NANO LETTERS
Conformational Molecular Rectifiers
2004 Vol. 4, No. 4 591-595
Alessandro Troisi*,† and Mark A. Ratner* Department of Chemistry, Materials Research Center and Center for Nanofabrication and Molecular Self-Assembly, Northwestern UniVersity, EVanston, Illinois Received December 18, 2003; Revised Manuscript Received February 10, 2004
ABSTRACT Unimolecular rectification based on voltage-controlled intramolecular stereochemical modification is suggested and computationally investigated. In sharp contrast to present molecular rectifiers, these conformational molecular rectifiers (CMRs) differ in principle from silicon structures, deriving their large, strongly temperature-dependent rectification from the differing current pathways in two dominant conformations, controlled by the interelectrode applied field. Two sorts of CMRs, one based on contact modulation the other on bridge modulation, are calculated: an ambient rectification ratio of 102 can be approached.
One of the goals of the emerging field of molecular electronics (ME) is the realization of molecular scale rectifiers, switches, or transistors coupled one another via metallic wiring.1,2 The extension of conventional electronics approaches requires that the molecular device is rigid, with functions entirely determined by electronic structure. With several remarkable exceptions,3 most current experiments in ME are focused on rigid molecules, with molecular motions generally regarded as unwanted complications. An example is the research on unimolecular rectification, largely focused on the study of donor-acceptor molecules rigidly oriented in organic monolayers.4-6 It is still not possible to determine a priori the properties of a given system, essentially because of the unpredictability of the structure (geometrical and electronic) of the molecule-metal interface.7-11 One way to circumvent the lack of control of the interface electronic structure is to rely on controlled molecular motion to realize functionalities usually determined only by the electronic structure properties. Conformational motions driven by the electric field might lead a molecular junction to exhibit switching behavior.12-14 Controllable dynamical stereochemistry breaks the analogy that sees the molecule only as the ultimately miniaturized “material” for electronics, and thereby opens many interesting mechanistic and device possibilities. Since chemical synthesis gives greater control of the mechanical and electrostatic properties than of the interface electronic structure, flexible molecular architectures are an attractive device modality. Similarly, molecular modeling can predict and drive the design of molecular devices. We present here two simple examples of conformational molecular * Corresponding authors. E-mail addresses:
[email protected];
[email protected] † Present address: Dipartimento di Chimica ‘G.Ciamician’, Universita ` di Bologna, via Selmi 2, 40126 Bologna (Italy). 10.1021/nl0352088 CCC: $27.50 Published on Web 03/12/2004
© 2004 American Chemical Society
rectifiers (CMR), molecular devices whose rectifying behavior is not affected by the interface structural details. The measured current across a flexible molecule in contact with two identical electrodes can be expressed to a good approximation as9 I)
〈g(E,V)〉TV e
∫0+∞ dE[f(E) - f(E + eV)]
(1)
where 〈g(E,V)〉TV is the conductance thermally averaged over the available conformations {R} at a given temperature (T) and potential, f(E) and f(E + eV) are the Fermi functions of the two electrodes, V is the applied potential and e the electronic charge. The external field influences the average because it changes the energy of the conformations R(V). The average conductance at constant external bias is then computed as 〈g(E,V)〉TV )
∑R gR(E,V) exp(-R(V)/kBT)/∑R × exp(-R(V)/kBT) (2)
Equations 1-2 are simple extensions of the expression used for rigid molecules.9 This formulation is valid if the nuclear motions included into the summation of eq 2 can be separated from the electronic flux across the junction, as is done when the Born-Oppenheimer approximation is invoked. We recently verified that this is generally a good approximation and that the corrections to the conductance due to the vibronic coupling are usually negligible.15 Equation 1 represents the average current measured over a large number of molecules or, assuming ergodicity, its average value after a long enough observation of a single molecule. Since eq 2 assumes an equilibrium nuclear conformation distribution,
it is valid if the observation time is slower than the equilibration time between conformations (τc), which is system dependent (vide infra). Moreover, if V is not constant in time, eq 2 can be used only if the switching rate of V is smaller than 1/τc. When the junction is rigid, molecular rectification can be observed only if g(E,V) is asymmetric with respect to the potential. This can arise from asymmetric response of the molecular energy levels to the external field, or from asymmetries in the spectral densities of the two electrodes.16 The dependence of 〈g(E,V)〉TV upon V through the population averaging in eq 2 generates another mechanism of rectification, one that requires no strong asymmetry of the g(E,V) functions, since the external bias can populate selectively conformations with different conductance. We limit our attention to the linear response regime that corresponds to low bias and Fermi levels far from molecular levels (offresonance). In this limit 〈g(E,V)〉TV = 〈g(EF,0)〉TV
(3)
I(V) ) 〈g(EF,0)〉TVV
(4)
with EF the Fermi energy of the two electrodes. Rectification will be observed if 〈g(EF,0)〉TV differs significantly for positive and negative bias. When the molecule has a large dipole moment the energy of each conformation can be approximated as12 µRz V (V) = (0) d R
R
(5)
where d is the distance between the electrodes and µRz the projection of the molecular dipole on the interelectrode axis. The simplest interesting case involves a molecular junction with two conformations of similar energies (1(0) ) 2(0)) but different dipole (µ1z ,µ2z ) and conductance (g(1),g(2)) giving
I(V) )
[
]
g(1) exp((µz1 - µz2)V/dkBT) + g(2) exp((µz1 - µz2)V/dkBT) + 1
V
(6)
This gives a rectifying junction if the conductances are sufficiently different and |µ1z - µ2z |V/d > kBT. We will show in the next sections how this can be realized with a realistic molecule. The rectification due to electric field induced stereochemical motions is not limited to low bias regime and is clearly extensible to the resonant case. We will not consider resonant behavior because it requires more detailed consideration of the interfacial electronic structure. Moreover, the resonant injection of charge in the junction could produce a stable charged state that undergoes undesired chemical transformations. It is convenient to base the design of CMR on standard building blocks of organic chemistry, thus providing both 592
Figure 1. (a,b) Schematic of the contact modulated CMR. The conformation of the polar CH2CN group is influenced by the applied potential. (c) The atoms included in the calculation of the relative conductance.
flexibility and viable synthesis. To realize switching between configurations driven by the external field it is necessary17 that a strong dipole, such as the one provided by one or more C-F or C-CN bonds, is present. The modeling is simplest in systems with a single flexible degree of freedom. The asymmetry of the junction can be preserved through a chemical bond between the molecule and least one electrode. We will use the standard benzenethiol link as the “alligator clip”. These initial considerations narrow the possibilities for CMR to molecules containing two rigid portions, one connected to the electrode and the other mobile and with a strong dipole. It is also helpful if the different conformations are very close in energy (with respect to kBT) and accessible through small barriers. Several groups are preparing materials based on mobile dipolar units to be arranged in predetermined arrays.18,19 One effective way to build dipolar rotors involves connecting the dipolar unit with the rigid unit through the sCtCs unit, permitting rotation around the triple bond with little or no barrier. A simpler molecular dipole is given by the cyanomethyl (-CH2CN) group connected to a rigid unhindered group such as phenyl. We will consider examples representative of these two classes. Finally, to have an efficient rectifier it is necessary that different conformations induced by the external field have the largest possible difference in conductance. The conductance may change with conformation because (i) the metalmolecule interaction changes, as in the first case we will consider, or (ii) the intramolecular interactions change, influencing the conductivity as illustrated by our second example. Figure 1ab illustrates a simple contact modulated system that may show conformational rectification. The benzenethiol meta-substituted with the cyanomethyl group can be easily chemisorbed on a gold surface. We suggest that an I/V measurement on this molecule (if aligned perpendicular to the electrode) should show rectifying behavior. The steps followed for modeling the I/V curve are easy: the potential energy surface (PES) for the rotation of the CH2CN group around the phenyl-C bond is computed at the B3LYP/6Nano Lett., Vol. 4, No. 4, 2004
compared to the π-orbitals. Both assumptions are substantiated by the experimental evidence that the conductance drops by several orders of magnitude in the absence of S-Au bonds or π-systems. Consequently, since the sulfur is connected to a benzene carbon atom, one can consider that all the current passes through the pπ atomic orbital of this carbon, i.e., its py orbital using the reference system outlined in Figure 1c. The electrons at the Fermi level of a Pt tip have d character, and the orbital with the largest coupling with the molecule is the dyz orbital. These considerations allow us to approximate the conductance as proportional to the square modulus of a single Green’s function matrix element:21
{
χ : orbital p on C gR(EF,0) ∝ |〈χ1|G(EF)|χ2〉|2 χ1: orbital dy on Pt1 2 yz
Figure 2. (a) Potential energy for the rotation of the -CH2CN group as affected by external bias. Curves are plotted for an external bias of -1 V(dashed), 0 V (solid), +1 V (dotted). The -CN group points toward the tip at positive bias, toward the surface at negative bias. (b) Relative conductance as a function of the dihedral angle R. (c) Simulated I/V curve at different temperatures.
31G* level for the model compound HS-C6H4-CH2CN and the effect of the external potential follows from eq 6 (the distance between the electrodes was taken as 13.8 Å). Figure 2a shows that even a small potential can drive the system toward one of the two conformations. To evaluate the tipsubstrate coupling, quantum chemical calculations were carried out on the model compound in Figure 1c where three Au atoms model the gold surface and a single Pt atom is used to simulate a platinum STM tip.20 These simulations aim not at computing the absolute value of the conductance but its relative value as the dihedral angle R changes. For this reason we make two reasonable assumptions that greatly simplify the calculation: (i) the current passes mainly through the S-Au bonds and (ii) the contribution of the benzene σ-orbitals to the conductance is negligible Nano Lett., Vol. 4, No. 4, 2004
(7)
If two atomic orbitals act as gateways for the incoming and outgoing electrons the conductance is proportional to the squared single Green’s function matrix element between these two orbitals; this is the basis for eq 7. The relative conductance as a function of the angle R, computed from eq 7 and plotted in Figure 2b, is much higher when the CN group points toward the tip. The thermal average conductance was computed according to eq 2, and the I(V) curve in the linear response regime (eq 4) is shown in Figure 2c. For the given rotating dipole the external field controls the conformation only at low temperature, where large rectification can be observed. At 50 K and V > 0.5 V only the high conductance conformation (R∼180°) is populated, while for V < -0.5 V the population shifts toward the low conductance (R∼0°) conformation. Rectification at room temperature is much reduced because all the conformations become populated. Several improvements can be introduced to make a more useful CMR: (i) a larger mobile dipole can give switching at higher temperatures, (ii) a fixed chemical connection with both electrodes is desirable to avoid interfacial complexity. These considerations suggest bridge-modulated rectification, based on a molecule such as that depicted in Figure 3, sandwiched between two gold electrodes. A rigid spacer made from fused cyclohexanes separates the two benzenethiol units connected to the metals. In analogy with donor-acceptor C-clamp molecules,22 the coupling between the two aromatic rings is negligible if not mediated by an intervening molecular unit. A dicyanonaphthalene unit, connected to the molecule though the sCtCs spacer, acts as a “drawbridge”. This can provide the coupling between the two electrodes only if placed between them in the conformation illustrated by Figure 3b. The bridge conformation is dictated by the external potential, favoring the conductive conformation when the left electrode is positive and the nonconductive conformation in the opposite case. More quantitative predictions require calculation of the potential energy under the influence of the external field, followed by an evaluation of the relative conductance. The PES shown in Figure 4a is computed with an ad hoc quantum chemical/molecular mechanics approach.23 The dipolar frag593
Figure 3. Schematic of the bridge-modulated CMR. The preferred conformation of the polar dicyanonaphthalene group depends on the applied potential. The conductance in (a) is much larger than in (b). The dashed line in (b) encloses the molecular fragment treated ab initio in the simulations.
ment can rotate about 180°, limited on one side by the electrode and on the other side by the aromatic ring. The barrier for the rotation is small and the PES in the presence of the electric field (eq 5, d ) 18.6 Å) shows that the external potential can control the system conformation. The relative conductance is computed as in eq 7. In this case χ1 is the pπ orbital on the carbon atom directly bonded to the left sulfur atom (Figure 3) and χ2 the analogous orbital on the carbon atom bonded to the right sulfur atom. Figure 4b shows the greater conductance expected when the dicyanonaphthyl bridge rotates to overlap well with the pπ orbital on the opposite benzenethiol. The simulated I(V) curve for this system at room temperature shows remarkable rectification (Figure 4c). The rectifying behavior is entirely determined by the molecule: the metal-molecule contact is invariant to the changed stereochemistry. The plots of Figure 2c and 4c simulate the observed I/V curve only if the voltage is changed more slowly than the conformational equilibration time τc (otherwise eq 2 would not be valid).24 For similar sytems25 τc was found to be in the 10-11 to 10-10 s-1 range26 so that we can expect the limiting switching rate for the proposed device to be near 1010Hz). It is clear, from these two examples, that one essential condition for viable CMRs is the possibility to control the molecule orientation at the interface. Other interfacial characteristics that do not interfere with the intramolecular PES (bonding site, electrode geometry) can modulate, even 594
Figure 4. (a) Potential energy for the rotation of the dicyanonaphthalene as affected by an external bias of -1 V (blue), 0 V (black), +1 V (red). The π bridge is preferentially between the electrodes at positive potential. (b) Relative conductance as a function of the dihedral angle. (c) Simulated I/V curve at 300 K; the calculated I(V ) +1 V)/I(V ) -1 V) is 66.
substantially, the I/V curve without affecting the rectifying nature of these junctions. Another essential condition is that the conductive and nonconductive conformations must be close in energy with respect to kBT (even if, in both considered cases, the less conductive conformation was the most stable, this is not a condition necessary to observe rectification).12 The prototypes presented here fully exploit the “molecularity” of ME devices and have no analogues in conventional electronics. We suggested that the lack of control of interfacial structure can be circumvented using Nano Lett., Vol. 4, No. 4, 2004
the rich toolbox of synthetic chemistry to build more sophisticated (and more controllable) molecular electronics devices. Acknowledgment. This work was supported by NSF Computational Electronics, by the DOD/MURI program, and by the DARPA Moletronics program. Supporting Information Available: Data of quantum chemical calculations performed with the GAMESS-US package. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Joachim, C.; Gimzewski, J. K.; Aviram, A. Nature 2000, 408, 541. (2) Molecular Electronics: Science and Tecnology; Aviram, A., Ratner, M., Eds.; New York Academy of Science: New York, 1998. (3) Wong, E. W.; Collier, C. P.; Behloradsky, M.; Raymo, F. M.; Stoddart, J. F.; Heath, J. R. J. Am. Chem. Soc. 2000, 122, 5831. (4) Martin, A. S.; Sambles, J. R.; Ashwell, G. J. Phys. ReV. Lett. 1993, 70, 218. (5) Metzger, R. M. Acc. Chem. Res. 1999, 32, 950-957. (6) Xu, T.; Peterson, I. R.; Lakshmikantham, M. V.; Metzger, R. M. Angew. Chem., Int. Ed. 2001, 40, 1749. (7) Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge University Press: Cambridge, 1995. (8) Nitzan, A. Annu. ReV. Phys. Chem. 2001, 52, 681. (9) Nitzan, A.; Ratner, M. A. Science 2003, 300, 1384. (10) Zhou, C.; Deshpande, M. R.; Reed, M. A.; Jones, L., II; Tour, J. M. Appl. Phys. Lett. 1997, 71, 611. (11) Chabinyc, M. L.; Chen, X. X.; Holmlin, R. E.; Jacobs, H.; Skulason, H.; Frisbie, C. D.; Mujica, V.; Ratner, M. A.; Rampi, M. A.; Whitesides, G. M. J. Am. Chem. Soc. 2002, 124, 11730. (12) Troisi, A.; Ratner, M. A. J. Am. Chem. Soc. 2002, 124, 14528. (13) Kornilovitch, P. E.; Bratkovsky, A. M.; Williams, R. S. Phys. ReV. B 2002, 66, 245413.
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(14) Ghosh, A. W.; Rakshit, T.; Datta, S. in preparation (preprint available at http://arxiv.org/pdf/cond-mat/0212166.pdf). (15) Troisi, A.; Ratner, M. A.; Nitzan, A. J. Chem. Phys. 2003, 118, 6072. (16) Mujica, V.; Ratner, M. A.; Nitzan, A. Chem. Phys. 2002, 281, 147. (17) Polarization-driven deformation can be also used to drive the stereochemical change. (18) Godinez, C. E.; Zepeda, G.; Garcia-Garibay, M. A. J. Am. Chem. Soc. 2002, 124, 4701. (19) Clarke, L. I.; Horinek, D.; Kottas, G. S.; Varaksa, N.; Magnera, T. F.; Hinderer, T. P.; Horansky, R. D.; Michl, J.; Price, J. C. Nanotechnology 2002, 13, 533. (20) B3LYP calculations with 6-31G* basis on the organic fragment and SBKJC pseudopotential for the metal atoms. S is placed in the hollow site, 1.9 Å from the surface. (21) For the definition of Green’s function operator and for a justification of eq 7, see, for instance, eqs 37-39 of ref 8. At low bias, the imaginary component of the self-energy (Γ) is sensibly constant leading to the proportionality between g and |G|2. Green’s function matrix elements are easily computed from molecular orbital quantum chemical calculations (e.g., see eq 31 of ref 15). (22) Zimmt, M. B.; Waldeck, A. M. J. Phys. Chem. A 2003, 107, 3580. (23) The subsystem treated quantum chemically is enclosed by a dotted line in Figure 3 (dangling bonds are saturated with hydrogen). The nonbonded interaction between the gold surface and the mobile bridge is added to the quantum chemical energy, including the image dipole interaction between the molecule and the electrodes. The left and right fragments are constrained to the distance and orientations fixed by the spacer. Single points on the PES and molecular dipoles were computed at the B3LYP/6-31G* level using the HF/3-21G* optimized structure. (24) Levine, R. D.; Bernstein, R. B. Molecular reaction dynamics and chemical reactiVity; Oxford University Press: New York, 1987. (25) Vacek, J.; Michl, J. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 5481. (26) τc is extremely dependent on the potential barrier for the interconversion Ebarr, according to the empirical rule of 1/τc ) A exp(-Ebarr/ kBT) with A ≈ 1013 s-1.
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