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Effect of torsion angle on electronic transport through different anchoring groups in molecular junction
Physics Letters A 373 (2009) 3787–3794
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Effect of torsion angle on electronic transport through different anchoring groups in molecular junction Cai-Juan Xia a,b , Chang-Feng Fang a , Peng Zhao a , Shi-Jie Xie a , De-Sheng Liu a,c,∗ a b c
School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China School of Science, Xian Polytechnic University, Xian 710048, China Department of Physics, Jining University, Qufu 273155, China
a r t i c l e
i n f o
Article history: Received 1 April 2009 Received in revised form 17 July 2009 Accepted 6 August 2009 Available online 12 August 2009 Communicated by A.R. Bishop PACS: 85.65.+h 73.63.-b 31.15.Ar
a b s t r a c t By applying nonequilibrium Green’s function formalism combined with first-principles density functional theory, we investigate effect of torsion angle on electronic transport properties of 4,4 -biphenyl molecule connected with different anchoring groups (dithiocarboxylate and thiol group) to Au(111) electrodes. The influence of the HOMO–LUMO gaps and the spatial distributions of molecular orbitals on the quantum transport through the molecular device are discussed. Theoretical results show that the torsion angle plays important role in conducting behavior of molecular devices. By changing the torsion angle between two phenyl rings, namely changing the magnitude of the intermolecular coupling effect, a different transport behavior can be observed in these two systems. © 2009 Elsevier B.V. All rights reserved.
Keywords: Torsion angle Anchoring groups Electronic transport Molecular electronics
1. Introduction In recent years, molecular electronics is rapidly developing with experimental techniques, such as scanning tunneling microscope, mechanically controllable break junction, atomic force microscope, and creative fabricated techniques, which made it possible to measure and design different molecular devices [1–9]. Various kinds of novel physical properties, including single-electron characteristics, negative differential resistance (NDR), electrostatic current switching, memory effects, Kondo effects, etc., have been found in molecular devices [10–15]. In these experiments, gold was used as electrodes for electronic current and the molecules are connected to gold electrodes via thiol anchoring groups. However, Tulevski et al. report that thiol linkage is considered to be only structural and lacks any subsequent useful “chemistry”, because the energy and the electron occupation of the sulfur 3p orbital are difficult to modify, which made people turn their attentions to search for better molecule-gold linkers [16]. Recently,
*
Corresponding author at: School of Physics and Microelectronics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China. Fax: +86 531 88377031. E-mail address: [email protected] (D.-S. Liu). 0375-9601/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2009.08.016
Querner et al. suggest that molecules with carbodithioate (−CS2 ) groups may have superior chemisorption properties, because the distances of S–S are nearly ideal for adsorption on Au surfaces [17]. Furthermore, Tivanski et al. found that the conductance of 4,4 -biphenylbis (dithiocarboxylate) (BDCT) molecule is larger than that of 4,4 -biphenyl dithiolate (BDT) molecule [18]. The conformations of two molecules are nearly the same except that the anchoring groups are different. BDT has the standard thiol groups, and BDCT is connected to Au surface through dithiocarboxylate groups. They suggest that the conjugated dithiocarboxylate anchoring group provides stronger molecule-electrode coupling which is the mainly mechanism for conductance enhancement. Recently, Li et al. theoretically propose that this conductance enhancement is depended on both of the molecule-electrode coupling strengths and the disparity in the electronic structure of thiol and dithiocarboxylate anchoring groups by investigating the coplanar BDT and BDCT molecular junctions [19]. However, in a real experiment environment, the performance of a device also can be affected by external factors during operation. Therefore the structure of the molecular device, including the torsion angle, the length of molecular bonds, the site where molecule is bonded on the metal surface, etc., may be influenced by these factors which may also have effects on the electronic transport properties of a molecular device [20–25]. Therefore, it is also very important to understand the
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electronic transport of a molecular junction by study the molecular conformation [26–28]. Here, we extend the previous work of Li’s and use nonequilibrium Green’s function formalism combined first-principles calculations to investigate the effect of the torsion angles on the transport properties by changing the torsion angels between two phenyl rings. The influence of the HOMO–LUMO gaps and the spatial distributions of molecular orbitals on the quantum transport through the molecular device are discussed in detail. The calculated results show that the intermolecular interaction deeply depends on the torsion angles, and plays an important role in the electronic transport of molecular devices. 2. Model and method In this work, the structure of free thiol (SH) capped molecule wire was first optimized. In self-assembled monolayers experiment, it is generally accepted that H atom are dissociated upon adsorption to metal surfaces [29]. In order to investigate the current– voltage ( I–V ) behavior, we use Au(111) surface in a 4 × 4 unit cell as the electrodes and the optimized molecule wire is connected to Au(111) electrodes, as shown in the insets of Fig. 1. The structure of free thiol(SH) capped molecule wire was first optimized. Then the atomic structures of the molecule and the distance between two electrodes are also optimized. The optimized perpendicular distance between the sulfur atom and the Au(111) surface plane is 2.0 and 1.9 Å for BDT and BDCT, respectively. The Au(111) surface is represented by a 4 × 4 supercell with the periodic boundary conditions so that it imitates bulk metal structures. The 4 × 4 supercell is large enough to avoid any interaction with molecules in the next supercell [30,31]. In the present work, we consider the torsion angles effects on the electronic transport properties by keeping one benzene ring fixed and twisting the other benzene ring with different torsion angles related to the first ring. The free molecular geometrical optimizations and the electronic transport properties of molecular junctions are calculated by a fully self-consistent NEGF formalism combined with first-principles DFT, which is implemented in ATK2.0 package [32–34]. In NEGF theory, the molecular wire junction is divided into three regions: left electrode ( L ), contact region (C ), and right electrode ( R ). The contact region includes extended molecule and two layers of gold from each electrode. The contact region contains parts of the electrodes include the screening effects in the calculations. The semi-infinite electrodes are calculated separately to obtain the bulk self-energy. In our calculations, the exchange-correlation potential is described by Ceperley–Alder local-density approximation (LDA) [35]. Core electrons are modeled with Troullier–Martins nonlocal pseudopotential [36] and valence electrons expanded in a SIESTA localized basis set [37]. Single-zeta plus polarization (SZP) basis set for Au atoms and double-zeta plus polarization (DZP) basis set for other atoms are adopted. The current through a molecular junction is calculated from the Landauer–Bütiker formula [38]:
I (V ) = G 0
n( E ) T ( E , V ) dE ,
(1)
where G 0 = 2e 2 /h is the quantum unit of conductance, h the Planck’s constant, n( E ) the distribution function and T ( E , V ) the transmission coefficient for electrons with energy E for voltage V . Furthermore, n( E ) is written as
n( E ) = f ( E − μ L ) − f ( E − μ R ), where f is the Fermi function and tential of the left/right electrode.
(2)
μL / R the electrochemical po-
3. Results and discussion In Fig. 1, the transmission coefficient T ( E ) of BDCT and BDT (see Fig. 1(a)), and the partial density of states (PDOS) projected on the BDCT molecular junction (see Fig. 1(b)) as a function of the electronic energy for different torsion angles between two phenyl rings at zero bias are plotted. In our calculation, the average Fermi level, which is the average value of the chemical potential of the left and right electrodes, is set as zero. Seen from Eq. (2), we can expect that only electrons with energies within a range near the Fermi level E F contribute to the total current. Therefore, a approximation with the range of the “voltage window”, i.e., [− V /2, + V /2] is enough to analyze a finite part of the transmission spectrum. Furthermore, it is well known that the PDOS represents the discrete energy levels of the isolate molecule including the effects of energy shift and line broadening due to the molecule-electrodes coupling, i.e., the coupling between molecular orbitals and the incident states from the electrodes. It is clearly seen from Fig. 1 that the transmission is strongly correlated to PDOS spectra, which are shown the similar qualitative features, especially in the location of their peaks. The transmission spectra of two molecules display extraordinarily different characteristics. For BDT molecule, it can be found that the position of peak at the range of 1.0 eV ∼ 2.5 eV is shifted toward the higher energy with the degree of torsion angle increasing, but there is no obvious change in the value of peak at the range of −2.0 eV ∼ −1.5 eV until torsion angle is equal to 75◦ . By comparing BDCT with BDT, we can find that when the torsion angles are small, i.e., 0◦ , 15◦ and 30◦ , the differences of the transmission in BDCT are small too. But when the torsion angle is large enough, i.e., 45◦ , 60◦ , 75◦ and 90◦ , the peak near the Fermi Level become smaller but broader. Especially, when the torsion angle is equal to 90◦ , the peak near the Fermi energy nearly disappears. The transmission peak can be related with the molecular orbitals of the molecule, which has been modified by the electrodes. In Fig. 1(b), the occupied and unoccupied molecular orbitals (RMO) with the vertical solid lines at zero bias ( V b = 0) for BDCT are also plotted. It is clear that these RMOs correspond well to the transmission peaks. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of BDCT molecule keep away from Fermi Level step by step with the increase in torsion angle, namely the HOMO–LUMO gap gets bigger and bigger. Furthermore, it can be found in PDOS (see Fig. 1(b)) that with the torsion angle increasing, the molecule-electrode coupling of BDCT also becomes weaker and weaker. It is because the PDOS represents the discrete energy levels of the isolate molecule, including the effects of energy shift and line broadening due to the molecule-electrode coupling. To get a further insight, the molecular projected self-consistent Hamiltonian (MPSH) of system is analyzed. MPSH is the selfconsistent Hamiltonian of the isolated molecule in the presence of the electrodes, namely the molecular part is extracted from the whole self-consistent Hamiltonian at the contact region. It contains the molecule-electrode coupling effects because during the selfconsistent iteration, the electron density is for the contact region as a whole [39]. The spatial distribution of the MPSH states corresponding to the HOMO and LUMO of BDCT and BDT are presented in Fig. 2. For BDCT molecule, when the torsion angle is equal to 0◦ , i.e., the two phenyl rings are coplanar, there are four mainly orbitals contribute to electronic transport, including HOMO, LUMO, LUMO + 1 and LUMO + 3 [19]. But our calculations show that when the two phenyl rings is noncoplanar, the transport behavior is mainly determined by HOMO and LUMO, which are falling into the voltage window. Therefore, we only give the MPSH of the HOMO and LUMO for BDCT when the two phenyl rings is noncoplanar. It can be found from Fig. 2a1 –a3 and b1 –b3 that when the torsion angle is smaller than 45◦ , the HOMO and LUMO of BDCT
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(a)
(b) Fig. 1. (Color online.) (a) Transmission coefficient for different torsion angles in the range 0◦ to 90◦ in steps of 15◦ , (a1 ) BDCT (a2 ) BDT. (b) The partial density of states (PDOS) projected of BDCT for torsion angle to 0◦ , 30◦ , 60◦ and 90◦ , respectively.
are delocalized π orbital which overlaps between two phenyl rings and provides the main electronic transport channel for molecule under small bias voltages. Meanwhile there is a high density on each side of two sulfur atoms. But when the torsion angle is larger than 45◦ , the HOMO and LUMO become more and more localized π orbital, while the density also becomes lower and is localized at one side of the sulfur atoms (see Fig. 2a4 –a7 and b4 –b7 ). The density on two sulfur atoms means that there is much stronger molecule-electrode coupling when the torsion angle is equal to 0◦ , 15◦ and 30◦ . But when the torsion angle is equal to 45◦ , 60◦ , 75◦ and 90◦ , the effect of molecule-electrode coupling become weaker, which is corresponding to the lower PDOS peaks in Fig. 1(b). It also can be seen from Fig. 2 that MPSH of BDT are much different from that of BDCT as the torsion angle changing. Firstly, we can find that there is nearly no change in MPSH of BDT at the range of 0◦ ∼ 60◦ , because the deloclization on HOMO and LUMO are not changed at this range (see Fig. 2c1 –c5 and d1 –d5 ). Then when the torsion angle increases to 75◦ , the HOMO is still de-
localized, but the LUMO become localized (see Fig. 2c6 and d6 ). Finally, both of them become localized at 90◦ (see Fig. 2c7 and d7 ). It can be concluded that the change in MPSH of BDT molecule is not obvious with the torsion angle increasing. However, in BDCT molecule, when the torsion angle is larger than 30◦ , the HOMO and LUMO both become absolutely localized. These results indicate that the BDCT molecule is more sensitive to the change of torsion angle than that of BDT molecule. Furthermore, the electrostatic difference potential of different torsion angles are shown in Fig. 3. The molecular electrostatic potential is the potential energy of a proton at a particular location near a molecule. It can be clearly seen that the conjugated dithiocarboxylate anchoring group provides stronger electrostatic potential than thiol anchoring groups. But there is few obvious change with different torsion angles for both of them. Table 1 gives the conductance of BDCT and BDT at zero bias for different torsion angle between two phenyl rings. It can be clearly seen that there is an abrupt decrease in conductance for BDCT as
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Fig. 2. (Color online.) Orbitals of the MPSH. Plots a1 –a7 and b1 –b7 , c1 –c7 and d1 –d7 are the HOMO and LUMO respectively for BDCT and BDT molecule corresponding to the torsion angle is equal to 0◦ , 15◦ , 30◦ , 45◦ , 60◦ , 75◦ and 90◦ .
torsion angle twisting from 0◦ to 90◦ . Especially, when the torsion angle is equal to 90◦ , namely the two phenyl rings are perpendicular to each other, the conductance become minimum. These results indicate that the conductance of BDCT is strongly dependent on the torsion angle. Differing from BDCT, as there is no abrupt decrease in conductance, the change of conductance of BDT is small. These differences of conductance can be realized from the MPSH analysis (see Fig. 2). The localization/deloclization of a molecular
orbital induced by the torsion angle leads to the different changes in the conductance. Thus, the conductance of BDCT and BDT will both decrease with the torsion angle increasing, but the decrease of conductance of BDCT is more obvious. Finally, we calculate the I–V characteristic of BDCT and BDT under the biases of −1.5 V to 1.5 V, which are dependent on different torsion angle between two phenyl rings. It can be seen from Fig. 4 that these two systems are asymmetrical when the torsion
C.-J. Xia et al. / Physics Letters A 373 (2009) 3787–3794
(a) Fig. 3. (Color online.) The electrostatic difference potential of different torsion angles for BDCT and BDT.
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(b) Fig. 3. Continued.
Table 1 Conductance with different torsion angles. Molecule structure
Torsion angles
Conductance (μA)
0◦ 15◦ 30◦ 45◦ 60◦ 75◦ 90◦
8.35 8.32 6.75 4.87 3.52 1.32 0.27
0◦ 15◦ 30◦ 45◦ 60◦ 75◦ 90◦
60.12 58.32 43.15 18.96 8.15 1.92 0.32
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the MPSH analysis of BDT (see Fig. 2), because there is no obvious change in HOMO and LUMO which contribute to electronic transport. The similar characteristic in I–V curve can be found in dimolecule device composed of two 1,4 -dithiolbenzenes molecules through the thiol anchoring group connected to Au electrodes like BDT [39]. Therefore, we can conclude that molecule with dithiocarboxylate anchoring group is sensitive to the change of torsion angle between two phenyl rings, because the conformations of BDCT and BDT molecule are the same except their different anchoring groups. Namely the conductance enhancement of BDCT is not only dependent on the molecule-electrode coupling and the disparity in the electronic structure of dithiocarboxylate anchoring groups [18,19], but also strongly on the intermolecular coupling effect.
(a)
4. Summary In summary, the effect of the torsion angle on electronic transport has been numerically simulated using the DFT + NEGF firstprinciples method in BDCT and BDT molecular devices. We showed that the reason for the conductance enhancement was not simply the difference in the molecule-electrode coupling strengths but also in the intermolecular coupling effect. The torsion angle plays a critical role in determining the electronic transport of BDCT molecular device. The results will be helpful to understand further the possible situation in experiments and design molecular electronic devices with specific properties. Acknowledgements
(b) Fig. 4. (Color online.) The I–V curves for different torsion angles in molecular junctions, (a) BDCT (b) BDT.
angle exists, but this asymmetry in molecular conformation does not strongly affect the I–V characteristics of BDCT and BDT. Because there is just a little asymmetry in I–V curve both for BDCT and BDT when the torsion angle is not equal to zero (see Fig. 4). It also can be found that when the torsion angle is equal to 0◦ , i.e., the two phenyl rings are coplanar, the current of BDCT is 3 times larger than that of BDT. But changing the torsion angle between two phenyl rings, namely changing the magnitude of the intermolecular interaction, a different transport behavior can be found in these two systems. As shown in Fig. 4(a), when the torsion angle of BDCT is smaller than 30◦ , the differences in I–V curves are small too. With the torsion angle increasing, i.e., the torsion angle is larger than 30◦ , the current decreases obviously and reaches its minimum at 90◦ . The localization of a molecular orbital and low density on sulfur atoms will lead to the localization of electron in molecule, which tends to decrease the current. Therefore we give the MPSH of BDCT to analyze these changes in current (see Fig. 2). There is no obvious change in HOMO and LUMO when the torsion angle changes from 0◦ to 30◦ (Fig. 2a1 –a3 and b1 –b3 ), which is corresponding to the small differences in I–V curve at this range. However, when the torsion angle is equal to 45◦ , the HOMO is still delocalized, but the LUMO becomes localized and the density on sulfur atoms becomes lower (Fig. 2a4 and b4 ). Therefore, there is an abrupt decrease in current at 45◦ . As the torsion angle increasing from 60◦ to 90◦ , the HOMO and LUMO both become absolutely localized that result in a obvious decrease in current. Differing from BDCT, the current of BDT is not strongly dependent on the change of torsion angle. It also can be understood from
This work was supported by National Basic Research Program of China (Grant No. 2009CB929204), the National Natural Science Foundations of China (Grant Nos. 10874100, 10574082) the Education Department Foundation of Shaanxi Province, China (Grant No. 09JK461) and the Research Fund for the Doctoral Program (Grant No. BS0813). References [1] R.H.M. Smit, Y. Noat, C. Untiedt, N.D. Lang, M.C. van Hemert, J.M. van Ruitenbeek, Nature (London) 419 (2002) 906. [2] A.N. Pasupathy, R.C. Bialczak, J. Martinek, L.A.K. Donev, P.L. McEuen, D.C. Ralph, Science 306 (2004) 86. [3] S. Csonka, A. Halbritter, O.I. Shklyarevskii, S. Speller, H. van Kempen, Phys. Rev. Lett. 93 (2004) 016802. [4] S. Yasutomi, T. Morita, Y. Imanishi, S. Kimura, Science 304 (2004) 1944. [5] G.V. Nazin, X.H. Qiu, W. Ho, Science 302 (2003) 77. [6] B. Xu, N.J. Tao, Science 301 (2003) 1221. [7] J.O. Lee, et al., Nanoletter 3 (2003) 113. [8] X.D. Cui, A. Primak, X. Zarate, J. Tomfohr, O.T. Sankey, A.L. Moore, D. Gust, G. Harris, S.M. Lindsay, Science 294 (2001) 571. [9] J.G. Kushnerick, J. Naciri, J.C. Yang, R. Shashidhar, Nanoletter 3 (2003) 897. [10] J. Chen, M.A. Reed, A.M. Rawlett, J.M. Tour, Science 286 (1999) 1550. [11] N.P. Guisinger, R. Basu, A.S. Baluch, M.C. Hersam, Nanotechnology 15 (2004) 452. [12] D.I. Gittins, D. Bethell, D.J. Schiffrin, R.J. Nichols, Nature 408 (2000) 67. [13] Z.J. Donhauser, B.A. Mantooth, K.F. Kelly, L.A. Bumm, J.M. Tour, P.S. Weiss, Science 292 (2001) 2303. [14] J. Chen, M.A. Reed, Chem. Phys. 281 (2002) 127. [15] J. Park, A.N. Pasupathy, J.I. Goldsmith, C. Chang, Y. Yaish, J.R. Petta, M. Rinkoski, J.P. Sethna, H.D. Abruna, P.L. McEuen, D.C. Ralph, Nature 417 (2002) 722. [16] G.S. Tulevski, M.B. Myers, M.S. Hybertsen, M.L. Steigerwald, C. Nuckolls, Science 309 (2005) 591. [17] C. Querner, P. Reiss, J. Bleuse, A. Pron, J. Am. Chem. Soc. 126 (2004) 11574. [18] A.V. Tivanski, Y. He, E. Borguet, H. Liu, G.C. Walker, D.H. Waldeck, J. Phys. Chem. B 109 (2005) 5398. [19] Z. Li, D.S. Kosov, J. Phys. Chem. B 110 (2006) 19116. [20] Y. Luo, C.K. Wang, Y. Fu, J. Chem. Phys. 117 (2002) 10283. [21] C.K. Wang, Y. Luo, J. Chem. Phys. 119 (2003) 4923. [22] Z.F. Liu, K. Hashimoto, A. Fujishima, Nature 347 (1990) 658. [23] R.H. Mitchell, B.J. van Wees, J. Am. Chem. Soc. 125 (2003) 2974.
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[24] P. Zhao, C.F. Fang, C.J. Xia, D.S. Liu, S.J. Xie, Chem. Phys. Lett. 453 (2008) 62. [25] P. Zhao, C.F. Fang, C.J. Xia, D.S. Liu, S.J. Xie, Appl. Phys. Lett. 93 (2008) 013113. [26] F. Jiang, Y.X. Zhou, H. Chen, R. Note, H. Mizuseki, Y. Kawazoe, Phys. Lett. A 359 (2006) 487. [27] L. Venkataraman, J.E. Klare, C. Nuckolls, M.S. Hybertsen, M.L. Steigerwald, Nature 442 (2006) 904. [28] R. Pati, S.P. Karna, J. Chem. Phys. 115 (2001) 1703. [29] T. Vondrak, J.C. Cramer, X.Y. Zhu, J. Phys. Chem. B 103 (1999) 8915. [30] P.S. Damle, A.W. Ghosh, S. Datta, Phys. Rev. B 64 (2001) 201403. [31] B. Das, S.J. Abe, J. Phys. Chem. B 110 (2006) 4247. [32] J. Taylor, H. Guo, J. Wang, Phys. Rev. B 63 (2001) 245407.
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Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Effect of torsion angle on electronic transport through different anchoring groups in molecular junction Cai-Juan Xia a,b , Chang-Feng Fang a , Peng Zhao a , Shi-Jie Xie a , De-Sheng Liu a,c,∗ a b c
School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China School of Science, Xian Polytechnic University, Xian 710048, China Department of Physics, Jining University, Qufu 273155, China
a r t i c l e
i n f o
Article history: Received 1 April 2009 Received in revised form 17 July 2009 Accepted 6 August 2009 Available online 12 August 2009 Communicated by A.R. Bishop PACS: 85.65.+h 73.63.-b 31.15.Ar
a b s t r a c t By applying nonequilibrium Green’s function formalism combined with first-principles density functional theory, we investigate effect of torsion angle on electronic transport properties of 4,4 -biphenyl molecule connected with different anchoring groups (dithiocarboxylate and thiol group) to Au(111) electrodes. The influence of the HOMO–LUMO gaps and the spatial distributions of molecular orbitals on the quantum transport through the molecular device are discussed. Theoretical results show that the torsion angle plays important role in conducting behavior of molecular devices. By changing the torsion angle between two phenyl rings, namely changing the magnitude of the intermolecular coupling effect, a different transport behavior can be observed in these two systems. © 2009 Elsevier B.V. All rights reserved.
Keywords: Torsion angle Anchoring groups Electronic transport Molecular electronics
1. Introduction In recent years, molecular electronics is rapidly developing with experimental techniques, such as scanning tunneling microscope, mechanically controllable break junction, atomic force microscope, and creative fabricated techniques, which made it possible to measure and design different molecular devices [1–9]. Various kinds of novel physical properties, including single-electron characteristics, negative differential resistance (NDR), electrostatic current switching, memory effects, Kondo effects, etc., have been found in molecular devices [10–15]. In these experiments, gold was used as electrodes for electronic current and the molecules are connected to gold electrodes via thiol anchoring groups. However, Tulevski et al. report that thiol linkage is considered to be only structural and lacks any subsequent useful “chemistry”, because the energy and the electron occupation of the sulfur 3p orbital are difficult to modify, which made people turn their attentions to search for better molecule-gold linkers [16]. Recently,
*
Corresponding author at: School of Physics and Microelectronics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China. Fax: +86 531 88377031. E-mail address: [email protected] (D.-S. Liu). 0375-9601/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2009.08.016
Querner et al. suggest that molecules with carbodithioate (−CS2 ) groups may have superior chemisorption properties, because the distances of S–S are nearly ideal for adsorption on Au surfaces [17]. Furthermore, Tivanski et al. found that the conductance of 4,4 -biphenylbis (dithiocarboxylate) (BDCT) molecule is larger than that of 4,4 -biphenyl dithiolate (BDT) molecule [18]. The conformations of two molecules are nearly the same except that the anchoring groups are different. BDT has the standard thiol groups, and BDCT is connected to Au surface through dithiocarboxylate groups. They suggest that the conjugated dithiocarboxylate anchoring group provides stronger molecule-electrode coupling which is the mainly mechanism for conductance enhancement. Recently, Li et al. theoretically propose that this conductance enhancement is depended on both of the molecule-electrode coupling strengths and the disparity in the electronic structure of thiol and dithiocarboxylate anchoring groups by investigating the coplanar BDT and BDCT molecular junctions [19]. However, in a real experiment environment, the performance of a device also can be affected by external factors during operation. Therefore the structure of the molecular device, including the torsion angle, the length of molecular bonds, the site where molecule is bonded on the metal surface, etc., may be influenced by these factors which may also have effects on the electronic transport properties of a molecular device [20–25]. Therefore, it is also very important to understand the
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electronic transport of a molecular junction by study the molecular conformation [26–28]. Here, we extend the previous work of Li’s and use nonequilibrium Green’s function formalism combined first-principles calculations to investigate the effect of the torsion angles on the transport properties by changing the torsion angels between two phenyl rings. The influence of the HOMO–LUMO gaps and the spatial distributions of molecular orbitals on the quantum transport through the molecular device are discussed in detail. The calculated results show that the intermolecular interaction deeply depends on the torsion angles, and plays an important role in the electronic transport of molecular devices. 2. Model and method In this work, the structure of free thiol (SH) capped molecule wire was first optimized. In self-assembled monolayers experiment, it is generally accepted that H atom are dissociated upon adsorption to metal surfaces [29]. In order to investigate the current– voltage ( I–V ) behavior, we use Au(111) surface in a 4 × 4 unit cell as the electrodes and the optimized molecule wire is connected to Au(111) electrodes, as shown in the insets of Fig. 1. The structure of free thiol(SH) capped molecule wire was first optimized. Then the atomic structures of the molecule and the distance between two electrodes are also optimized. The optimized perpendicular distance between the sulfur atom and the Au(111) surface plane is 2.0 and 1.9 Å for BDT and BDCT, respectively. The Au(111) surface is represented by a 4 × 4 supercell with the periodic boundary conditions so that it imitates bulk metal structures. The 4 × 4 supercell is large enough to avoid any interaction with molecules in the next supercell [30,31]. In the present work, we consider the torsion angles effects on the electronic transport properties by keeping one benzene ring fixed and twisting the other benzene ring with different torsion angles related to the first ring. The free molecular geometrical optimizations and the electronic transport properties of molecular junctions are calculated by a fully self-consistent NEGF formalism combined with first-principles DFT, which is implemented in ATK2.0 package [32–34]. In NEGF theory, the molecular wire junction is divided into three regions: left electrode ( L ), contact region (C ), and right electrode ( R ). The contact region includes extended molecule and two layers of gold from each electrode. The contact region contains parts of the electrodes include the screening effects in the calculations. The semi-infinite electrodes are calculated separately to obtain the bulk self-energy. In our calculations, the exchange-correlation potential is described by Ceperley–Alder local-density approximation (LDA) [35]. Core electrons are modeled with Troullier–Martins nonlocal pseudopotential [36] and valence electrons expanded in a SIESTA localized basis set [37]. Single-zeta plus polarization (SZP) basis set for Au atoms and double-zeta plus polarization (DZP) basis set for other atoms are adopted. The current through a molecular junction is calculated from the Landauer–Bütiker formula [38]:
I (V ) = G 0
n( E ) T ( E , V ) dE ,
(1)
where G 0 = 2e 2 /h is the quantum unit of conductance, h the Planck’s constant, n( E ) the distribution function and T ( E , V ) the transmission coefficient for electrons with energy E for voltage V . Furthermore, n( E ) is written as
n( E ) = f ( E − μ L ) − f ( E − μ R ), where f is the Fermi function and tential of the left/right electrode.
(2)
μL / R the electrochemical po-
3. Results and discussion In Fig. 1, the transmission coefficient T ( E ) of BDCT and BDT (see Fig. 1(a)), and the partial density of states (PDOS) projected on the BDCT molecular junction (see Fig. 1(b)) as a function of the electronic energy for different torsion angles between two phenyl rings at zero bias are plotted. In our calculation, the average Fermi level, which is the average value of the chemical potential of the left and right electrodes, is set as zero. Seen from Eq. (2), we can expect that only electrons with energies within a range near the Fermi level E F contribute to the total current. Therefore, a approximation with the range of the “voltage window”, i.e., [− V /2, + V /2] is enough to analyze a finite part of the transmission spectrum. Furthermore, it is well known that the PDOS represents the discrete energy levels of the isolate molecule including the effects of energy shift and line broadening due to the molecule-electrodes coupling, i.e., the coupling between molecular orbitals and the incident states from the electrodes. It is clearly seen from Fig. 1 that the transmission is strongly correlated to PDOS spectra, which are shown the similar qualitative features, especially in the location of their peaks. The transmission spectra of two molecules display extraordinarily different characteristics. For BDT molecule, it can be found that the position of peak at the range of 1.0 eV ∼ 2.5 eV is shifted toward the higher energy with the degree of torsion angle increasing, but there is no obvious change in the value of peak at the range of −2.0 eV ∼ −1.5 eV until torsion angle is equal to 75◦ . By comparing BDCT with BDT, we can find that when the torsion angles are small, i.e., 0◦ , 15◦ and 30◦ , the differences of the transmission in BDCT are small too. But when the torsion angle is large enough, i.e., 45◦ , 60◦ , 75◦ and 90◦ , the peak near the Fermi Level become smaller but broader. Especially, when the torsion angle is equal to 90◦ , the peak near the Fermi energy nearly disappears. The transmission peak can be related with the molecular orbitals of the molecule, which has been modified by the electrodes. In Fig. 1(b), the occupied and unoccupied molecular orbitals (RMO) with the vertical solid lines at zero bias ( V b = 0) for BDCT are also plotted. It is clear that these RMOs correspond well to the transmission peaks. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of BDCT molecule keep away from Fermi Level step by step with the increase in torsion angle, namely the HOMO–LUMO gap gets bigger and bigger. Furthermore, it can be found in PDOS (see Fig. 1(b)) that with the torsion angle increasing, the molecule-electrode coupling of BDCT also becomes weaker and weaker. It is because the PDOS represents the discrete energy levels of the isolate molecule, including the effects of energy shift and line broadening due to the molecule-electrode coupling. To get a further insight, the molecular projected self-consistent Hamiltonian (MPSH) of system is analyzed. MPSH is the selfconsistent Hamiltonian of the isolated molecule in the presence of the electrodes, namely the molecular part is extracted from the whole self-consistent Hamiltonian at the contact region. It contains the molecule-electrode coupling effects because during the selfconsistent iteration, the electron density is for the contact region as a whole [39]. The spatial distribution of the MPSH states corresponding to the HOMO and LUMO of BDCT and BDT are presented in Fig. 2. For BDCT molecule, when the torsion angle is equal to 0◦ , i.e., the two phenyl rings are coplanar, there are four mainly orbitals contribute to electronic transport, including HOMO, LUMO, LUMO + 1 and LUMO + 3 [19]. But our calculations show that when the two phenyl rings is noncoplanar, the transport behavior is mainly determined by HOMO and LUMO, which are falling into the voltage window. Therefore, we only give the MPSH of the HOMO and LUMO for BDCT when the two phenyl rings is noncoplanar. It can be found from Fig. 2a1 –a3 and b1 –b3 that when the torsion angle is smaller than 45◦ , the HOMO and LUMO of BDCT
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(a)
(b) Fig. 1. (Color online.) (a) Transmission coefficient for different torsion angles in the range 0◦ to 90◦ in steps of 15◦ , (a1 ) BDCT (a2 ) BDT. (b) The partial density of states (PDOS) projected of BDCT for torsion angle to 0◦ , 30◦ , 60◦ and 90◦ , respectively.
are delocalized π orbital which overlaps between two phenyl rings and provides the main electronic transport channel for molecule under small bias voltages. Meanwhile there is a high density on each side of two sulfur atoms. But when the torsion angle is larger than 45◦ , the HOMO and LUMO become more and more localized π orbital, while the density also becomes lower and is localized at one side of the sulfur atoms (see Fig. 2a4 –a7 and b4 –b7 ). The density on two sulfur atoms means that there is much stronger molecule-electrode coupling when the torsion angle is equal to 0◦ , 15◦ and 30◦ . But when the torsion angle is equal to 45◦ , 60◦ , 75◦ and 90◦ , the effect of molecule-electrode coupling become weaker, which is corresponding to the lower PDOS peaks in Fig. 1(b). It also can be seen from Fig. 2 that MPSH of BDT are much different from that of BDCT as the torsion angle changing. Firstly, we can find that there is nearly no change in MPSH of BDT at the range of 0◦ ∼ 60◦ , because the deloclization on HOMO and LUMO are not changed at this range (see Fig. 2c1 –c5 and d1 –d5 ). Then when the torsion angle increases to 75◦ , the HOMO is still de-
localized, but the LUMO become localized (see Fig. 2c6 and d6 ). Finally, both of them become localized at 90◦ (see Fig. 2c7 and d7 ). It can be concluded that the change in MPSH of BDT molecule is not obvious with the torsion angle increasing. However, in BDCT molecule, when the torsion angle is larger than 30◦ , the HOMO and LUMO both become absolutely localized. These results indicate that the BDCT molecule is more sensitive to the change of torsion angle than that of BDT molecule. Furthermore, the electrostatic difference potential of different torsion angles are shown in Fig. 3. The molecular electrostatic potential is the potential energy of a proton at a particular location near a molecule. It can be clearly seen that the conjugated dithiocarboxylate anchoring group provides stronger electrostatic potential than thiol anchoring groups. But there is few obvious change with different torsion angles for both of them. Table 1 gives the conductance of BDCT and BDT at zero bias for different torsion angle between two phenyl rings. It can be clearly seen that there is an abrupt decrease in conductance for BDCT as
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Fig. 2. (Color online.) Orbitals of the MPSH. Plots a1 –a7 and b1 –b7 , c1 –c7 and d1 –d7 are the HOMO and LUMO respectively for BDCT and BDT molecule corresponding to the torsion angle is equal to 0◦ , 15◦ , 30◦ , 45◦ , 60◦ , 75◦ and 90◦ .
torsion angle twisting from 0◦ to 90◦ . Especially, when the torsion angle is equal to 90◦ , namely the two phenyl rings are perpendicular to each other, the conductance become minimum. These results indicate that the conductance of BDCT is strongly dependent on the torsion angle. Differing from BDCT, as there is no abrupt decrease in conductance, the change of conductance of BDT is small. These differences of conductance can be realized from the MPSH analysis (see Fig. 2). The localization/deloclization of a molecular
orbital induced by the torsion angle leads to the different changes in the conductance. Thus, the conductance of BDCT and BDT will both decrease with the torsion angle increasing, but the decrease of conductance of BDCT is more obvious. Finally, we calculate the I–V characteristic of BDCT and BDT under the biases of −1.5 V to 1.5 V, which are dependent on different torsion angle between two phenyl rings. It can be seen from Fig. 4 that these two systems are asymmetrical when the torsion
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(a) Fig. 3. (Color online.) The electrostatic difference potential of different torsion angles for BDCT and BDT.
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(b) Fig. 3. Continued.
Table 1 Conductance with different torsion angles. Molecule structure
Torsion angles
Conductance (μA)
0◦ 15◦ 30◦ 45◦ 60◦ 75◦ 90◦
8.35 8.32 6.75 4.87 3.52 1.32 0.27
0◦ 15◦ 30◦ 45◦ 60◦ 75◦ 90◦
60.12 58.32 43.15 18.96 8.15 1.92 0.32
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the MPSH analysis of BDT (see Fig. 2), because there is no obvious change in HOMO and LUMO which contribute to electronic transport. The similar characteristic in I–V curve can be found in dimolecule device composed of two 1,4 -dithiolbenzenes molecules through the thiol anchoring group connected to Au electrodes like BDT [39]. Therefore, we can conclude that molecule with dithiocarboxylate anchoring group is sensitive to the change of torsion angle between two phenyl rings, because the conformations of BDCT and BDT molecule are the same except their different anchoring groups. Namely the conductance enhancement of BDCT is not only dependent on the molecule-electrode coupling and the disparity in the electronic structure of dithiocarboxylate anchoring groups [18,19], but also strongly on the intermolecular coupling effect.
(a)
4. Summary In summary, the effect of the torsion angle on electronic transport has been numerically simulated using the DFT + NEGF firstprinciples method in BDCT and BDT molecular devices. We showed that the reason for the conductance enhancement was not simply the difference in the molecule-electrode coupling strengths but also in the intermolecular coupling effect. The torsion angle plays a critical role in determining the electronic transport of BDCT molecular device. The results will be helpful to understand further the possible situation in experiments and design molecular electronic devices with specific properties. Acknowledgements
(b) Fig. 4. (Color online.) The I–V curves for different torsion angles in molecular junctions, (a) BDCT (b) BDT.
angle exists, but this asymmetry in molecular conformation does not strongly affect the I–V characteristics of BDCT and BDT. Because there is just a little asymmetry in I–V curve both for BDCT and BDT when the torsion angle is not equal to zero (see Fig. 4). It also can be found that when the torsion angle is equal to 0◦ , i.e., the two phenyl rings are coplanar, the current of BDCT is 3 times larger than that of BDT. But changing the torsion angle between two phenyl rings, namely changing the magnitude of the intermolecular interaction, a different transport behavior can be found in these two systems. As shown in Fig. 4(a), when the torsion angle of BDCT is smaller than 30◦ , the differences in I–V curves are small too. With the torsion angle increasing, i.e., the torsion angle is larger than 30◦ , the current decreases obviously and reaches its minimum at 90◦ . The localization of a molecular orbital and low density on sulfur atoms will lead to the localization of electron in molecule, which tends to decrease the current. Therefore we give the MPSH of BDCT to analyze these changes in current (see Fig. 2). There is no obvious change in HOMO and LUMO when the torsion angle changes from 0◦ to 30◦ (Fig. 2a1 –a3 and b1 –b3 ), which is corresponding to the small differences in I–V curve at this range. However, when the torsion angle is equal to 45◦ , the HOMO is still delocalized, but the LUMO becomes localized and the density on sulfur atoms becomes lower (Fig. 2a4 and b4 ). Therefore, there is an abrupt decrease in current at 45◦ . As the torsion angle increasing from 60◦ to 90◦ , the HOMO and LUMO both become absolutely localized that result in a obvious decrease in current. Differing from BDCT, the current of BDT is not strongly dependent on the change of torsion angle. It also can be understood from
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