red line) are nearly the same regardless of the molecule. However, the T(E,V)0) is closely correlated with the PDOS of a molecule (blue line), and transmission peaks appear when the PDOS of the molecule is dominant. Therefore, it can be known that transmission peaks are an intrinsic feature of a molecule regardless of Au atoms included in the extended molecule. Upon comparing the shift of the level position between the isolated and coupled extended molecule, it is seen that the contact with the metallic electrodes significantly shifts the molecular levels of the frontier molecular states. Furthermore, the change is found to be larger for the occupied states than for the unoccupied states for both molecules. Apart from such similar features between PTP and CPTP molecules, their intrinsic properties evoke different electron transport characteristics. Because antiaromatic molecules are unstable and usually have a small HOMO-LUMO gap due to the increase in the HOMO level and the decrease in the LUMO level, the HOMO level of CPTP lies closer to the Fermi level in comparison to PTP. In addition, it is seen that the responses

Control of Electron Transport

Figure 5. I-V curves of p-terphenyl and its derivatives.

of the HOMO levels of both molecules to the perturbation induced by the molecule-contact coupling are different, as seen in Figure 4. The HOMO levels are shown in the PDOS as a main contribution of PTP and CPTP molecules. The HOMO level shift of PTP is larger than that of CPTP. Therefore, the transmission peak corresponding to the HOMO level of CPTP remains close to the Fermi level. As the current is the integral of the transmission coefficient within the bias window around the Fermi level, it becomes higher in CPTP as compared to PTP. The result shows that the incorporation of an antiaromatic component into a conjugated framework gives a less intense response to the molecule-contact coupling and eventually increases the current. Effects of the Conjugated Frameworks Including Aromatic, Nonaromatic, and Antiaromatic Components. To obtain a deeper understanding of the relationship between the electron transport characteristics and the conjugated framework, we have incorporated metallocene molecules therein due to their ability to form complexes with several types of rings, such as antiaromatic and nonaromatic rings. Furthermore, it is wellknown that antiaromatic and nonaromatic ring compounds are stabilized by the complexation with a transition metal in the formation of metallocene. Figure 5 shows the I-V curves of PTP, CPTP, and metallocene incorporated PTP derivatives. Because the molecules are classified into three groups (I, II, and III) according to the incorporated component (antiaromatic, nonaromatic, and aromatic), NiPTP, CoPTP4, and CPTP belong to group I, CoPTP5 and FePTP to group II, and PTP to group III. A striking feature of the I-V curves is that their behavior is unique for each group. The order of the current follows the manner of group I > group II > group III at 0.0 V < V < 2.0 V applied bias voltages. Although the I-V curve of FePTP (group II) shows a negative differential resistance (NDR) and the current is lower at 1.4 V < V < 2.0 V applied bias voltages than the current through PTP (group III), it is clearly seen that the order of the current is group I > group II > group III at low applied bias voltages, 0.0 V < V < 1.0 V. The results are consistent with the previous conclusion that the current through a molecule containing an antiaromatic component (CPTP) is higher than the current through a molecule containing an aromatic component (PTP). Looking at the I-V curves, we find that the I-V characteristics show little difference within the same group, and the order of currents through molecules is [NiPTP > CoPTP4 > CPTP] > [CoPTP5 > FePTP] > [PTP]. Although NiPTP and CoPTP4 have the same conjugated framework as group I, NiPTP contains

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Figure 6. Equilibrium transmission curves, T(E,V)0), within the range of -1.0 eV < E - Ef < 0.4 eV. Arrows point out the closest transmission peak to the Fermi level.

a metallocene molecule composed of two antiaromatic cyclobutadiene rings and shows a higher current in comparison to CoPTP4, which has one antiaromatic cyclobutadiene and one nonaromatic cyclopentadiene ring. Comparing CoPTP5 with FePTP (group II), it is seen that substitution of the antiaromatic cyclobutadiene with nonaromatic cyclopentadiene results in a decrease in the current. However, the results include the influence of different frameworks and different transition metals. To evaluate the influence of the transition metal as compared to the effect of the conjugated framework, we analyzed the T(E,V)0) and PDOS of the framework, transition metal, and Au atoms in the metallocene incorporated systems (Supporting Information). The T(E,V)0) is closely correlated with the PDOS of the framework, whereas the contribution of the transition metal to transmission is not significant near the Fermi level, except for Fe. In the case of FePTP, the Fe metal plays a remarkable role in the electron transport characteristics. However, when we consider conformational isomers such as CoPTP4 and CoPTP5, the dependency of the electron transport characteristics on the type of conjugated framework, regardless of the transition metal, can be clearly seen. CoPTP4 shows a higher current because it possesses an antiaromatic component (C4H4) in the conjugated framework, whereas CoPTP5 has a nonaromatic component (C5H5) in the conjugated framework. From this, it can be expected that the type and number of ring components composing the metallocene molecule and the conjugated framework are important factors in the control of electron transport. These distinguishable I-V characteristics originate from the transmission peaks lying near the Fermi level. Figure 6 shows T(E,V)0) curves within the range of -1.0 eV < E - Ef < 0.4 eV and arrows indicates peaks corresponding to the HOMO level. The curves imply that the closer the peak lies to the Fermi level, the greater the current becomes in the low bias regime. In fact, only the low-bias I-V characteristics can be reasonably well reproduced by the equilibrium transmission characteristics, T(E,V)0). The deviation in both the magnitude and the peak position of transmission becomes significant at a large bias as can be seen from looking at the shift of the peak near the Fermi level by the applied bias voltage. The bias dependence of the transmission characteristics, T(E,V), is shown in Figure. 7. Upon increasing the applied bias voltage, the transmission peaks, especially those closest to the Fermi level, move away from the Fermi level following a dotted white line indicating the bias window, and their magnitude gradually decreases. In group I

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Figure 7. Bias dependence of the transmission curves, T(E,V), calculated at every 0.2 bias voltage: (a) NiPTP, (b) CoPTP4, (c) CPTP, (d) CoPTP5, (d) FePTP, and (e) PTP. Dotted white lines indicate the range of current integration around the Fermi level (Ef ) -5.1 eV).

(NiPTP, CoPTP4, and CPTP), the transmission peak moves away from the Fermi level as closely follows the bias window. And then, the transmission peak turns to the inside of bias window around 1.0 V applied bias voltage. The fact that the transmission peak lies close to the Fermi level describes the reason why group I has the highest current under the bias voltage, because the current is an integration of the transmission coefficient within the bias window around the Fermi level. In group II (of CoPTP5, FePTP) and group III (PTP), there is a larger gap between the transmission peak and the Fermi level at zero applied bias voltage and the magnitude of the transmission peak is quickly degraded before crossing the bias window. Therefore, groups II and III result in a low current. For the

FePTP, the magnitude of the peak starts to be degraded before entering the bias window and the peak scarcely enters into the window when it begins to disappear. This arises the negative differential resistance (NDR). 4. Conclusion We have performed a systematic analysis of molecular level alignments and electron transport characteristics for six conjugated molecules that can be classified into three groups (I, II, and III) according to the component incorporated into the conjugated framework. The response to the molecule-contact coupling and applied bias voltage distinctively affects molecular

Control of Electron Transport levels and electron transport characteristics. Combining nonand antiaromatic components increases the conductance due to the fact that the HOMO level lies close to the Fermi level. Consequently, the order of the current follows the manner of group I > group II > group III, ([NiPTP > CoPTP4 > CPTP] > [CoPTP5 > FePTP] > [PTP]). It is worth mentioning that the manipulation of the conjugated framework is an important factor controlling the electron transport characteristics. It is concluded, then, that due to the significant influence of the incorporated component of the conjugated framework on the electron transport characteristics, further control of these characteristics can be achieved by modification of the chemical functions of the conjugated framework. Acknowledgment. The authors sincerely thank the crew of the Center for Computational Materials Science of the Institute for Materials Research, Tohoku University, for their continuous support of supercomputing facilities. Supporting Information Available: Complete ref 55, the molecular level alignment analysis of PDT (at different contact configurations including the I-V curve), NiPTP, CoPTP4, CoPTP4, and FePTP through T(E,V)0), PDOS, and energy level diagrams at the isolated extended model and the coupled extended model. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Aviram, A.; Ratner, M. A. Chem. Phys. Lett. 1974, 29, 277. (2) Eigler, D. M.; Schweizer, E. K. Nature 1990, 344, 524. (3) Ohnishi, H.; Kondo, Y.; Takayanagi, K. Nature 1998, 395, 780. (4) Joachim, C.; Gimzewski, J. K.; Aviram, A. Nature 2000, 408, 541. (5) Joachim, C.; Gimzewski, J. K.; Schlittler, R. R.; Chavy, C. Phys. ReV. Lett. 1995, 74, 2102. (6) Reed, M. A.; Zhou, C.; Muller, C. J.; Burgin, T. P.; Tour, J. M. Science 1997, 278, 252. (7) Reichert, J.; Ochs, R.; Beckmann, D.; Weber, H. B.; Mayor, M.; Lo¨hneysen, H. v. Phys. ReV. Lett. 2002, 88, 176804. (8) Smit, R. H. M.; Noat, Y.; Untiedt, C.; Lang, N. D.; van Hemert, M. C.; van Ruitenbeek, J. M. Nature 2002, 419, 906. (9) Xue, Y.; Datta, S.; Ratner, M. A. J. Chem. Phys. 2001, 115, 4292. (10) Damle, P. S.; Ghosh, A. W.; Datta, S. Phys. ReV. B 2001, 64, 201403. (11) Xue, Y.; Datta, S.; Ratner, M. A. Chem. Phys. 2002, 281, 151. (12) Damle, P. S.; Ghosh, A. W.; Datta, S. Chem. Phys. 2002, 281, 171. (13) Brandbyge, M.; Mozos, J. L.; Ordejo´n, P.; Taylor, J.; Stokbro, K. Phys. ReV. B 2002, 65, 165401. (14) Xue, Y.; M. A. Phys. ReV. B 2003, 68, 115406. (15) Xue, Y.; M. A. Phys. ReV. B 2003, 68, 115407. (16) Fujimoto, Y.; Hirose, K. Phys. ReV. B 2003, 67, 195315. (17) Calzolari, A.; Marzari, N.; Souza, I.; Nardelli, M. B. Phys. ReV. B 2004, 69, 035108. (18) Rocha, A. R.; Garcı´a-Sua´rez, V. M.; Baily, S. W.; Lambert, C. J.; Ferrer, J.; Sanvito, S. Nat. Mater. 2005, 4, 335. (19) Keldysh, L. V. SoV. Phys. JETP 1965, 20, 1018. (20) Zhang, C.; Du, M.-H.; Cheng, H.-P.; Zhang, X.-G.; Roitberg, A. E.; Krause, J. L. Phys. ReV. Lett. 2004, 92, 158301.

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