Theoretical Studies of Electron Transport in Thiophene Dimer: Effects

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Theoretical Studies of Electron Transport in Thiophene Dimer: Effects of Substituent Group and Heteroatom Shundong Yuan,† Chunlei Dai,† Jiena Weng,† Qunbo Mei,† Qidan Ling,*,†,‡ Lianhui Wang,†,§ and Wei Huang† †

Jiangsu Key Laboratory of Organic Electronics & Information Displays and Institute of Advanced Materials, Nanjing University of Posts and Telecommunications, Nanjing 210046, People's Republic of China ‡ Fujian Key Laboratory of Polymer Materials and College of Chemistry and Materials Science, Fujian Normal University, Fuzhou 350108, People's Republic of China § Laboratory of Advanced Materials, Fudan University, 2205 Songhu Road, Shanghai 200438, People's Republic of China

bS Supporting Information ABSTRACT: The electron-transport properties of various substituted molecules based on the thiol-ended thiophene dimer (2Th1DT) are investigated through density functional theory (DFT) combined with nonequilibrium Green’s function (NEGF) method. The current
voltage (I
V) curves of all the Au/2Th1DT/Au systems in this work display similar steplike features, while their equilibrium conductances show a large difference and some of these I
V curves are asymmetric distinctly. The results reveal the dependence of conductance on the energy level of the substituted 2Th1DT molecules. Rectification ratios are computed to examine the asymmetric properties of the I
V curves. The rectifying behavior in the 2Th1DT molecule containing the amino group close to the molecular end is more prominent than that in the other molecules. The rectifying behavior is analyzed through transmission spectra and molecular projected self-consistent Hamiltonian (MPSH) states. Slight negative differential resistance (NDR) can be observed in some of the systems. The electrontransport properties of 2Th1DT molecules containing different heteroatoms are also investigated. The results indicate that the current in heteroatom-containing molecules is larger than that in their pristine analogues, and lighter heteroatoms are more favorable than heavier heteroatoms for electron transport of the thiophene dimer.

1. INTRODUCTION Accompanying the progress of microelectronics, which has changed our world significantly in the past decades, the utmost of the silicon electronic devices, caused by the physical limit from its extremely small scales, is about to be reached. Molecular devices with nanometer scale, which are regarded as the next-generation electronic device, have attracted more and more interest among researchers all over the world.1
7 Many experimental techniques and methods, including mechanically controllable break junction (MCBJ),8,9 scanning tunneling microscopy (STM), conducting probe atomic force microscopy (CP-AFM),10 Langmuir
Blodgett (LB) films,11 and self-assembled monolayers (SAM),12 have been employed to fabricate the molecular junction between two metal electrodes. On the basis of the molecular junction, measurement of the current through the molecule is feasible. Significant advances have also been made in the field of theoretical studies for the molecular device,13
25 since Aviram and Ratner26 first proposed the assumption of the molecular rectifier through a donor
σ-bridge
acceptor (DσA) molecule in 1974. Recently, one extensively employed method for theoretical study of electron-transport properties in molecular junctions is based on density functional theory (DFT) combined with nonequilibrium r 2011 American Chemical Society

Green’s function (NEGF).17,23,27
34 The DFT-NEGF method has been described in detail in the papers of Brandbyge et al.17 and Ke et al.28 The method is considered to be highly reliable in studying electron-transport properties. The reliability of the method has been demonstrated in some works, in which calculated results could be compared with experimental data.35
37 The molecule is the key component for its role in molecular devices. Different transport properties of the molecular device can be obtained by chemical modification (e.g., group substituting, introducing heteroatom) or by physical controls on the molecule while the other components of the molecular device are kept unchanged. Molecular and electronic structures of the short-chain molecules are usually easier to be influenced by chemical modification relative to the long-chain molecules. Therefore, molecular devices based on short-chain molecules may be more promising for future applications. However, there are only a few systematic investigations of electron-transport properties of a molecular device using one particular short-chain Received: January 31, 2011 Revised: March 17, 2011 Published: April 05, 2011 4535

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The Journal of Physical Chemistry A molecule with different chemical modifications or physical controls. Emberly and Kirczenow38 investigated theoretically the socalled smallest molecular switch, based on 1,4-benzenedithiolate (BDT). Ke et al.29 also investigated the transport properties of different Au/BDT/Au molecular junctions. Their results demonstrated that transport properties of the molecular junction employing simple molecules are more easily changed in different ways. Conjugated materials based on thiophene moieties are good candidates for applications in organic and molecular electronics because of their outstanding chemical and thermal stabilities and their excellent charge-transport properties.39 In addition, they are processable materials and their properties can be easily tailored chemically.40 The transport properties of the oligothiophene molecule between two metal electrodes have been investigated by theoretical computations and experimental measurements41
46 in the past decade. In these works, the results show large differences, which are caused primarily by the computational methodologies, experimental technologies, length of the oligothiophene molecule, etc. As for theoretical investigations, the discrepancy of the previous results is still noticeable even for the same thiophene dimer molecule, that is, the shortest oligothiophene. The substituent group on the conjugated molecule usually plays an important role in electron transport, as suggested in many previous works,16,24,47
50 although the influence of the substituent group on electron transport may be minor in some cases.27 However, the substituent effects on the transport properties of oligothiophene-based molecules have yet to be investigated. Therefore, it is necessary to study systematically the electrontransport properties of the oligothiophene molecule, especially the thiophene dimer, through the current extensively employed DFT-NEGF method and computational implementations. This is expected to result in a more comprehensive understanding and more reliable results on transport properties of the oligothiophene molecules. The results will be helpful for studies of the molecular device based on the short-chain molecule. The oligothiophene-based molecules studied in this work are the thiol-ended thiophene dimer (2Th1DT) and its derivatives, in which the hydrogen atom on the thiophene monomer is substituted with a representative electron-donating group (
NH2) and electron-withdrawing group (
NO2). The current
voltage (I
V) characteristics, conductances, rectification ratios, and negative differential resistance (NDR) properties of these molecules were investigated systematically. The results were analyzed by the electronic structures of the isolated molecules, transmission spectra, and molecular projected self-consistent Hamiltonian (MPSH) states of the Au/2Th1DT/Au systems. The effects of substituent groups on electron-transport properties of the 2Th1DT derivatives were analyzed emphatically. Furthermore, the effects of different heteroatoms in the thiophene molecule on electron-transport properties of the 2Th1DT derivatives were also investigated.

2. COMPUTATIONAL DETAILS A representative model of the molecular junction with metal/ molecule/metal structure, in which a thiol-ended trans-thiophene dimer is sandwiched between two Au electrodes, is schematically illustrated in Figure 1. 2Th1DT is self-assembled to the gold electrode surface via the thiol end groups (
SH). When
SH is adsorbed to the Au surface, the hydrogen atom is dissociated and the strong Au
S covalent bond is formed

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Figure 1. Schematic illustration of molecular junction: thiol-ended thiophene dimer (2Th1DT) self-assembled on Au (111) 3  3 surface.

Figure 2. Modeling isolated molecules with the hydrogen atom in the thiol-ended thiophene dimer (2Th1DT) substituted by an amino or nitro group. The molecules are denoted a
i.

subsequently. This technique has been widely used in both experimental and theoretical studies.19,51
53 The 2Th1DT derivatives studied in the present work are (a) pristine 2Th1DT, (b) 2ThNO21DT-1, (c) 2ThNO21DT-2, (d) 2ThNH21DT-1, (e) 2ThNH21DT-2, (f) 2ThNO2NH21DT-1, (g) 2ThNO2NH21DT-2, (h) 2ThNO2NH21DT-3, and (i) 2ThNO2NH21DT-4. Their structures are illustrated in Figure 2. Considering the short backbone of thiophene dimer, the position of the congeneric substituent group on one of the monomers is also expected to play an important role in electron-transport properties. The whole computation includes two main processes. The first process is optimization of the geometries. First, the geometries of the isolated 2Th1DT molecules are optimized by the 4536

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The Journal of Physical Chemistry A Gaussian03 program54 at the hybrid DFT/B3LYP55,56 level of theory with the 6-31G(p,d) basis set. Second, a gold cluster is added to each side of the optimized isolated molecule.14 Each gold cluster consists of three gold atoms that are placed as an equilateral triangle with an Au
Au bond length of 2.88 Å to simulate the Au (111) surface. The sulfur atoms are bonded directly to the gold clusters, and all components configure the extended molecule. The sulfur atom is located on top of the center of the gold triangle, that is, a hollow site, which is in agreement with suggestions in the literature.23,57
59 The specific distance between the sulfur atom and the center of the triangle is determined by comparing the total energies of the extended molecule as a function of the different distances. The optimal distance corresponds to the lowest total energy. In the present models, the optimal distance between sulfur atom and the center of the triangle is 2.30 Å. Third, the relative positions of the gold atoms in each gold cluster and the S
Au distance are fixed. The geometries of the extended molecules are optimized through Gaussian03 program,54 at the hybrid DFT/B3LYP55,56 level of theory with the 6-31G(p,d) basis set for all atoms, except for Au atoms with the LANL2DZ basis set. The geometries of the isolated molecules without Au clusters are extracted after the above geometric optimizations and translated into the region between the left and right electrodes (Figure 1). The semi-infinite left and right electrodes are modeled by two Au (111)
(3  3) surfaces (i.e., each layer consisting of nine Au atoms). The Au/2Th1DT/Au system is divided into three parts: left electrode (L), right electrode (R), and central scattering region (C). There are three layers in the left and right electrode unit cells. The scattering region includes the central molecule together with the respective two gold layers on the left- and right-hand sides. The distance between the Au (111) surface and the molecule is 2.30 Å, which is in accordance with the aforementioned computational result. The end S atom is located at the hollow site of the Au surface. The transport properties of the Au/2Th1DT/Au system can be obtained when the continuous bias voltages are applied to the system. The VNL/ATK 2008.10 program,60 which is based on density functional theory (DFT) combined with the first-principle nonequilibrium Green’s function (NEGF) formalism,17,61 was used in this work. In our calculation, a double-ζ with polarization (DZP) basis set is chosen for all atoms except for Au atoms, for which a single-ζ with polarization (SZP) is used. The exchange
correlation potential is described by the Perdew
Zunger local density approximation (LDA.PZ). 62,63 The convergence criterion of 1  10
5 is set for the grid integration to get accurate results. In order to choose appropriate k-point sampling in the direction along the Au (111) surface, zero-bias transmission spectra of the 2Th1DT two-probe system using different k-point samplings with aforesaid parameters were calculated. The results (also see Supporting Information) indicate that 2  2 k-point sampling for the self-consistent calculation and 4  4 k-point sampling for the transmission calculation are the most favorable combination for the sake of more accurate results and saving computational time. A kpoint sampling of 500 is used in the electron-transport direction, that is, the direction perpendicular to the Au (111) surface. The current
voltage (I
V) characteristics of the Au/2Th1DT/ Au system can be obtained from the Landauer
B€uttiker formula:64
66 2e2 IðVb Þ ¼ h

Z

μR

μL

½f ðE
μL Þ
f ðE
μR ÞTðE, Vb Þ dE ð1Þ

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Figure 3. Frontier molecular orbital shapes of thiol-ended thiophene dimer and its derivatives.

where 2e2/h = G0 is the conductance quantum, e is the elementary charge, h is the Planck constant, and f is the Fermi function. μL and μR are the electrochemical potentials of the left and right electrodes, respectively: μL(Vb) = EF
eVb/2 and μR(Vb) = EF
eVb/2. EF is the Fermi energy that can be set to zero. The energy region [μL(Vb), μR(Vb)] contributing to the current integral is referred to as the bias window. T(E, Vb) is the total transmission probability for an electron incident at energy E through the device under potential bias Vb.

3. RESULTS AND DISCUSSION 3.1. Electronic Structures of the Isolated Molecules. The molecular electronic structure can affect the conductance of the molecular transport junction. As suggested by Cohen et al.,67 the density distribution of frontier molecular orbital is intrinsic to the molecule rather than to the junction and does not depend on the structure of the molecule
electrode interface. It is an important factor determining the conductance of the molecular transport junction. Therefore, the electronic structures of the isolated molecules were investigated before the electron-transport calculations were performed. Figure 3 shows the frontier molecular orbital diagrams of HOMO and LUMO. The orbital density distributions of the highest occupied molecular orbitals (HOMO) for all the molecules are delocalized almost completely. However, the cases of the lowest unoccupied molecular orbitals (LUMO) of these molecules exhibit some obvious differences. 4537

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Figure 4. Molecular energy levels HOMO
1, HOMO, LUMO, and LUMO þ 1 of the isolated molecules and their HOMO
LUMO gaps (HLGs).

For pristine 2Th1DT (a), the LUMO density distributions are also fully delocalized. The LUMOs of molecules b, g, and i are all localized strongly on the specific thiophene monomer, which contains a nitro group located close to the tail of the thiophene dimer. The localizing behavior can be interpreted in terms of the strong electron-withdrawing capability of the nitro group. For the LUMOs of molecules c, f, and h, there is no orbital density distribution on the
SH group, which is closer to the nitro group side. This also results partly from the modification of the nitro group. In the following text, the effect of the molecular orbital density distribution on the electrical conductance is discussed briefly. The energy levels of the frontier molecular orbital and the related HOMO
LUMO gaps (HLGs) are shown in Figure 4. Generally, the LUMO energy levels for molecules b and c, which contain only
NO2 groups, are in the lowest region, while those for molecules d and e, which contain only
NH2 groups, are in the highest region. For molecules f
i, which contain
NH2 and
NO2 simultaneously, the LUMO energy levels are in the medium region. The change tendency of HOMO energy level for all the molecules is similar to that of LUMO energy level except for the pristine 2Th1DT molecule. Different positions for the same substituent group on the 2Th1DT molecule do not affect the energy levels obviously. Thus, it can be concluded that the electron-withdrawing nitro substituent leads to an energy-level reduction for the 2Th1DT molecule, while the electron-donating amino substituent leads a rise oppositely. In addition, the combination of nitro and amino substituents leads a reduction of unoccupied molecular orbital (LUMO and LUMO þ1) energy levels but a rise of occupied molecular orbital (HOMO and HOMO
1) energy levels. As a result, the HLGs of molecules f
i are reduced obviously. For the HLGs, the molecules can be categorized in terms of the substituent group, and they exhibit the relative sequence a > d, e > b, c > f
i. 3.2. Electron-Transport Characteristics. 3.2.1. I
V Characteristics. All of the current
voltage (I
V) curves of the molecule systems a
i shown in Figure 5 are nonlinear. For the thiophene dimer 2Th1DT and its derivative molecules studied here, the I
V curves exhibit similar change trends. The currents increase rapidly around the zero bias (about 0 to (1.0 V). Subsequently, the currents increase steadily and keep constant approximately. The currents increase rapidly again when the bias is above about (2.4 V. Thus, the I
V curves display two plateaus in the bias

Figure 5. I
V characteristics for all computed molecule systems: (a) 2Th1DT, (b) 2ThNO21DT-1, (c) 2ThNO21DT-2, (d) 2ThNH21DT1, (e) 2ThNH21DT-2, (f) 2ThNO2NH21DT-1, (g) 2ThNO2NH21DT-2, (h) 2ThNO2NH21DT-3, and (i) 2ThNO2NH21DT-4.

range of
3.0 to þ3.0 V. The steplike features can also be found in some previous experimental investigations based on the oligothiophene molecule.41,42 The results reveal the intrinsic transport character of the oligothiophene molecules. There are some differences in the I
V curves for the thiophene dimer 2Th1DT and its derivative molecules, though their change trends are similar. At the positive bias region, the current of molecule a is almost the largest before 1.8 V. Thus, it is suggested that the substituent groups [
NH2], [
NO2], or [
NH2 and
NO2] have no obvious effect in enhancing the electron transport of thiophene dimer at lower positive bias voltage. The obvious effect of substituent groups is observed only for molecule d in the negative bias region. The current of molecule d is always larger than that of molecule a from 0 to
3.0 V. Generally, substituent groups are not expected to enhance the electrontransport capability of 2Th1DT effectively. The results agree well with the theoretical results obtained with the same molecule in a small range around zero bias in previous works.43,46 With the diversities of currents in the different two-probe systems taken into account, the differential conductance (dI/dV) against voltage was computed on the basis of I
V curves in 4538

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Figure 6. Differential conductance (dI/dV) against voltage curves of the computed molecule systems (a
i). The part of the curve below the horizontal dotted line corresponds to the NDR feature.

Figure 7. Differential conductances of all computed molecule systems (a
i) at a bias of 0 V.

Figure 5. The resulting (dI/dV)
V curves are presented in Figure 6. The molecular conductances at 0 V bias, that is, equilibrium conductances, exhibit large differences. The difference in differential conductance between systems d and b approaches 30 μS. In order to compare the effects of substituent group and reveal the relationship between conductance and the molecular electronic structure, the equilibrium conductances of all molecule systems are shown separately in Figure 7. The equilibrium conductances of systems b, c, and f
i are smaller than those of systems a, d, and e. As discussed in section 3.1, the density distributions of LUMOs of isolated molecules b, c, and f
i are all localized (Figure 3). It is believed that the localizing character is not favorable for electric transport since there is no contribution from this orbital. However, the density distributions of LUMOs of isolated molecules a, d, and e are delocalized and their LUMOs contribute to electron transport. On the other hand, by comparison between Figures 7 and 4, it seems that the equilibrium conductances of these molecule families are in good agreement with their HOMO energy levels except the pristine molecule a. For the other molecular systems b
i, when the HOMO energy level is higher, the equilibrium conductance is larger and vice versa. As shown in Figure 4, the HOMO level of each molecule is aligned closer to the Fermi level of gold, which approximates the work function of gold (about
5.1 eV).68 Thus, the HOMO energy level dominates the molecular conductance around the zero bias, as also suggested by Cohen et al.67 For amino-substituent molecules d and e, their HOMO energy levels are the highest and their transport conductances at low bias voltage are the largest accordingly. The correlation is in good

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Figure 8. Rectification ratios (R) as a function of applied bias voltage for systems a
i. R(V) is defined as R(V) = |I(þV)/I(
V)|.

agreement with the suggestion by Smeu et al.25 that the electrondonating substituent group would raise the HOMO energy level and bring it closer to Fermi level, thus increasing its participation in low-bias conductance. The calculation result revealed the energy-level dependence of the conductance for all molecules except the pristine molecule 2Th1DT. This may be a useful reference for the design of molecular devices. 3.2.2. Rectification Ratio. Molecular rectifiers are one of the most widely studied molecular devices. In 1974, Aviram and Ratner26 proposed first that rectifying behavior can be observed through a donor
σ-bridge
acceptor (DσA) molecule, in which electron transfer will be more favorable from A to D rather than in the opposite direction. Aviram and Ratner’s suggestion makes molecular rectification more and more promising in the field of molecular electronics, though there was a contrary opinion on the direction of the electron transfer by Ellenbogen and Love.69 In Figure 5, it is evident that all I
V curves are asymmetric at about zero bias, and the asymmetry can also be observed through the (dI/dV)
V curves in Figure 6. The asymmetric feature of electron transport may be attributed to some factors such as asymmetric molecular structure, two different electrodes, and unequal couplings between the molecule and the surfaces of the two electrodes. Some theoretical explanations for the rectifying phenomenon in molecular devices were proposed by many research groups previously.19,23,58,70
74 In the present work, the observed asymmetry in Figure 5 is primarily attributed to the inherent asymmetry of molecular structure. For the 2Th1DT molecule with symmetric structure, its I
V curve should be symmetric in principle. However, the slight asymmetry of its I
V curve can be observed in Figure 5. It may be due to the slight asymmetry of the optimized molecular structure and the slightly unequal couplings of the molecule with the two electrodes. In order to reveal the detailed features of the asymmetry, the rectification ratios of all the systems were computed. Figure 8 depicts the rectification ratio R(V) versus bias voltage. R(V) = 1 means that there is no rectification. R(V) > 1 means that the current is larger in the positive direction than in the negative direction, and vice versa. In Figure 8, there are deviations more or less from R(V) = 1 for the rectification ratios of all the systems. Deviations are more prominent for systems d, h, and i. The molecular structures of d, h, and i have similar features in that they all contain the group
NH2 and this substituent group is 4539

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Figure 9. Transmission spectra of molecule systems a, d, h, and i in the energy range from
2 to þ2 eV at different bias voltages of
3.0 to þ3.0 V. Blue dashed lines indicate the bias window at each bias voltage.

located close to the end of each molecule. Therefore, it is believed that the amino group, especially its position on the thiophene dimer, plays a critical role in rectification in the present computational model. In this work, the rectifying behavior for the molecule systems was interpreted by analyzing the transmission spectrum and the molecular projected self-consistent Hamiltonian (MPSH) at different bias voltages. According to the Landauer
B€uttiker formula, the current depends on the transmission amplitude. Consequently, the current through a molecule system is determined by the transmission spectra within the bias window [μL(Vb), μR(Vb)]. The region of the bias window is actually [
Vb/2, þVb/2] if the Fermi level is set to zero. Theoretically, the transmission is determined by the molecular electronic structure modified by the applied bias and the coupling between molecule and electrode, etc. Figure 9 illustrates the transmission spectra of the two-probe systems a, d, h, and i in the energy range from
2 to þ2 eV at different bias voltages of
3.0 to þ3.0 V. In the transmission curve, the peaks correlate with resonant tunneling through molecular states. The transmission peaks shift when the

applied bias voltage changes. In Figure 9, the transmission spectra of system a at positive and negative bias are almost symmetric because of the intrinsic symmetric configuration of the system. It is noted that transmission spectra of system a exhibit a very small difference at higher positive and negative bias voltages. The present computational model is not perfectly symmetric as conjectured above. As a result, the currents of system a at positive and negative bias voltages are not symmetric completely, and the rectification ratios approach 1 except at bias above 2.8 V. For system d, the transmission spectra are similar to those of system a and there are two transmission resonance peaks in the energy range of
1.6 to 0 eV. The two peaks are the main contributions for the current of system d. Generally, the transmission peaks within the bias window at the negative bias are higher and broader than those at the positive bias over most of the bias range except
0.6 to þ0.6 V. In addition, another high and broad peak in the positive energy region appears within the bias window when the bias rises above
2.4 V. However, the corresponding transmission peak appears only partially in the bias window in the case of positive bias. Therefore, the 4540

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Figure 10. MPSH states of molecule system a at (0.4 and (2.8 V.

rectification ratios of system d in Figure 8 exhibit R > 1 slightly at V < 0.6 V and R < 1 apparently at V > 0.6 V. In systems h and i, similarity can be observed for the distribution of transmission peaks below the Fermi level. There are two adjacent transmission peaks below the Fermi level under the condition of positive bias in both systems h and i. The height of the second resonance peak in the lower-energy region increases gradually with rising positive bias voltage, and the peak appears in

the bias window at higher bias voltages. However, the second peak almost disappears when the negative bias voltage is applied to the two-probe system. Consequently, the transmission spectra at the positive and negative bias voltages exhibit asymmetry obviously, and it gives rise to asymmetric current. In Figure 8, the rectification ratios of systems h and i deviate from R = 1 significantly and the maximum approaches 2.2. The rectification ratios of systems h and i are not always greater than 1. At the bias 4541

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Figure 11. MPSH states of molecule system i at (0.4 and (2.8 V.

voltage of V < 0.6 V, the rectification ratios are less than 1. The reason for R < 1 is that the transmission peak close to the Fermi level appears completely within the bias window at the bias of 0∼(
0.6) V. However, the peak appears only partially in the bias

window at the bias of 0∼(þ0.6) V. The two transmission peaks below the Fermi level under the condition of positive bias play a critical role in determining R > 1 above 0.6 V in the two systems h and i. The different change tendencies of systems h and i in 4542

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The Journal of Physical Chemistry A Figure 8 can also be observed in the curve of system h rising from 0.6 to 2.0 V and then fluctuating above 2.0 V. However, the curve of system i rises all along above 0.6 V and it is supposed to keep the tendency when the bias voltage further increases. In order to understand the characteristics of the transmission spectra, it is necessary to identify the molecular orbitals involved in the transmission. Thus, an effective method, suggested by previous theoretical works,20,23,37,75 was employed. In this method, the self-consistent Hamiltonian of the molecular junction is projected onto the molecule and the molecular projected selfconsistent Hamiltonian (MPSH) matrix is diagonalized. The MPSH states are the eigenstates of the molecule in the two-probe circumstance and the self-energies of two electrodes are excluded. The MPSH states delocalized throughout the scattering region will contribute to the transmission and the MPSH states localized on any one of the electrodes will not give any contribution to the transmission.20,23,37,75 In the present work, systems a and i were chosen as the compared paradigms because they have obvious differences in rectifying behavior. Figure 10 illustrates the spatial distribution of the MPSH states of system a. Bias voltages of (0.4 and (2.8 V are chosen because the rectification ratios of system i are R = 0.9 at 0.4 V and R = 2.1 at 2.8 V. However, the difference in rectification ratios between 0.4 and 2.8 V in system a is only slight (see Figure 8). The energy levels of the MPSH eigenstates in Figure 10 locate in the energy region confined by the bias window, and each level correlates with a transmission tunneling channel. Apparently, the spatial distribution of MPSH states in system a exhibits a symmetric feature at þ0.4 and
0.4 V, though the values of the corresponding MPSH energy levels are not well accordant. Therefore, the MPSH states at þ0.4 V make contributions to the transmission as much as those at
0.4 V. The corresponding rectification ratio is about R(0.4 V) = 1, which is in agreement with the value in Figure 8. In the case of 2.8 V bias, the MPSH states of the positive and negative bias are all symmetric except for state 243 which is localized at þ2.8 V and delocalized at
2.8 V. Consequently, the MPSH states at þ2.8 V give less contributions to the transmission than those at
2.8 V. The corresponding R(2.8 V) is less than 1, which is also in agreement with the value in Figure 8. In the two-probe system i, it is expected that the MPSH states have an evident difference between þ2.8 and
2.8 V. The difference is responsible for the rectification ratio of R(2.8 V) = 2.1. Figure 11 illustrates the spatial distribution of MPSH states in system i. At the bias of þ2.8 V, most MPSH states, for example, 249, 251, 252, 254, 255, and 257, except 256, are delocalized completely. However, at the bias of
2.8 V, only MPSH states 249, 252, 256, and 257 are delocalized completely, while states 250, 251, and 253 are delocalized only partially. Therefore, the transmission contributions from the MPSH states at þ2.8 V are greater than those at
2.8 V. This results in a large rectification coefficient of R(2.8 V) = 2.1. The MPSH states do not exhibit distinct regularity at þ0.4 and
0.4 V. Their total contributions for the respective transmissions are equivalent approximately. Therefore, the rectification ratio for system i at 0.4 V is 0.9, just as illustrated in Figure 8. 3.2.3. NDR Behavior. Negative differential resistance (NDR) means that the current decreases with an increase in voltage. NDR is regarded as the most prominent feature of molecular electronic devices for its circuit applications such as organic memory. NDR behaviors in the different molecular junctions can be attributed to the following different mechanisms, for example,

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a two-step reduction process that modifies charge transport through the molecule,1 change of the molecular conformation due to change of the electronic charge state of the molecule under increasing bias,16 molecular-level crossing in an organometallic molecular double dot system,76 and resonant tunneling originating from shifting of the molecular energy level by external electric field.47 In the present investigation, it is observable that slight NDR behaviors occur in most of the two-probe systems at about 2.0 V in Figure 6. The NDR behavior of the thiophene dimer system in the present simulation is similar to the result by Jalili and RafiiTabar.43 Bai et al.46 also investigated the electron-transport properties of a thiophene dimer, and the I
V characteristics in the bias range of
2.0 to þ2.0 V are in very good agreement with our results. However, the NDR feature was not mentioned in their work because the current above 2.0 V was not calculated. The difference of NDR behaviors in the present molecule systems can be observed from Figure 6. System a shows symmetric conductance characteristic approximately about zero bias voltage, and NDR is evident relatively. System f exhibits clear NDR in the positive bias direction but no NDR in the contrary direction. Other cases have no NDR at all in either direction of electron transport, for example, system c. The NDR character of the molecules based on thiophene dimer in this work is mainly attributed to the particular electronic structure. When the external electric field is applied to the molecule, the molecular electronic structure will be modified and the molecular energy level will shift. Thus, the resonant tunneling originated from the shift of the molecular energy level by external electric field, as suggested by Karzazi et al.,47 may be a reasonable interpretation for the NDR mechanism in the present model. In addition, interaction between the molecule and the gold electrode may be another factor. Generally, the substituent groups affect the NDR of the thiophene dimer indistinctively. 3.2.4. Effect of Heteroatom. The electronic structure and energy level of the molecule will be modified when a heteroatom is introduced. Thus, the electron-transport properties of the molecule containing a heteroatom will change. In this work, the electron-transport properties of different 2Th1DT molecules were studied. Different heteroatoms are introduced into the 2Th1DT molecules to examine the effects of the heteroatom on electron transport. The pristine analogue of the molecules, which are illustrated in Figure 12, is the thiol-ended cis-thiophene dimer. The whole computational procedure and parameters for these systems are the same as that in section 2. The I
V characteristics of the thiol-ended cis-thiophene dimer and transthiophene dimer are compared before we discuss the effect of the heteroatom. The I
V curves are plotted in Figure 13. It is evident that the two curves nearly coincide with each other, just as in the result reported by Bai et al.46 This feature suggests that the electron-transport characteristics of cis- and trans-thiophene dimers may be treated equivalently. Thus, the I
V characteristics of the molecules in Figures 2 and 12 are comparable. Figure 14 shows the I
V curves of the different Au/molecule/Au systems in which the molecules are cis-2Th1DT, 2Th1DTþC, 2Th1DTþN, 2Th1DTþS, 2Th1DTþO, 2Th1DTþSi, and 2Th1DTþP, respectively. Here, the applied bias voltage range is only from 0 to þ3.0 V because the currents at the positive and negative directions should be symmetric due to the symmetric molecular structure. In Figure 14, currents in the molecules containing heteroatoms are larger to some extent than those in their pristine analogues. It is suggested that the heteroatom bridging the two 4543

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Figure 14. I
V characteristics of the different Au/molecule/Au systems in the bias voltage range of 0 to þ3.0 V. The molecules are cis2Th1DT, 2Th1DTþC, 2Th1DTþN, 2Th1DTþS, 2Th1DTþO, 2Th1DTþSi, and 2Th1DTþP.

Figure 12. Modeling isolated molecules: cis-2Th1DT and 2Th1DTbased molecules obtained by introducing different heteroatoms into cis2Th1DT. The heteroatoms are C, N, O, S, Si, and P.

Figure 13. I
V characteristics of cis-2Th1DT and trans-2Th1DT in the bias voltage range of
3.0 to þ3.0 V.

thiophene monomers plays a role of providing an additional transport channel for the electron. It is obvious that the curves display an order array in the bias voltage range of 0 to þ2.0 V. It denotes that the electron-transport properties of 2Th1DTþC, 2Th1DTþN, and 2Th1DTþO molecules are similar. There is not much discrepancy in the electron-transport properties of 2Th1DTþS, 2Th1DTþSi, and 2Th1DTþP molecules. The character of the curves suggests that, for the heteroatom, lighter atoms are more favorable than heavier atoms for electron transport of the 2Th1DT molecule. This may be helpful for the selection of molecules similar to the thiophene dimer for device applications. It is worth mentioning that slight NDR behavior also occurs in these molecules at the bias range of about 2.0
2.4 V. The NDR characteristic of 2Th1DT molecule is still not enhanced through

addition of a heteroatom. Sen and Chakrabarti77 investigated NDR in thiol-ended fused thiophene trimers and the result shows a large NDR at the bias range of (1.6 to (2.45 V. The discrepancy of NDR behavior between their work and ours may be caused primarily by the different configurations of Au/molecule/Au system. In their work, the terminal sulfur atoms are located on the top sites of Au (111) surface, however, the sulfur atoms are located on the hollow sites in our work.

4. CONCLUSIONS In summary, the electron-transport properties of the various molecules based on the thiol-ended thiophene dimer (2Th1DT) were computed systematically through density functional theory (DFT) combined with nonequilibrium Green’s function (NEGF) technique. For the 2Th1DT molecule and the substituted 2Th1DT molecules, their I
V curves display similar change trends, but the conductances of these molecules at 0 V bias exhibit large differences. The comparison between the conductance and the HOMO
LUMO level of molecule reveals the energy-level dependence of the conductance for all substituted molecules. Subsequently, rectification ratios of all systems were computed to examine the asymmetry of the I
V curves at about zero bias voltage. The rectifying behavior in the 2Th1DT molecule containing the amino group close to the molecular end is more prominent than in the other molecules. The rectifying behavior was discussed emphatically through analyzing transmission spectra and MPSH states at different bias voltages. The results indicate that transmission spectra and MPSH states are effective means for studying transport properties in molecular devices. The slight NDR observed in some of the systems may be primarily attributed to the particular electronic structure of the molecule. Finally, the electron-transport properties of the different 2Th1DT molecules were studied by introducing different heteroatoms into the 2Th1DT molecules. Computational results show that the currents in molecules containing heteroatoms are larger than those in their pristine analogues. For the heteroatom, lighter atoms are more favorable than heavier atoms for electron transport of the thiophene dimer. In addition, the heteroatom cannot enhance the NDR of the 2Th1DT molecule. 4544

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’ ASSOCIATED CONTENT

bS

Supporting Information. Additional text and one figure showing transmission spectra under different k-point samplings of 2Th1DT molecule at zero bias voltage. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel þ86-25-8586 6333; fax þ86-25-8586 6396. e-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the National Basic Research Program of China (973 Program, 2009CB930601), National Natural Science Foundation of China (NSFC 60976019, 90813010), Program for New Century Excellent Talents in University (NCET-07-0446), Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP 20093223110002), and Scientific and Technological Innovation Teams of Colleges and Universities in Jiangsu Province (TJ207035, TJ208027). ’ REFERENCES (1) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550. (2) Tour, J. M. Acc. Chem. Res. 2000, 33, 791–804. (3) Park, J. E. A. Nature 2002, 417, 722–725. (4) Nitzan, A.; Ratner, M. A. Science 2003, 300, 1384–1389. (5) Salomon, A.; Cahen, D.; Lindsay, S.; Tomfohr, J.; Engelkes, V. B.; Frisbie, C. D. Adv. Mater. 2003, 15, 1881–1890. (6) Heath, J. R.; Stoddart, J. F.; Williams, R. S. Science 2004, 303, 1136–1137. (7) Wassel, R. A.; Gorman, C. B. Angew. Chem., Int. Ed. 2004, 43, 5120–5123. (8) Reed, M. A.; Zhou, C.; Muller, C. J.; Burgin, T. P.; Tour, J. M. Science 1997, 278, 252. (9) Halbritter, A.; Csonka, S.; Mihaly, G.; Jurdik, E.; Kolesnychenko, O. Y.; Shklyarevskii, O. I.; Speller, S.; van Kempen, H. Phys. Rev. B 2003, 68, No. 035417. (10) McCarty, G. S.; Weiss, P. S. Chem. Rev. 1999, 99, 1983–1990. (11) Talham, D. R. Chem. Rev. 2004, 104, 5479–5501. (12) Ulman, A. Chem. Rev. 1996, 96, 1533–1554. (13) Emberly, E. G.; Kirczenow, G. Phys. Rev. B 1998, 58, 10911. (14) Yaliraki, S. N.; Kemp, M.; Ratner, M. A. J. Am. Chem. Soc. 1999, 121, 3428–3434. (15) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Phys. Rev. Lett. 2000, 84, 979. (16) Seminario, J. M.; Zacarias, A. G.; Tour, J. M. J. Am. Chem. Soc. 2000, 122, 3015–3020. (17) Brandbyge, M.; Mozos, J.; Ordejon, P.; Taylor, J.; Stokbro, K. Phys. Rev. B 2002, 65, No. 165401. (18) Xue, Y.; Datta, S.; Ratner, M. A. Chem. Phys. 2002, 281, 151–170. (19) Taylor, J.; Brandbyge, M.; Stokbro, K. Phys. Rev. Lett. 2002, 89, No. 138301. (20) Stokbro, K.; Taylor, J.; Brandbyge, M.; Mozos, J.-L.; Ordejon, P. Comput. Mater. Sci. 2003, 27, 151–160. (21) Ke, S.; Baranger, H. U.; Yang, W. J. Am. Chem. Soc. 2004, 126, 15897–15904. (22) Galperin, M.; Ratner, M. A.; Nitzan, A. Nano Lett. 2005, 5, 125–130. (23) Staykov, A.; Nozaki, D.; Yoshizawa, K. J. Phys. Chem. C 2007, 111, 11699–11705.

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