Measurement of Single-Molecule Conductance - Arizona State University

ANRV308-PC58-20 ARI 22 February 2007 11:34

Measurement ofSingle-MoleculeConductanceFang Chen, Joshua Hihath, Zhifeng Huang,Xiulan Li, and N.J. TaoDepartment of Electrical Engineering and Center for Solid State ElectronicsResearch, Arizona State University, Tempe, Arizona 85287;email: [email protected]

Annu. Rev. Phys. Chem. 2007. 58:535–64

First published online as a Review in Advanceon November 29, 2006

The Annual Review of Physical Chemistry isonline at http://physchem.annualreviews.org

This article’s doi:10.1146/annurev.physchem.58.032806.104523

Copyright c© 2007 by Annual Reviews.All rights reserved

0066-426X/07/0505-0535$20.00

Key Words

molecular electronics, break junction, quantum point contact

AbstractWhat is the conductance of a single molecule? This basic and seem-ingly simple question has been a difficult one to answer for bothexperimentalists and theorists. To determine the conductance of amolecule, one must wire the molecule reliably to at least two elec-trodes. The conductance of the molecule thus depends not only onthe intrinsic properties of the molecule, but also on the electrodematerials. Furthermore, the conductance is sensitive to the atomic-level details of the molecule-electrode contact and the local envi-ronment of the molecule. Creating identical contact geometries hasbeen a challenging experimental problem, and the lack of atomic-level structural information of the contacts makes it hard to comparecalculations with measurements. Despite the difficulties, researchershave made substantial advances in recent years. This review pro-vides an overview of the experimental advances, discusses the advan-tages and drawbacks of different techniques, and explores remainingissues.

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Molecular electronics:science and technologyrelated to theunderstanding, design, andfabrication of electronicsdevices based on molecules

Contact geometry: theatomic-scale geometry of anelectrode, and the bindingsite and orientation of amolecule on the electrode

1. INTRODUCTION

The ability to measure and control electrical current through a molecule is a criticalrequirement toward the goal of building electronic devices using individual molecules(1, 2). This ability also offers us a unique opportunity to understand charge transport,an important phenomenon that occurs in many chemical and biological processes(3, 4), on a single-molecule basis. Furthermore, it allows us to read the chemicalinformation of a single molecule electronically (5), which opens the door to chemicaland biosensor applications based on the electrical detection of individual molecularbinding events (6).

The most fundamental quantity that describes the electrical properties of a bulkmaterial is conductivity, based on which materials are often divided into conductors,insulators, and semiconductors. Conductivity is defined as σ = (I/V) × L/A, whereI is the electrical current, V is the applied bias voltage, L is the length, and A is thecross sectional area of the material. For a small molecule, A and L are difficult todefine precisely, and a more well-defined quantity is the conductance, G, given byG = I/V. So a basic question in molecular electronics is, what is the conductance ofa single molecule?

To determine the conductance of a molecule, one must first bring it into contactwith at least two external electrodes (Figure 1). The contact must be robust, repro-ducible, and able to provide sufficient electronic coupling between the molecule andthe electrodes (7–11). One way to meet the contact requirements is to attach themolecule covalently to the electrodes via proper anchoring groups at two ends of themolecule. Clearly, the measured conductance depends not only on the molecule, itself,but also on the properties of the electrodes and the atomic-scale molecule-electrodecontact geometry (12–17). Another factor that may affect the measured conductanceis the local environment of the molecule, which includes solvent molecules (vacuumor air), pH, and ions (18, 19). Finally, an electron traversing through the molecule

I

Vbias

I

Vbias

a b

Figure 1(a) Current through a molecule covalently bound to two electrodes. (b) Current through ametal atom attached to two electrodes made of the same metal.

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Molecule-electrodecontact: contact between amolecule and an electrodeprovides sufficient andstable electronic couplingbetween the molecule andthe electrode

Quantum point contact: asmall constriction betweentwo conducting regionsthrough which electronstraverse ballistically andexperience a quantumwaveguide effect

Conductance quantumunit: a basic unit ofconductance given by G0 =2e2/h, where e is theelectron charge and h is thePlanck constant

may exchange energy with the vibration modes of the molecule or surrounding sol-vent molecules (20, 21). Consequently, the measured conductance may be sensitiveto temperature (22–24). Precisely controlling these measurement details, especiallythe molecule-electrode contacts, has been a difficult task, which is a major reasonfor the large disparities between different measurements for even a relatively simplemolecule, such as alkanedithiols (25, 26). In this chapter, we review recent experimen-tal advances and discuss remaining issues in measuring single-molecule conductance.

A related problem is to determine the conductance of a single metal atom or alinear chain of metal atoms bridged between two electrodes made of the same metalas the atoms in the chain (27–32). This system is known as a quantum point contact.For metals, such as Au, the conductance of a quantum point contact is close to G0 =2e2/h = 77.4 μS, where e is the electron charge, h is the Planck constant, and S isthe conductance unit. G0 is the conductance quantum unit corresponding to 100%transmission of electrons from one electrode to the other through the point contact.Therefore, the conductance of a molecule given in units of G0 tells us how conductivethe molecule is in comparison with a metal atom, which is why we use G0 as the unitof conductance here.

Molecular electronics is a diverse and rapidly growing field, and many excellentreviews have appeared in recent years, covering general concepts (4, 33–36), theo-retical aspects (21, 37, 38), and experimental methods (39–42). In the present review,we mainly focus on the measurements of single molecules covalently bound to twoelectrodes. We refer the readers interested in molecule-film measurements to re-cent reviews by Metzger (42) and Wang et al. (41). The remainder of the chapter isarranged as follows: Section 2 provides a brief overview of experimental tools thatmeasure the conductance of molecular thin films, and Section 3 describes techniquesand methods for single-molecule conductance measurements, in which we discussboth the advantages and difficulties of different techniques. Section 4 addresses somecritical issues that affect single-molecule conductance, and Section 5 provides a sum-mary and outlook.

2. MEASUREMENTS OF MOLECULAR FILMS

To date, many experimental techniques have been developed to measure and controlcurrent through molecules. We can divide these techniques into two broad categories:molecular film and single-molecule measurements. We briefly describe the first cate-gory in this section, whereas we discuss single-molecule conductance measurementsin more detail in Section 3.

2.1. Bulk Electrodes

The basic idea of the bulk electrode approach is to sandwich a molecular film, eithera monolayer or multiple layers, between two electrodes. The molecules are typicallyfirst immobilized on one electrode surface, via self-assembly or Langmuir-Blodgettmethods (40, 42). Both self-assembly and Langmuir-Blodgett methods provide or-dered molecular films, which are highly desired for successful measurement and data

www.annualreviews.org • Single-Molecule Conductance 537

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Molecular junction: amolecule is attached to twoelectrodes to form anelectrode-molecule-electrode structure

interpretation. A second electrode is then placed on top of the molecular film, andthe electrical current between the two electrodes is measured as a function of biasvoltage.

The placement of the top electrode is often the most difficult part of the mea-surement, and many methods have been developed (43). One is to evaporate a metallayer onto the molecular film in vacuum. To avoid a short circuit between the topelectrode and the bottom electrode, one must ensure that energetic metal atoms donot damage the molecular film and the deposited metal does not penetrate into themolecular film via defect sites to reach the bottom electrode (44, 45). To minimizethe short-circuit problem, Akkerman et al. (46) put a conducting polymer layer ontothe molecular film before the deposition of the top electrode. Another method is toprint a metal layer onto the molecular film by transferring a metal film evaporatedon a stamp via direct contact (47, 48).

Electrodeposition methods have also been investigated (49–51). For example,Manolova et al. (52) used a 4,4′-dithiodipyridine-modified Au electrode to allow Pdor Pt ions to adsorb preferentially onto the pyridine moiety of the molecules. The ad-sorbed metal ions were then reduced electrochemically to metallic Pd or Pt that couldserve as the second electrode in a metal ion-free acidic solution (52). Angle-resolvedX-ray photoelectron spectroscopy showed that the second electrode was indeed ontop of the molecular film without penetrating into the molecule film via defect sites.Instead of using a solid metal as the top electrode, an alternative approach is to place adrop of mercury onto the molecular layer (53–57). The mercury approach is relativelysimple and has shown high device yields.

2.2. Nanoelectrodes

The molecular film measurements described above involve many molecules, whichcan be reduced using nanoscale electrodes. For example, a conducting atomic-force-microscope tip with a radius of curvature on the nanometer scale can serve as thetop electrode to measure conductance of a relatively small number of molecules (58,59). Another method is the cross-wire junction, which sandwiches a molecular layerbetween two perpendicular metal wires (60–62). The contact area between the twowires is small, so a relatively small number of molecules is measured.

One may also reduce the number of molecules by confining the molecular filminside a nanopore fabricated in a thin solid membrane (63, 64). One side of themembrane is first covered with a metal layer, and molecules are allowed to forma monolayer on the metal surface inside of the nanopores. A second metal layer isthen deposited on top of the molecular film in the nanopores. Nanopores can also beused as templates to fabricate nanoscale metal-molecule-metal junctions (65). Metalis first deposited electrochemically into the nanopores in an alumina membrane topartially fill up the nanopores. Sample molecules are then allowed to adsorb on themetal surface inside of the nanopores, which is followed by the chemical depositionof a top metal layer into the nanopores to form nanoscale molecule junctions. Afterdissolving the alumina, these molecular junctions in a solution are assembled ontoelectrode arrays for conductance measurements.

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Electromigration:transport of material causedby the movement of the ionsin a conductor owing to themomentum transferbetween conductingelectrons

STM: scanning tunnelingmicroscopy

AFM: atomic forcemicroscopy

The molecular film measurements have played an important role in the under-standing of the electron-transport properties of molecules (66, 67) and for demonstra-tions of many device functions, including rectification (44, 68–70), molecular switch-ing (62, 71, 72), and negative differential resistance effects (56, 63, 73). When applyingthese techniques to a particular sample molecule, one needs to consider the followingfactors: First, not all the molecules of interest can form well-ordered films, whichlimits the choice of molecules for the studies. Second, molecular films often have de-fects, and additional defects may be created during the fabrication of the top electrode(51) and application of bias voltage (61). It is important to ensure that the defects andelectromigration-induced effects do not dominate the measured conductance. Third,in a close-packed film, a molecule interacts with the neighboring molecules, whichmay suppress its conformational change and affect its electron-transport properties(74). As a result, the average conductance per molecule calculated from the molecularfilm measurements may not be directly comparable with single-molecule conductancemeasurements. Finally, the molecules in the films are not exposed to the outside world,which makes it difficult to introduce a gate electrode and prevents one from studyingmolecular binding processes between the sample molecules and analytes.

3. MEASUREMENTS OF SINGLE MOLECULES

To determine the conductance of a single molecule, one must (a) provide a signatureto identify that the measured conductance is a result of not only the sample molecules,but also a single sample molecule, (b) ensure that the molecule is properly attached tothe two probing electrodes, and (c) perform the measurement in a well-defined envi-ronment. The current methods fall into three categories: scanning probe methods,fixed electrodes, and mechanically controlled molecular junctions.

3.1. Scanning Probe Techniques

Scanning tunneling microscopy (STM) has played a unique role in the field of molec-ular electronics (75). This is because it allows one to image individual molecules ad-sorbed on a conductive substrate with submolecular resolution. By placing a scanning-tunneling-microscope tip over a molecule, one can perform tunneling spectroscopymeasurements on the molecule (76–78). In addition, the tip can be used to manip-ulate atoms and molecules on surfaces (79). A closely related technique is atomicforce microscopy (AFM). Although AFM has typically a lower resolution than STM,it measures both the mechanical and electrical properties of molecules when a con-ducting tip is used (80, 81). To date, STM and AFM have revealed many interestingphenomena important to the development of molecular electronics. Examples in-clude reversible redox switching (82–85), an electromechanical molecular amplifier(86), the negative differential resistance-like effect (59, 87–89), molecular switching(90, 91), and the study of field effects on electron transport in molecules (92).

In the STM or AFM method, a molecule adsorbs onto a substrate to form awell-defined molecule-substrate contact, but the tip-molecule contact is often lesswell defined, which prevents one from determining the absolute conductance of the


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Tip

Substrate

Tip

Substrate

Metal particle

a b

Figure 2(a) Scanning tunneling microscopy (STM) study of electron transport through a targetmolecule inserted into an ordered array of reference molecules. (b) STM or conducting atomicforce microscopy (AFM) measurement of conductance of a molecule with one end attached toa substrate and the other end bound to a metal nanoparticle.

molecule. One way to reduce this problem is to embed a molecule of interest intothe matrix of another, often less conducting molecule (Figure 2a). Bumm et al. (90)used this approach to study current through molecular wire candidates inserted intoan insulating alkanethiol monolayer and observed much higher current through themolecular wires than through the surrounding alkanes. Tao (82) studied Fe-porphyrincoadsorbed in the ordered array of porphyrin molecules in an electrochemical cell.Fe-porphyrin is redox active, whereas porphyrin is similar in structure but redoxinactive. The work shows that the current through the redox active molecule is muchhigher than that through the redox inactive molecule when the electrode potential istuned near the redox potential of Fe-porphyrin.

Another STM approach demonstrated by Langlais et al. (93) is to attach one endof a molecule to a step edge on a metal substrate. The STM image of the molecule andthe metal substrate provides spatially resolved electronic penetration of the metallicelectronic states from the step edge into the molecule, which the researchers used todetermine the electron tunneling decay constant along the molecule.

A third approach is to attach one end of a molecule onto a substrate and theother end to an Au nanoparticle covalently (Figure 2b). One then places a scanning-tunneling-microscope tip (94) or a conducting atomic-force-microscope tip (7) on topof the nanoparticle. Because Au nanoparticles are typically coated with an organicsurfactant layer, the tip and the nanoparticle form a tunneling junction. Consequently,the nanoparticle behaves similar to a Coulomb island, and the electron transportbetween the tip and the substrate via the nanoparticle exhibits Coulomb blockadeeffect (7, 94). By fitting the measured I-V curves with the Coulomb blockade model,one can extract the conductance of the sample molecule between the nanoparticleand the substrate (95, 96).

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Ho et al. (97) recently made a significant step toward the goal of creating a metal-molecule-metal junction with atomic-scale precision. They assembled a copper(II)phthalocyanine molecule bound to two Au atomic chains on an NiAl(110) surfaceby manipulating individual Au atoms and copper(II) phthalocyanine molecules witha scanning-tunneling-microscope tip. The spatially resolved electronic spectroscopyrevealed that the electronic states of the metal-molecule-metal junction change sig-nificantly when varying the number of Au atoms in the chains one by one. TheNiAl(110) is conducting, so the electronic coupling between the molecule and thesubstrate is strong. To reduce the electronic coupling, Repp et al. (98) introduced aninsulating layer of NaCl between the sample molecule (pentacene) and a Cu substrate.By manipulating an Au atom with a scanning-tunneling-microscope tip, they createdan Au-pentacene contact and studied the dependence of the molecule’s electronicstates on the formation of the Au-molecule contact (Figure 3). These STM stud-ies not only provided the atomic-scale structural information of the metal-moleculecontacts but also determined the mixing of the electronic states of the molecules withthose of the metal electrodes.

Figure 3Making and breaking a chemical bond between a single pentacene molecule and an Au atomon an NaCl bilayer supported by a Cu(100) substrate. (a) Scanning tunneling microscopy(STM) image showing the molecule and the Au atom before bond formation. (b) Imageshowing a molecule-metal complex (6-Au-pentacene) after resonant tunneling through thelowest unoccupied molecular orbital of the pentacene molecule. (c) Calculated geometry of theadsorbed 6-Au-pentacene complex. C, H, and Au atoms are represented by gray, white, andgold spheres, respectively. Reprinted with permission from Reference 98.


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In both examples described here, the metal electrodes, consisting of a single orseveral Au atoms, are too small to develop full continuous density of states of metalliccharacter. The coupling between the molecule and metal substrate is reduced by thethin NaCl layer, but it is still finite as it is needed for STM imaging. Therefore, theresults may not be compared directly with the molecular conductance measurementsthat use large or bulk metal electrodes. Another challenge is to connect the metalelectrodes to two external electrodes to carry out electron-transport measurementson the molecular junctions created by STM.

3.2. Fixed Electrodes

A conceptually simple method to measure single-molecule conductance is to fabri-cate a pair of facing electrodes on a solid substrate and then bridge the electrodeswith a molecule terminated with proper anchoring groups that can bind to the elec-trodes (Figure 4a). A key requirement of this method is to fabricate electrodes with amolecular-scale gap, which has been a difficult task. This is because most molecules area few nanometers or less, and fabrication of such a small gap between electrodes is be-yond the reach of conventional micro- and nanofabrication facilities. Unconventional

a

Source Drain

Gate

Oxide

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Electrode Electrode

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Substrate

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Figure 4Schematic illustrations ofsingle-moleculeconductance studies usingdifferent methods. (a) Asingle molecule bridgedbetween two electrodeswith a molecular-scaleseparation prepared byelectromigration,electrochemical etching ordeposition, and otherapproaches. (b) Formationof molecular junctions bybridging a relatively largegap between twoelectrodes using a metalparticle. (c) A dimerstructure, consisting oftwo Au particles bridgedwith a molecule,assembled across twoelectrodes.

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Redox molecule: moleculethat can be reversiblyoxidized or reduced viaelectron transfer betweenthe molecule and electrodes

PZT: piezoelectrictransducer

fabrication techniques—such as electromigration (99, 100), electrochemical etchingor deposition (101–104), and other novel methods (105–109)—have been developedto create electrodes separated with a molecular-scale gap.

One attempt to avoid the requirement of molecular-scale gaps is to use metalnanoparticles as bridges (Figure 4b). This technique starts with a pair of electrodesseparated with a gap that is much larger than a sample molecule. After covering theelectrodes with a layer of sample molecules, one drives a metal nanoparticle with adiameter greater than the electrode gap into the gap to bridge the two electrodes,either using dielectrophoresis (110) or a magnetic field when Au-coated Ni particlesare used (71). This results in two metal-molecule-metal junctions in series, whichmay complicate the data analysis. Dadosh et al. (111) reported another strategy basedon synthesizing a dimer structure, consisting of two Au nanoparticles connected bya dithiolated organic molecule, and electrostatically trapping the dimer structurebetween two metal electrodes (Figure 4c).

Because the fixed electrodes are supported on a solid substrate, the molecular junc-tions are mechanically stable, which is ideal for studying electron transport throughmolecules as a function of temperature, magnetic field, and other external parame-ters. Another advantage of this approach is that one can use the substrate (e.g., heavilydoped Si) as a gate electrode to control the electron transport through the molecules.Researchers have applied this approach to study various interesting phenomena, in-cluding single-electron charging (99, 100, 107, 112) and Kondo effects (99, 100, 113)in molecules at low temperatures.

Further improvements are desired to address the following issues. First, the device-to-device variation is large, which calls for statistical analysis. However, the fabricationyield is usually rather low, making it difficult to perform statistical analysis (104,105). Second, for redox molecules, the single-electron charging effect was used as asignature to identify measurements attributed to a single molecule (99, 100, 107, 112).But, in general, it is difficult to determine how many molecules are bridged acrossthe electrodes and how many contribute to the measured current. Because metal-nanoparticle complexes often form during the fabrication processes of the molecular-scale gaps, it is important to distinguish that the measured transport properties area result of the sample molecule rather than the nanoparticles or a nanoparticle-molecule complex (114). Third, even though the molecules have two linker groups,it is difficult to determine if the molecules are indeed covalently bound to the twoelectrodes. Finally, the structure of the electrodes and the position of the moleculeare not precisely known, so a technique that can provide atomic-scale structuralinformation of the molecular junction is highly desired.

3.3. Mechanically Formed Molecular Junctions

It is difficult to fabricate electrodes separated with a gap that can fit a sample moleculeprecisely. This difficulty may be overcome by bringing two electrodes together orseparating them apart mechanically. Using a piezoelectric transducer (PZT) or othermechanical actuation mechanisms, one can control the gap with subangstrom preci-sion, making it possible to fabricate molecular junctions and measure the conductance


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MCBJ: mechanicallycontrollable break junction

of various molecules. Several techniques based on this concept have been developed,which are described below.

3.3.1. Mechanically controllable break junction. The basic principle of the me-chanically controllable break junction (MCBJ) method (115, 116) is to break a thinmetal wire supported on a solid substrate into a pair of facing electrodes (32). Theprocess is controlled by bending the substrate with a mechanical actuator, such asa PZT and stepping motor (Figure 5a). An MCBJ device can be built manually byfixing a metal wire with a notch near the middle of the wire (116). An alternativemethod is to create a nanobridge connecting two microelectrodes on a substrate us-ing electron-beam lithography (Figure 5b) (117). Because the bending is achieved byfixing two ends of the substrate while pushing the middle part of the substrate ver-tically, the vertical movement of the PZT is demagnified when the substrate is thincompared to its width. This allows one to accurately control the width of the gap.

Moreland & Ekin (115) first used the MCBJ to study electron tunneling, andMuller et al. (116) pioneered the technique to create metallic quantum point contactsand to demonstrate conductance quantization (29). Reed et al. (118) applied MCBJto measure electron transport in molecules. They first formed a molecular-scale gapbetween two electrodes and then exposed the electrodes to a solution containingbenzenedithiol. After evaporation of the solvent, they measured a finite current be-tween the electrodes and attributed it to electron transport through the molecules.Kergueris et al. (119) measured electron transport through oligothiophenes termi-nated with dithiols using an MCBJ in a similar way. These pioneering works demon-strate the feasibility of studying electron transport in molecules using the MCBJ;however, how many molecules were involved in the conduction and whether themolecules were bound to both electrodes were not clear.

Reichert et al. (120) provided strong evidence of single-molecule conductancemeasurements using an MCBJ setup. In their experiment, they first applied a dropletof a solvent containing dithiol molecules to the electrode pair formed with the MCBJto allow the molecules to adsorb onto the electrodes. The gap was then closed whilemaintaining a fixed voltage across the electrodes, during which time they recordedthe current (Figure 5c). Initially, the current grew exponentially, owing to electrontunneling across the gap. When the gap was decreased to a certain width, sometimesthe current locked into a stable value weakly dependent on the gap width (121).At that point, the first molecule was presumably attached to the opposite side. Themeasured I-V (Figure 5d) curves were asymmetric for asymmetric molecules, whichsuggests a single or a small number of molecules bridging the gap. Smit et al. (122)reported that a hydrogen molecule forms a stable bridge between platinum electrodesin their quantum point contact measurements in the presence of H2. The measuredconductance determined from the hydrogen bridge is close to 1G0, nearly perfectconductance or 100% transmission through H2. They also studied the vibrations ofthe molecules using point contact spectroscopy (123).

3.3.2. Scanning-tunneling-microscopy-based break junction. Xu & Tao (124)developed an STM–break junction method that quickly creates thousands of

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Figure 5(a) Schematics of a microfabricated mechanically controllable break junction (MCBJ) (88). (b)Scanning-electron-microscope picture of the lithographically fabricated break junction (92).(c) Change of current recorded during the formation of a molecular junction. After a region ofroughly exponential increase of the current, the current suddenly locks into a remarkablystable value (plateau), nearly independent of the distance. (d) I-V and dI/dV of a molecularjunction. Images reprinted with permission from References 32, 117, 120, and 121.

molecular junctions by repeatedly moving a scanning-tunneling-microscope tip intoand out of contact with the substrate electrode in the presence of sample molecules(Figure 6). The molecules in the study have two end groups that can bind to the tipand the substrate electrodes, respectively. The process can be divided into three steps:(a) A PZT drives the tip toward the substrate surface until it contacts the moleculesbound to the substrate. During the contact period, one or more molecules may bindto the tip via the second end group. (b) The tip is pulled away from the substrate, andthen the molecules break contact with one of the two electrodes individually, which


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Conductance histogram:a statistical distribution ofconductance values of alarge ensemble of molecularjunctions withmicroscopically differentcontact geometries

Figure 6(a) Measurement of single-molecule conductance using a scanning tunneling microscopy(STM) break junction. A scanning-tunneling-microscope tip is pushed into contact withmolecules adsorbed on an electrode with a piezoelectric transducer (PZT) in a solutioncontaining the sample molecules, during which the molecules have a chance to bridge the tipand substrate electrodes. The tip is then pulled away from the substrate to break the moleculesfrom contacting the electrodes. (b) The current (conductance) for viologen dithiol (N,N′-bis(6-thiohexyl)-4,4′-bipyridinium bromide) recorded during the pulling process showsstepwise features. Bias voltage = −0.1 V. These curves reflect the typical current features forthousands of molecular junctions repeatedly formed under the same conditions.(c) Conductance histogram constructed from the individual measurements reveals well-definedpeaks near integer multiples of a fundamental value, ∼1 nS, which is identified as theconductance of a single molecule. Reprinted with permission from Reference 85.

is shown as a series of stepwise decreases in the current (Figure 6b). (c) The processis repeated until a large number of molecular junctions are created and measured.The conductance histogram of these molecular junctions exhibits peaks located nearinteger multiples of a fundamental value, which is used as a signature to identify asingle-molecule conductance. During the approaching stage, one may control the tipto either make contact with the substrate to form a quantum point contact or avoidthe formation of a point contact between the tip and the substrate.

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Unlike most of the MCBJ experiments that record the approaching processes,this method focuses on the separation process. Because only those molecules boundto two electrodes can be stretched until breakdown during the separation process,this method selectively measures the conductance of those molecules bound to bothelectrodes. Another difference is that the creation of the molecular junctions and themeasurement of the conductance are performed in an organic solvent or aqueouselectrolyte, so one can easily introduce the sample molecules via the solution andcontrol the electron transport through the molecules electrochemically. Finally, thescanning-tunneling-microscope tip images the substrate surface before performingthe electron-transport measurement, so one can place the tip on an atomically flatarea or move the tip laterally to a fresh area of the substrate during the measurement.This freedom comes at the cost of mechanical and thermal stability, however, whichis typically not as good as the MCBJ. Different groups have used this or similarapproaches to determine the conductance of many molecules (85, 125–127). Despitethe success, several issues remain to be resolved and understood (see Section 4).

3.3.3. Conducting atomic-force-microscopy break junction. The stepwisechange in the conductance curves shown in Figure 6b was attributed to the break-down of individual molecules during the separation of the electrodes. Xu et al. (80)confirmed this by measuring the electromechanical properties of the molecular junc-tions with a conducting atomic force microscope (Figure 7). Each abrupt conduc-tance decrease is accompanied by an abrupt decrease in the force, corresponding tothe breakdown of a molecule from contacting the electrodes. Further pulling causesonly a slight change in the conductance but an approximately linear increase in theforce. When the force reaches a certain threshold, another molecule junction breaks

4

4

8

0

Force

b

Stretching

a

Conductance

0

2

6

Fo

rce (n

N)

Co

nd

ucta

nce (

10

–4 G

0)

Figure 7(a) Simultaneous conductance and force measurements of a molecular junction duringbreakdown using a conducting atomic force microscope setup. (b) As the individual moleculesbreak, the conductance decreases in a stepwise fashion (red), and associated with eachconductance step, the force (blue) also decreases abruptly (83).


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down, resulting in additional abrupt decreases in the conductance and the force. Theaverage breakdown force required to break Au-octanedithiol junctions is ∼1.5 nN(128), which is about the same as the force required to break an Au-Au bond underthe same conditions, indicating the breakdown probably takes place at the Au-Aubond. The conducting AFM break junction method also allows one to study theelectromechanical properties of single molecules.

3.3.4. Other scanning-tunneling-microscopy-controlled point contact mea-surements. The STM break junction method described above forms a molecularjunction by first contacting the molecules with the tip and then pulling the tip away.Haiss et al. (129) developed an STM trapping method to bridge molecules betweenthe tip and the substrate. The tip was brought close to but not into contact with thesubstrate covered with the dithiol molecules. They observed sudden jumps in the tun-neling current, which they attributed to the spontaneous chemical-bond formationbetween the tip and the molecule.

Yasuda et al. (130) showed recently that one can form a molecular junction bymoving the tip toward a given molecule until a chemical bond formed betweenthe tip and the molecule. They first imaged isolated target molecules [α,ω-bis-(acetylthio)terthiophene and α,ω-bis-(acetylseleno)terthiophene] embedded in anoctanemonothiol monolayer. The target molecules are terminated either with twothiol or selenium groups that can bridge the substrate and the tip, but the oc-tanemonothiols are bound to the substrate via its sole thiol group. They first locatedthe target molecules and then placed the tip above a molecule and moved it towardthe chosen molecule. When the tip formed a chemical bond with the terminal group(S or Se) of the molecule, the conductance jumped to a much higher conductance.

4. CRITICAL ISSUES IN SINGLE-MOLECULECONDUCTANCE MEASUREMENTS

The mechanical methods, especially when combined with force measurements andstatistical analysis, have the following distinctive features: (a) Peaks in the conductancehistogram located at integer multiples of a fundamental value can be used as a signatureto identify the conductance of a single molecule. (b) The simultaneously measuredforce tells us if a molecule is properly bound to two electrodes. (c) Statistical analysisreduces the chances of mistaking impurities as sample signals. (d ) Mechanical methodswork in solution and in vacuum, which not only makes it easy to introduce varioussample molecules into the measurement, but also provides a controlled and inertenvironment for the measurement. However, there are several issues that requirefurther study.

4.1. Molecule-Electrode Contact Geometry

In STM– or conducting AFM–break junction methods, a large number of molecularjunctions are repeatedly created, but these molecular junctions differ in their contactgeometries (Figure 8). In fact, the conductance of the last step, corresponding to

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Figure 8(a) Different contact geometries of a 1,6-hexanedithiol molecule bound to two Au electrodes.(b) Calculated conductance values of the molecule for the different contact geometries plottedversus the number of atoms protruding out of the crystal planes of the electrodes.(c) Distribution of conductance values with 1296 different contact geometries. Reprinted withpermission from References 14 and 16.

the formation of a single-molecule junction, varies considerably from one junctionto another, which reflects atomic-scale variations in the contact geometries (13, 14,16, 17). Guo and colleagues (16) calculated the conductance values of molecules withhundreds of different contact geometries (Figure 8c). By assuming that the statisticalweight of each geometry is equal, they obtained a distribution of the conductance


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HOMO: highest occupiedmolecular orbital

LUMO: lowest unoccupiedmolecular orbital

values. The distribution for 1,6-hexanedithiol bound to Au electrodes has a peak near∼2 × 10−3 G0, which is in good agreement with the experimental peak position at∼1.2 × 10−3 G0 (124). In addition to various binding sites of the anchoring groups(e.g., S) on Au electrodes, Muller (14) considered the possibility that the anchoringgroups may bind to one or more Au atoms protruding out of the electrode crystalplanes (Figure 8a). For 1,6-hexanedithiol, most of the 16 different contact geometrieshave conductance values close to ∼2 × 10−3 G0 (Figure 8b), in close agreement withboth the experiment and the calculations by Guo et al. (16).

In the case discussed above, pronounced peaks appear in the conductance his-togram, which are used to identify the conductance of single molecule. This methodfails if the distribution is too broad, as shown by Ulrich et al. (131). We also foundin our lab that some molecules, especially small conjugate molecules, exhibit well-defined steps in the individual conductance traces, but the conductance histogramsdisplay only broad distributions (132). Another possibility is that for (at least) somemolecules, more than one set of conductance peaks appear in the histograms. Li et al.(133) studied the conductance of single N-alkanedithiols (N = 6, 8 and 10) covalentlybound to Au electrodes. For each molecule, the conductance histogram reveals threesets of well-defined peaks near integer multiples of different conductance values.The two higher conductance sets can be described by the tunneling model with anidentical decay constant of 0.84 A−1 and interpreted in terms of different molecule-electrode contact geometries (134). The lowest one is thermally activated, which waspreviously reported by Haiss et al. (23), and is attributed to the thermal fluctuationof the molecular conformation.

The distribution of different contact geometries appears to depend on the waythe molecular junctions are formed. For example, Wandlowski and colleagues (85)measured the conductance of dithiol molecules using an STM break junction bycarefully avoiding the contact of the tip with the Au substrate. They found oneset of pronounced peaks in the conductance histograms. Conversely, Venkataramanet al. (127) reported that diamine-terminated molecules gave well-defined peaks in theconductance histograms by forcing the two electrodes to form a point contact duringthe approaching stage. In their case, the formation of point contacts was believed tobe crucial for the formation of an amine-Au bond.

4.2. Molecule-Electrode Energy-Level Alignment

The conductance of a molecule depends on the alignment of the molecular energylevels, especially the highest occupied molecular orbital (HOMO) and lowest oc-cupied molecular orbital (LUMO), relative to the Fermi levels of the electrodes.Typically, the Fermi level is positioned in the LUMO-HOMO gap of the moleculebecause if the HOMO or LUMO is close to the Fermi level of an electrode, electronstransfer between the molecule and the electrode, and consequently the molecules areoxidized or reduced spontaneously. The energy-level alignment is determined by theintrinsic properties of the molecule and the electrodes, and also by the interactionsbetween the molecule and the two electrodes, which are often difficult to determinefor both theory and experiment (135, 136).

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Surface spectroscopy techniques, such as ultraviolet photoelectron spectroscopyand X-ray photoelectron spectroscopy, can provide useful information about theenergy-level alignments of molecules adsorbed on surfaces (137). STM tunnelingspectroscopy has also been used to study the electronic states of molecules adsorbedon surfaces. Hipps and colleagues combined the tunneling spectroscopy with ultra-violet photoelectron spectroscopy to study metallo-porphyrins and phthalocyanineson Au (138) and resolved different molecular energy levels and their relative positionsto the Au Fermi level (77).

In electrolytes, one may gain valuable insights into the energy-level alignmentby measuring the oxidization or reduction potentials (Figure 9) (139). One mayeven tune the alignment by adjusting the potentials of the electrodes relative toa reference electrode inserted in the electrolyte. When the LUMO or HOMO isbrought close to the Fermi levels, electrochemical oxidation or reduction occurs. Formolecules that can be reversibly oxidized or reduced, significant changes in the con-ductance occur. This has lead to electrochemical gate control of the conductance ofsingle redox molecules that is analogous to field effect transistors (82, 140–142). Thisbehavior has been observed in several redox systems (82, 140–143). For example,Haiss et al. (140) reported an interesting potential-dependent conductance in violo-gen derivatives. Another example is perylene tetracarboxylic diimide terminated withthiol groups (Figure 9c) (141). The conductance of a single perylene tetracarboxylicdiimide molecule covalently bound to two Au electrodes increases reversibly overnearly three orders of magnitude as one shifts the LUMO of the molecule towardthe Fermi level of the electrodes.

4.3. Effect of External Force

The mechanical methods can create a molecular junction by controlling the separa-tion between two electrodes. It is natural to ask how the applied force affects the mea-sured conductance of the molecules. In the individual conductance traces recordedduring the breakdown of the molecular junctions, the step is rather flat, which meansthe force does not significantly affect the measured conductance until the contactbreaks down. However, carefully examining the steps, one can see a finite decrease,on average, in the conductance upon stretching. In the case of alkanedithiols, the de-crease is only 10%–20% before breakdown (81). Another observation is that the dis-tance over which a molecular junction can be stretched is typically several angstroms.Clearly a small molecule cannot be stretched over such a large distance without tear-ing the molecule apart. The reason for such a large stretching distance is that mostof the stretching actually takes place in the Au atoms near the molecule-electrodecontact rather than in the molecule, itself. When the force reaches ∼1.5 nN, thecontact breaks, and the maximum force that one applies to the molecule is ∼1.5 nN.For molecules such as alkanedithiols, such a force is not sufficient to change the elec-tronic states of the molecules or distort the structure of the molecule significantly.However, for conjugated molecules, such as oligothiophenes, the force can cause amuch greater change in the conductance, owing to a stronger coupling between theelectronic states and the structures of the molecule than that for alkanedithiols (81).


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O

OO

N N VsdSource Drain

Gate

Vg

a

Fermi levelFermi level

b

Redox molecule

O

Reference electrode

Working electrode 1 Working electrode 2

Molecular level

–0.8 –0.6 –0.4 –0.2

0.1

1

10

Vg (V vs. Ag/AgCl)

c

Cu

rren

t (n

A)

Figure 9(a) A redox molecule iscovalently linked to twoelectrodes in anelectrochemical cell.(Counter electrode is notshown here for clarity.)(b) In terms of the energydiagram, theelectrochemical gate voltage(Vg) shifts the molecularenergy levels up and downrelative to the Fermi energylevels of the source anddrain electrodes, and thecurrent is driven by a finitebias voltage (Vsd) betweenthe two electrodes. (c) Thecurrent through a singleperylene tetracarboxylicdiimide molecule as afunction of electrochemicalgate voltage (Vg).

One may also expect a stronger effect of the applied force on the conductance forsofter molecules.

4.4. Effect of Environment

The local environment (such as solvent molecules, ions, pH, and dopants) of amolecule can significantly affect the conductance of the molecule. Xiao et al. (144)measured conductance on several oligopeptides terminated with dithiols as a functionof solution pH and observed the dependence of the conductance on pH (Figure 10).

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0 2 4 6 8 10 12 14

pH

4.0

4.4

4.8

Cysteamine-Gly-Cys

NH

O NH2

O

SH

HN

HS

a b

G(1

0–

3G

0)

Figure 10(a) Molecular structure of a peptide, Cysteamine-Gly-Cys. (b) Dependence of peptideconductance on the solution pH.

Local heating: heatingeffect in a molecularjunction owing to anelectrical current passingthrough the junction

They traced the pH dependence to the protonation or deprotonation of NH2 andCOOH in the peptides, which changes electronic states and local charge distributionsof the molecules. The conductance of a molecule may also depend on the surround-ing ions (6). For example, the presence of Cu2+ and Ni2+ in solution changes theconductance of cysteamine-Gly-Cys by ∼300 and ∼100 times, respectively, owingto strong binding of the metal ions to the molecule. In a recent study by STM in anultrahigh vacuum environment, a charged dangling bond of Si induced a large changein the electronic states of a nearby adsorbed molecule, and the researchers attributedthis observation to the electric field by the charge (92). In the case of peptides, thebinding of Ni2+ and Cu2+ is strong and known to induce conformational changes inthe peptides. Therefore, in addition to an electrostatic effect, conformational changesmay be responsible for the change in conductance.

For certain molecules, the dependence of conductance on local environment maybe traced to the change in doping. Chen et al. (145) measured the conductance of ahepta-aniline oligomer attached to Au electrodes in toluene and in electrolyte. Thesingle-molecule current-voltage characteristic is linear in toluene but displays nega-tive differential resistance in an acidic electrolyte. The conductivity of bulk polyanilineincreases dramatically when it is oxidized in an acidic medium, in which acid playsthe role of doping the polymer materials. Similar to the bulk polyaniline, the conduc-tance of a single aniline oligomer also increases in the oxidized form in acid. Theseresults show the sensitive dependence of the conductance of the redox molecule onthe solvent, and on the doping condition.

4.5. Current-Induced Local-Heating Effects

Local heating is known to be a critical factor in the design of conventional silicon-based microelectronics. When current passes through a single molecule, how hot itgets is an important question. In a nanoscale junction, the inelastic electron mean free


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path is often large compared with the size of the junction, so each electron is expectedto release only a small amount of its energy to phonons (heat) during transport inthe junction (66, 67). However, substantial local heating may still arise owing to thelarge current density and thus power per atom.

Recently, researchers have reported experimental studies of local-heating effectsin quantum point contacts (146, 147). In the case of molecules, the current densityis much lower, but the thermal conduction of molecules may also be poorer thanthat of the metal contacts. Theoretical calculations have found a finite increase inthe temperature of the molecules as a result of the inelastic scattering of electrons(148, 149). Huang et al. (150) reported on an experimental approach to determinethe local temperature in a single molecule covalently bound to two Au electrodes.They measured the force required to break the attachment of the molecules to theelectrodes. Because the breakdown process is thermally activated, the average break-down force is sensitive to the local temperature of the molecule-electrode contact andcan be used to estimate the effective local temperature of the molecular junction. Foroctanedithiol, the temperature with a bias voltage of 1 V (current ∼20 nA) increasesby ∼25 K above room temperature.

5. OUTLOOK

The conductance of a single molecule depends not only on the intrinsic properties ofthe molecule and the probing electrodes, but also on the molecule-electrode contactsand its local environment. To determine the conductance unambiguously, one wishesto fabricate a molecular junction with molecule-electrode contacts that are well de-fined on the atomic scale and carry out the measurement in a controlled environment.Fabricating such contacts reproducibly has been a challenge. Despite the difficulty,researchers have made solid advances recently. For example, STM has been used tocreate a well-defined metal-molecule-molecule junction by precisely placing individ-ual metal atoms into contact with a molecule adsorbed on a substrate. To measure theconductance, the remaining challenges are to wire the two metal ends to an externalcircuit and to ensure that the electronic coupling between the molecular junction andthe underlying substrate is negligible.

Another important development is various break junction techniques. By com-bining a mechanical break junction with simultaneous force and conductance mea-surements, one can determine if the measured conductance is a result of a singlemolecule and how the molecule is bound to the probing electrodes. The approachalso allows one to create a large ensemble of molecular junctions with microscopi-cally different molecule-electrode contacts and to perform statistical analysis on theconductance values of the molecular junctions. A peak in the distribution gives anaveraged conductance of the molecule. The approach is simple and has been usedto measure the electron-transport properties of many different molecules in vacuumand in solutions. However, the exact molecule-electrode contact geometries createdby the break junction methods are usually unknown, and techniques that can provideatomic-scale structural information of the molecule-electrode contact will be of greatimportance to the field.

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SUMMARY POINTS

1. Determining the conductance of single molecule is a basic task in molecularelectronics.

2. To measure the conductance of a molecule, one must provide a reliable andreproducible contact between the molecule and two probing electrodes.

3. Measurement of single-molecule conductance has been difficult owing tothe lack of a technique that can provide reliable and well-defined molecule-electrode contacts.

4. STM-based methods can place metal atoms into contact with a singlemolecule on a substrate with atomic precision. Remaining challenges areto connect the metal atoms to the external electrodes for conductance mea-surements and to ensure the electronic coupling between the molecule andthe substrate does not interfere with the conductance measurement.

5. Break junction methods can create a large number of molecular junctionswith different contact geometries. Although these contact geometries arenot known precisely, the methods allow one to perform statistical analysisand to determine an average conductance of a molecule.

6. The conductance of a molecule depends also on its local environment.

7. By carrying out the measurement in an electrochemical environment, onecan tune the alignment of the molecular energy levels relative to the Fermienergy levels of the electrodes and thus control the conductance of themolecule.

8. Future techniques that can fabricate molecular junctions with molecule-electrode contacts that are well defined on the atomic scale and that cancharacterize the atomic-scale structures of the molecule-electrode contactswill contribute enormously to the field of molecular electronics.

ACKNOWLEDGMENTS

We thank NSF, DOE, VW, and DARPA (via AFOSR) for financial support.

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AR308-FM ARI 23 February 2007 13:44

Annual Review ofPhysical Chemistry

Volume 58, 2007Contents

FrontispieceC. Bradley Moore � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �xvi

A Spectroscopist’s View of Energy States, Energy Transfers, andChemical ReactionsC. Bradley Moore � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Stochastic Simulation of Chemical KineticsDaniel T. Gillespie � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 35

Protein-Folding Dynamics: Overview of Molecular SimulationTechniquesHarold A. Scheraga, Mey Khalili, and Adam Liwo � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 57

Density-Functional Theory for Complex FluidsJianzhong Wu and Zhidong Li � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 85

Phosphorylation Energy Hypothesis: Open Chemical Systems andTheir Biological FunctionsHong Qian � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �113

Theoretical Studies of Photoinduced Electron Transfer inDye-Sensitized TiO2

Walter R. Duncan and Oleg V. Prezhdo � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �143

Nanoscale Fracture MechanicsSteven L. Mielke, Ted Belytschko, and George C. Schatz � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �185

Modeling Self-Assembly and Phase Behavior inComplex MixturesAnna C. Balazs � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �211

Theory of Structural Glasses and Supercooled LiquidsVassiliy Lubchenko and Peter G. Wolynes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �235

Localized Surface Plasmon Resonance Spectroscopy and SensingKatherine A. Willets and Richard P. Van Duyne � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �267

Copper and the Prion Protein: Methods, Structures, Function,and DiseaseGlenn L. Millhauser � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �299

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AR308-FM ARI 23 February 2007 13:44

Aging of Organic Aerosol: Bridging the Gap Between Laboratory andField StudiesYinon Rudich, Neil M. Donahue, and Thomas F. Mentel � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �321

Molecular Motion at Soft and Hard Interfaces: From PhospholipidBilayers to Polymers and LubricantsSung Chul Bae and Steve Granick � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �353

Molecular Architectonic on Metal SurfacesJohannes V. Barth � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �375

Highly Fluorescent Noble-Metal Quantum DotsJie Zheng, Philip R. Nicovich, and Robert M. Dickson � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �409

State-to-State Dynamics of Elementary Bimolecular ReactionsXueming Yang � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �433

Femtosecond Stimulated Raman SpectroscopyPhilipp Kukura, David W. McCamant, and Richard A. Mathies � � � � � � � � � � � � � � � � � � � � �461

Single-Molecule Probing of Adsorption and Diffusion on SilicaSurfacesMary J. Wirth and Michael A. Legg � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �489

Intermolecular Interactions in Biomolecular Systems Examined byMass SpectrometryThomas Wyttenbach and Michael T. Bowers � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �511

Measurement of Single-Molecule ConductanceFang Chen, Joshua Hihath, Zhifeng Huang, Xiulan Li, and N.J. Tao � � � � � � � � � � � � � � �535

Structure and Dynamics of Conjugated Polymers in Liquid CrystallineSolventsP.F. Barbara, W.-S. Chang, S. Link, G.D. Scholes, and Arun Yethiraj � � � � � � � � � � � � � � �565

Gas-Phase Spectroscopy of Biomolecular Building BlocksMattanjah S. de Vries and Pavel Hobza � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �585

Isomerization Through Conical IntersectionsBenjamin G. Levine and Todd J. Martínez � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �613

Spectral and Dynamical Properties of Multiexcitons in SemiconductorNanocrystalsVictor I. Klimov � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �635

Molecular Motors: A Theorist’s PerspectiveAnatoly B. Kolomeisky and Michael E. Fisher � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �675

Bending Mechanics and Molecular Organization in BiologicalMembranesJay T. Groves � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �697

Exciton Photophysics of Carbon NanotubesMildred S. Dresselhaus, Gene Dresselhaus, Riichiro Saito, and Ado Jorio � � � � � � � � � � � �719

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Documents

Measurement of Single-Molecule Conductance - Arizona State University