Gate Control of Artificial Single-Molecule Electric Machines - The

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Gate Control of Artificial Single-Molecule Electric Machines Liang-Yan Hsu, Chun-Yin Chen, Elise Y. Li, and Herschel A. Rabitz J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511941w • Publication Date (Web): 09 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Gate Control of Artificial Single-Molecule Electric Machines Liang-Yan Hsu,∗,† Chun-Yin Chen,‡ Elise Y. Li,∗,‡ and Herschel Rabitz∗,† Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States, and Department of Chemistry, National Taiwan Normal University, Taipei 11677, Taiwan E-mail: [email protected]; [email protected]; [email protected]

∗ To

whom correspondence should be addressed of Chemistry, Princeton University, Princeton, New Jersey 08544, United States ‡ Department of Chemistry, National Taiwan Normal University, Taipei 11677, Taiwan † Department

1 ACS Paragon Plus Environment


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Abstract Artificial molecular machines are a growing field in nanoscience and nanotechnology. This study proposes a new class of artificial molecular machines, the second-generation singlemolecule electric revolving doors (2G S-MERDs), a direct extension of our previous work [L.-Y. Hsu, E.-Y. Li, and H. Rabitz, Nano Lett. 13, 5020 (2013)]. We investigate destructive quantum interference with tunneling and conductance dependence upon molecular conformation in the 2G S-MERDs by using the Green’s function method together with density functional theory. The simulations with four types of functionals (PBE, PZ, PW91, and BLYP) show that the 2G S-MERDs have a large on-off conductance ratio (> 104 ), and that their open and closed door states can be operated by an experimentally feasible external electric field (∼ 1 V/nm). In addition, the simulations indicate that the potential energy difference between the open and closed states of the S-MERDs can be engineered. Conductance - gate electric field characteristics are also introduced to illustrate the operation of the 2G S-MERDs.

KEYWORDS: molecular machine, molecular electronics, quantum transport, conductance, molecular switch, density-functional theory.


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Artificial molecular machines (AMMs) – synthetic compounds capable of mechanical motions – have attracted considerable attention in nanoscience and synthetic chemistry during the past two decades. The design of the AMMs often draws inspiration from macroscopic devices such as rotors, 1–8 cars, 9,10 turnstiles, 11–13 motors, 14 revolving doors, 15 elevators, 16 shuttles, 17,18 as well as human muscles. 19,20 Powered by light, 1–3 heat, 9 or chemical reactions, 12,13,16,17,19,20 the AMMs could function as switching devices and perform specific tasks, and their states can be detected via electrochemical 16,17,19 or spectroscopic means. 1–3 Recently, a new class of AMMs – singlemolecule electric machinery – has been put forward including surface rotors, 21 electric motors 14 and single-molecule electric revolving doors (S-MERDs). 15 Amongst them, the electric motors and S-MERDs have similar basic architectures, for example, they consist of three components (stators, axles, and rotors) and are operated by a gate. However, until now, the electric motors and S-MERDs have not been experimentally realized. Potential challenges include difficulty aligning two separate stators into a coplanar configuration, making it hard to detect the conductance variation. 14 Or in other cases, the control may involve a strong electric field, e.g., E ∼ = 1.5 – 2.0 V/nm, resulting in possible current leakage through the gate. 15 To address these issues, we propose two improved S-MERDs, as shown in Figure 1(a), based on our previous design. 15 The operating principles of these second-generation S-MERDs (2G S-MERDs) are illustrated by the transmission function, conductance variation with respect to the twist angle, as well as conductance dependence on a gate electric field.

As shown in Figure 1(a), the 2G S-MERD is a composite system. Molecule M1 or M2, with the structure of a phenyl-acetylene macrocycle (PAM) chopped in half, is coupled to two electrodes (a source and a drain), and can be operated by a gate electrode. Electrons flow in from the source, pass through the molecule, and arrive at the drain, giving rise to an electric current. Similar to most AMMs, M1 and M2 are composed of three components: stators, axles, and rotors. For example, the outer half ring is stationary and lies parallel to the gate, corresponding to a stator, while the inner plate rotates around the triple-bond axles, corresponding to a rotor.



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Different from traditional AMMs, the central concept of the S-MERDs is “an all-electric singlemolecule machine” – the closed and the open door states of the S-MERDs are (I) controlled by an electric field and (II) detected by the variation of conductance (currents). The closed (open) door states of M1 and M2, as shown in Figure 1(b), is formed when the inner plate rotates to a coplanar (perpendicular) orientation, relative to the outer half ring. The door states can be manipulated by a gate electric field via the electric-dipole interaction, i.e., the gate electric field enables the opening (closing) of the door.

The conductance variation of the S-MERDs originates from molecular conformational change combined with destructive quantum interference. Conductance dependence upon molecular conformation has been experimentally 22–24 and theoretically investigated 25–27 during the past few years, e.g., the conductance g with respect to the twist angle θ between the two phenyl rings in π conjugated biphenyl systems scales as g ∼ cos2 θ . 22–24 Recent theoretical reports show a scaling as g ∼ cos4 θ in first generation S-MERDs (1G S-MERDs) 15 and in electric motors. 14 Note that the basic structure of S-MERDs and electric motors are different. In particular, the 1G S-MERD has an outer ring as a stator while the electric motor has two anchoring groups as two stators. Therefore, the conductance variation of the electric motor is sensitive to the relative orientation between the two stators, leading to difficulties in experimental setup and characterization of g ∼ cos4 θ . In order to avoid this problem, the 1G S-MERD incorporates a bridge connected to two stators forming the outer ring. The outer ring is an excellent insulator since the meta-benzene connections lead to strong destructive quantum interference with tunneling, so electrons cannot pass through the outer ring. 28–32 The only pathway electrons can flow through is via the inner aromatic plate, which is connected to the benzene units on both sides in the conductive para-orientation, when it is coplanar with the outer ring. In the absence of the gate electric field, the coplanar configuration is more stable than the perpendicular configuration due to the large domain of π -electron conjugation. Thus, the opening of the door state requires an applied electric field. For 1G S-MERDs, the


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energy barrier between the coplanar and the perpendicular configurations is about 170 meV, which requires a gate field of up to E ∼ = 1.5 – 2.0 V/nm in order to rotate the inner plate. With the aim of reducing the π -electron conjugation (i.e., reducing the energy barrier between two configurations and lowering the operational field strength), we chop the phenyl-acetylene macrocycles in half in the 2G S-MERDs, and explore whether the door states can be operated with a smaller external electric field. Furthermore, to enhance the rigidity of the outer half ring, we added one additional benzene unit, forming a triangle motif as in M2, and we will investigate if such structural modifications have any effect on the transmission profile.

To demonstrate the operation of the 2G S-MERD, we adopt the Landauer formula in the framework of density functional theory. Note that the current theoretical analysis only holds in the coherent elastic tunneling regime or for molecules with short chain length 33,34 as well as large injection gaps since they have a short Landauer-Büttiker tunneling time. 35,36 In the zero-bias limit, the conductance is proportional to the transmission function of the system at the Fermi level, 37,38 2

G = 2eh T (EF ). The zero-bias transmission function is derived from the retarded (advanced) molecular Green’s function GR(A) mol (E) and the molecule-electrode coupling function for the left (right) A electrode ΓL(R) , i.e., T (EF ) = Tr(ΓL (EF )GR mol (EF )ΓR (EF )Gmol (EF )). The molecular Green’s

functions of the H-terminated M1 and M2 are obtained from the density-functional method in a maximally-localized Wannier function (MLWF) representation 39,40 using the Quantum-ESPRESSO distribution 41 and the Wannier90 39 code. For the electrodes we adopt the wide-band-limit (WBL) approximation, which is appropriate as long as the electron density of states in the electrodes remains relatively flat around the Fermi level. 32 The metal-WBL approach has been shown to give similar and comparable results with Post-SCF and Full-SCF approaches for aromatic molecules at zero bias. 42 The WBL approximation allows the self-energy of the electrodes to be represented by a γL(R) |αL(R) ihαL(R) |, where |αL(R) i is the constant imaginary number and takes the form ΣL(R) = −i 2 pz orbital of the carbon atom linked to the left (right) electrode. Here we set the coupling constant

γL(R) to be 0.5 eV, following typical estimates from other studies. 28,31 The use of a MLWF rep-



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(a)

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Figure 1: (a) Illustration of a 2G S-MERD. Molecules M1 and M2 are linked to the source and the drain via two contact atoms A. To facilitate the theoretical analysis, we study hydrogen terminated molecules. 15 The 2G S-MERD includes a frame (the outer half ring), two axles (the triple bonds), and a door (the inner plate). The outer half rings (red part) of molecules M1 and M2 are assumed to be parallel to the gate electrode, and the inner plate (green part) can rotate along the axles. (b) The open and closed door state and their corresponding molecular geometries.


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resentation may become more advantageous than other localized basis sets (e.g. a Gaussian basis set that includes many polarization and diffuse functions for a single atom) in that it identifies the optimal |αL(R) i projector basis coupled to the electrodes so that one can single out the π -electron from σ -electron contribution to electron transport. 43 Note that in the current WBL approximation we only consider the coupling between the left (right) electrode and the pz orbital of the carbon connected to the contact atom, i.e., the transmission originates purely from π -electrons. As for the effects of σ -electrons on transmission, previous studies have confirmed that the transmission contribution from σ -electrons can be neglected in aromatic systems. 15 General computational details can be found in the supporting information regarding the functional and the basis set used in geometry optimizations and electron transport calculations.

The transmission spectra for M1 and M2 in the absence of the gate electric field within the WBL approximation are shown in Fig 2, in which the transmission dips and peaks correspond to the antiresonant and resonant states of a tunneling electron, respectively. 29,44 As the molecules and the two electrodes are not strongly coupled, the position of the transmission peaks correspond to molecular orbitals of isolated H-terminated molecules (see the supporting information), e.g., the peaks at −0.7 and 0.7 eV below and above the Fermi level corresponding to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the closed door state of M1. Note that we assume that the Fermi level of the electrodes lies at the mid-gap between the HOMO and LUMO. For the closed door states of M1 and M2 (the solid lines), we observe that the transmission between the HOMO and LUMO almost coincide with each other, indicating that the tunneling electrons mainly pass through the inner plate so the geometry changes of the outer half ring do not influence the transmission. The MO amplitudes on the contact atoms and their nearest-neighbor carbons in M1 and M2 also support our observation. 44 On the other hand, the open door states of M1 and M2 (the dashed lines) exhibit a wide range of transmission suppression in the window from −0.8 eV to 1.4 eV and −0.6 eV to 0.9 eV, respectively. Moreover, between −0.6 eV to 0.7 eV the transmission dramatically drops down below 10−6 , and



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Figure 2: The transmission spectra of M1 (the blue line) and M2 (the green line) with the closed (the solid line) or open door state (the dashed line) in the absence of the gate electric field, where the abscissa is the energy of the tunneling electron with respect to the Fermi level. at the Fermi level the transmission even decreases to 10−7 − 10−8 . This phenomenon originates from destructive quantum interference for tunneling through the meta-benzene connections in the outer half ring. 28–32 The main transport characteristics of the open door state between the HOMO and LUMO are not affected when the outer stator is rendered asymmetric (the phenyl-acetylene macrocycle chopped in half) or when an extra benzene unit is attached to the outer ring (the extra triangular motif in the outer stator of M2) – that is, the chemical modification of the outer ring does not change the extremely small transmission of the open door states. In either M1 or M2, the transmission of the closed door state is ∼ 10−3 while the transmission of the open door state is ∼ 10−7 − 10−8 , indicating that M1 and M2 may serve as good switching devices. Note that the main characteristics in the transmission spectra for M1 and M2 are less sensitive to the range of experimentally feasible field strength, although the transmission function can be altered via the gate electric field. (see Fig. S5 in the supporting information).

To demonstrate how to switch the closed and open door states of the 2G S-MERDs via the ex8 ACS Paragon Plus Environment

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ternal electric field, we calculate the potential energy of M1 and M2 at different field strengths in the framework of density-functional theory in the Perdew-Burke-Ernzerhof generalized-gradient approximation (PBE-GGA) with plane wave basis sets. Additionally, in order to obtain the potential energy profile with respect to the twist angle between the inner rotor and outer stator, we adopt a rigid rotor approximation and compute the energy of this twisted conformation without further geometry optimization. That is, first, the molecule is fully relaxed to its planar configuration (the most stable) in the absence of the gate electric field. Second, the inner rotor as a whole (a rigid body) is rotated to an angle (from 0 to 90 degrees) with respect to the outer ring while the outer ring remains stationary. Third, we calculate the potential energy at different field strengths. Figure 3(a) and (c) show the potential energy of M1 and M2 at different field strengths, respectively. In the absence of the gate electric field, the potential energy surface calculation confirms that the closed door state is the most stable conformation in an isolated M1 or M2 molecule. Both M1 and M2 exhibit nearly the same energy difference between the closed and open door states, indicating that the structural modification on the outer ring does not influence the potential energy barrier between the two states. Furthermore, the potential energy barrier in M1 and M2 is ∼ 120 meV, smaller than that in the 1G S-MERD (∼ 170 meV). This result implies that the 2G S-MERDs may possibly be operated in a smaller gate electric field, and it is feasible to engineer the potential energy difference between the open and closed door states of S-MERDs by changing the area of π -conjugation. The reduction in the area of π -conjugation can decrease the energy difference between the open and closed door states. Figure 3 clearly shows that as soon as the field increases to 0.5 V/nm, the tilted conformations with a twist angle between −35◦ and −45◦ become more stable than the coplanar configurations. At the field strength ∼ 1.5 – 2.0 V/nm, the potential energy curve of M1 (M2) reaches the highest and the lowest values at the 90◦ and −90◦ , which correspond to the parallel and the anti-parallel dipole moment alignment, respectively, of the inner anthracene rotor with the gate electric field. Moreover, when the field strength is 1 V/nm, 1.5 V/nm, or 2.0 V/nm (the blue, black, and light blue curves), Figure 3(a) shows that the energy differences between −90◦ and 0◦ are up to 136, 279, and 433 meV, respectively, indicating that the open and closed door states



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cannot easily transform into each other when the gate electric field is greater than 1 V/nm.

Figure 3(b) and (d) show the conductance at the Fermi level of M1 and M2, respectively, in zero or a gate electric field of 2.0 V/nm. All curves show the same characteristics: the conductance decreases gradually from the closed door state to the open door state (90◦ or −90◦ ) and the conductance curve is insensitive to the gate electric field or the chemical modification on the outer half ring. Similar to the previous studies, 14 the conductance G shows a cos4 θ relationship, confirmed by the least square fitting (cos4 θ results from the fact that the π -orbitals of the anthracene rotor overlap with those of the naphthalene units on both sides). Note that when the twist angle becomes 90◦ or −90◦ , the conductance does not reach zero since the σ -orbitals are involved in the tunneling process. As shown by Figure 3(a) and (c), the relatively flat potential energy curve between −90◦ and −60◦ indicates that the open-door state may be easily influenced by thermal fluctuations. For example, at the field strength 1.5 V/nm, the energy difference between −90◦ and −60◦ is ∼ 18 meV, which is smaller than kT ∼ 26 meV at room temperature. Even in such cases, the estimated conductance ratio between the 0◦ to −60◦ conformation using G ∝ cos4 θ is still as large as 16 (The first-principle calculation shows approximately 17 in a zero field and 18 in a gate electric field of 2.0 V/nm.). This result implies that the on-off switching ratio of the 2G S-MERD is at least up to 16 times even if the flat potential energy between −90◦ to −60◦ leads to a swing of the inner rotor.

The operation of the 2G S-MERDs can be more straight-forwardly represented by the conductance - gate voltage characteristics, which are extensively used in modern microelectronics to study the electron transport properties of metal-oxide-semiconductor field effect transistors. 45 To explore the conductance - gate voltage characteristics, we performed geometry optimization of M2 at varying gate electric fields, and computed the conductance at the Fermi level of M2 based on its minimum energy structure at varying gate electric fields. Figure 4 shows the conductance dependence on the gate electric field for M2. The conductance decreases with increasing gate electric field and drops dramatically to ∼ 10−8 GQ at 1.25 V/nm, when the door is completely open. The


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Figure 3: (a) (c) The potential energy curve profile of M1 (left panel) and M2 (right panel) at different gate electric field strengths and (b)(d) the conductance at the Fermi level of M1 (left panel) and M2 (right panel) in the absence of a gate electric field or E = 2.0 V/nm (0.2V/Å), versus the twist angle between the inner rotor and outer stator. The zero value of the potential energy is assigned to the flat configuration (0 degree) of M1 (M2) for each curve. GQ = 2e2 /h is the so-called conductance quantum. The complete overlapping conductance curves in the absence or presence of the electric field demonstrates that the gate electric field does not have a significant influence on the conductance variation with respect to the twist angle.


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electric field (V/nm) Figure 4: Conductance – gate electric field characteristics of M2: the conductance of the minimum energy structure of M2 at different field strength plotted against the applied gate field. conductance ratio upon going from 0 to 1.25 V/nm is up to 104 –105 , indicating that M2 can serve as a good switching device. Recall that when the gate electric field is above 1 V/nm (the typical breakdown field of Al2 O3 ), current leakage may start to occur. The advantage of the 2G S-MERD is that even in a limited gate electric field of 1 V/nm, when the door is not perfectly open, the on-off switching ratio of M2 is still over ∼ 100. Note that the actual operation gate voltage depends on the device setup.

In an experiment setup, the molecule-electrode coupling is strongly influenced by contact geometries, which may lead to different conductance ratios. To account for this effect, we modeled the molecule-electrode coupling strength γL(R) from 0.1 to 5.0 eV and computed the corresponding single-molecule conductance. Figure 5 shows that the conductance of the closed and open door


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states of M2 increases as the molecule-electrode coupling strength increases. In addition, when

γL(R) < 1 eV, we find that the conductance values of two states are nearly proportional to the square of γL(R) , consistent with the previous studies 44–46 (In the condition of off-resonant tunneling and weak molecule-electrode coupling, conductance is proportional to the square of γL(R) ). Nevertheless, regardless of the coupling strength, the conductance ratios nearly remain the same (7.27 × 105 for γL(R) = 0.1 eV and 6.79 × 105 for γL(R) = 5 eV.), indicating that the switching ratio of the SMERDs should be less sensitive to contact geometries. In the field of molecular electronics, the uncertainty of contact geometries makes it difficult to reproduce of single-molecule conductance measurements. For the 2G S-MERDs, the conductance varies dramatically with the moleculelead couplings (contact geometries), but the on-off switching ratio remains the same magnitude. This study may provide a new direction to explore electron transport in molecular junctions. The conductance values in Figure 5 and the on-off switching ratios can be found in the Supporting Information. According to the previous studies, 47 the conductance caused by tunneling with destructive quantum interference has been shown to be sensitive to the treatment of the electronic structure. To account for the factor, we computed the quantum conductance of the closed and open states of M2 at zero bias as well as their corresponding switching ratio using density-functional theory with additional three types of functionals: PZ, PW91, and BLYP. The result is shown in Table 1. The conductance of the open door state (ranging from 10−8 to 10−10 GQ ) is sensitive to the treatment of the electronic structure due to the shifting of destructive quantum interference dips. However, all methods show that the switching ratios of M2 are larger than 104 , indicating that the property of the 2G S-MERDs as excellent switching devices is credible. To summarize, we investigate the transmission functions, the conductance variation with respect to the twist angle, as well as the conductance variation with respect to the gate electric field of the 2G S-MERDs and show that M2 functions as a good switching device. The simulations illustrate that the conductance dependence G ∝ cos4 θ is not affected by chopping the phenyl-acetylene macrocycle into two halves, or by adding an extra triangular motif to the outer stator as in M2.



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Figure 5: Conductance plotted against the molecule-electrode coupling strength. The conductance at the Fermi level of the closed and open door states of M2 increases as the molecule-electrode coupling strength increases. Compared to previously proposed 1G S-MERD, the 2G S-MERDs have much smaller and simpler structures, and the structural similarity between the 2G S-MERDs and the phenyl-acetylene macrocycles suggest that the 2G S-MERDs may be synthesized in a straight-forward manner. In addition, the study shows that the potential energy difference between the open and closed states of the S-MERDs can be engineered by changing the area of π -conjugation. Hopefully, this result will motivate synthesis efforts at creating varieties of chemically distinct S-MERDs. Compared with the 1G S-MERDs, M2 has a more rigid structure and enables operation at a smaller gate electric field (∼ 1 V/nm). Furthermore, the 2G S-MERDs consisting of a fewer number of atoms should also enable real-time simulations using molecular dynamics techniques. We also hope that this work will motivate additional experimental and theoretical studies of S-MERDs to explore the practical construction of molecular level electric machines. 14 ACS Paragon Plus Environment

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Table 1: Switching Ratio of M2 Computed by Using Different Types of Functionals Functional PZ PBE PW91 BLYP

Closed Door State Conductance (GQ ) 1.06 × 10−3 1.14 × 10−3 1.60 × 10−3 1.80 × 10−3

Open Door State Conductance (GQ ) 7.32 × 10−8 1.95 × 10−8 1.72 × 10−8 9.54 × 10−10

Switching Ratio 1.46 × 104 7.27 × 104 9.29 × 104 1.89 × 106

a

The quantum conductance at zero bias is computed by using density-functional theory with four types of functionals: PZ, PBE, PW91, and BLYP. b The geometries of the closed and open door states of M2 are optimized by using the PBE functional.

Supporting Information The supporting information contains computational details, the electronic structure of model systems, the potential energy surface of M1 and M2, the conductance values in Figure 5, and the influence of a gate electric field on transmission functions. This material is available free of charge via the Internet at http://pubs.acs.org

Acknowledgement The authors thank Professor Chun-hsien Chen for useful discussions. This research is supported by the NSF (Grant Number CHE-1058644), ARO (Grant Number W911NF-13-1-0237) and Program in Plasma Science and Technology and the Ministry of Science and Technology (Grant number 101-2113-M-003-009-MY2), Taiwan, R.O.C.

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TOC GRAPHICS Gate Oxide

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Gate Control of Artificial Single-Molecule Electric Machines - The

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