Analyzing the Motion of Benzene on Au{111}: Single Molecule

J. Phys. Chem. C 2007, 111, 6167-6182

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FEATURE ARTICLE Analyzing the Motion of Benzene on Au{111}: Single Molecule Statistics from Scanning Probe Images Brent A. Mantooth,†,§ E. Charles H. Sykes,†,| Patrick Han,†,⊥ Amanda M. Moore,† Zachary J. Donhauser,†,# Vincent H. Crespi,‡ and Paul S. Weiss*,†,‡ Departments of Chemistry and Physics, The PennsylVania State UniVersity, 104 DaVey Laboratory, UniVersity Park, PennsylVania 16802-6300 ReceiVed: September 27, 2006; In Final Form: February 1, 2007

Analyses of time-resolved sequences of molecular-resolution images allow the characterization and quantification of site-specific interactions and dynamics of adsorbed species. We have used scanning tunneling microscopy to probe and to quantify the weak substrate-mediated interactions in benzene overlayers on Au{111} at 4 K. We observed that benzene molecules exhibit three types of motion; two-dimensional (2D) desorption, 2D adsorption, and simultaneous cooperative shifts (2.4 ( 0.6 Å) of many molecules in molecular cascades. Correlating the probability of 2D desorption with the number of nearest neighbors of the desorbing molecules enables the calculation of the magnitude of the adsorbate-adsorbate, substrate-mediated interactions. We observed molecular cascades in chains of up to 12 molecules simultaneously moving in the same direction. These molecular cascades arise from translation of the overlayer structure and are highly correlated with 2D desorption and 2D adsorption.

1. Introduction Since the inception of atomic imaging with field ion microscopy, the ability to observe the dynamics of single atoms has elucidated new diffusion mechanisms and adsorbateadsorbate interactions.1,2 The ability of scanning tunneling microscopy (STM) to image molecules has led to similar insights on the dynamics and motion of molecules.3,4 This includes the diffusion of single adsorbates monitored with tracking tunneling microscopy5-7 and correlation techniques applied to observe high coverage systems yielding adsorption sites, ordering, and interaction energies.8,9 Time-resolved sequences of STM images have been used to measure diffusion rates and adsorbate-adsorbate interactions.10-16 Most of these techniques image only one molecule at a time or measure only a few molecules in an image. In contrast, using digital image processing, we are able to identify and to characterize all of the molecules (in this case about 120 molecules in each frame) in the field of view. Using this technique, we can locate many molecules in an image or series of images and characterize each molecule individually. We have applied these techniques to characterize stochastic and driven * To whom correspondence should be addressed. E-mail: [email protected]. † Department of Chemistry, The Pennsylvania State University. ‡ Department of Physics, The Pennsylvania State University. § Current address: Research and Technology Directorate, U.S. Army Edgewood Chemical Biological Center, Aberdeen Proving Ground, Maryland 21010-5424. | Current address: Department of Chemistry, Pearson Lab, Tufts University, Medford, MA 02155. ⊥ Current address: The Texas A&M University, College Station, TX 77842. # Current address: Department of Chemistry, Vassar College, 124 Raymond Avenue, Poughkeepsie, NY 12604.

conductance switching17-21 and to correlate the adsorption of CO with the Friedel oscillations on a Ag{111} surface.22 Here, we apply these techniques to characterize the dynamics of benzene adsorbed on Au{111}. This system was chosen because benzene has well-defined electronic interactions with metal surfaces,23,24 and the thermodynamics of adsorption and desorption have been characterized for some metal surfaces.25 Compared with other metals, the benzene-Au bond strength is relatively weak, allowing the adsorbate-adsorbate interactions to play a significant role. 2. Benzene on Au{111} Measurements were performed in a custom-built low temperature, ultrahigh vacuum (UHV) STM, described elsewhere.26 This instrument can operate at fixed low temperatures of 4 and 77 K. A Au{111} substrate was prepared from a Au on mica sample (purchased from Molecular Imaging) by repeated cycles of sputtering and annealing (sputtering at 1 keV Ar+ at ∼800 K, annealing at ∼800 K for 3 min). Liquid benzene (99.9% purity, Sigma Aldrich) was degassed by repeated freeze-pump-thaw cycles. The 4 K sample was dosed with room temperature benzene (through a leak valve) via line-of-sight dosing.26 All images were acquired at 4 K in constant-current mode with a mechanically cut Pt/Ir (85/15%) tip. Unlike our previous work on Pt{111}27 and Cu{111},29-31 the Au{111} surface was dosed at 4 K, allowing higher coverages of benzene. Studies of benzene adsorbed on Au{111} and other face-centered cubic (fcc) {111} noble metal surfaces have shown that the planes of the molecules lie parallel to the surface, and that bonding to the surface occurs predominantly through π molecular orbitals.23,24,32-37 Temperature-programmed

10.1021/jp0663558 CCC: $37.00 © 2007 American Chemical Society Published on Web 04/04/2007

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Brent A. Mantooth is a research chemist for the research and technology directorate of the Edgewood Chemical Biological Center at Aberdeen Proving Ground, MD. He received his B.A. in Computer Science and B.S. in Chemistry from Mercer University in 1999. He received his Ph.D. in Chemistry from The Pennsylvania State University in 2005 where he worked with Prof. Paul S. Weiss.

Charles Sykes is currently an assistant professor of chemistry at Tufts University. He obtained his M.Chem. from Oxford University, U.K., in 1998, and Ph.D. in Chemistry from Cambridge University, U.K., in 2002. His postdoctoral work at The Pennsylvania State University focused on substrate-mediated interactions between molecules. He undertook further postdoctoral work in the Center for Optoelectronics and Optical Communications at the University of North Carolina at Charlotte.

desorption (TPD) results indicate that the bonding of benzene on Au{111} is stronger than on Ag{111} or Cu{111} but weaker than on Ni{111}, Pd{111} and Pt{111}.36 We have previously described the coverage-dependent overlayer structures of benzene on Au{111}.38 Similar to its behavior on Cu{111},29-31 at coverages of ∼0.1 monolayers (ML), benzene forms a two-phase system on the Au{111} surface: a two-dimensional (2D) solid at the substrate step edges and a 2D gas on the terraces.38 Even at 4 K, when imaged by STM, the benzene molecules are mobile over the Au{111} terraces, forming a 2D gas phase with the molecules confined to the surface.39,40 Due to the relatively slow acquisition rate of STM images, these fast-moving 2D gas molecules are imaged only in part (i.e., as streaks) or not at all; the 2D solid-phase yields well-resolved molecules. This mismatch in time scale is present even for high-speed scanning tunneling microscopes designed to measure dynamics with image acquisition rates of ca. 200 Hz, which is still slow relative to many chemical processes.41 At low coverage, a 2D solid-phase exists at step edges and defect sites. The step edges have a different electronic structure than the terrace. Electrons shift from the top of the step to the bottom; filled states are enhanced below the step riser, and empty states

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Patrick Han is a postdoctoral fellow at Texas A&M University. He obtained his B.S. in chemistry at Ithaca College, Ithaca, NY, and his Ph.D. in 2005 from The Pennsylvania State University, University Park, PA. His current research involves the use of variable pressure, variable temperature scanning tunneling microscopy to investigate supported metallic and bimetallic catalytic model systems, aiming to understand the “pressure gap” that still splits the perspectives from surface science and industrial catalytic systems.

Amanda M. Moore is currently working toward a Ph.D. degree in Chemistry at The Pennsylvania State University, University Park, where she works with Prof. Paul S. Weiss. She received her B.S. degree in chemistry and music (with honors) from Pacific University, Forest Grove, OR, in 2002. She investigates nanoscale systems focusing on potential molecular electronic devices and semiconductor devices developing and applying novel instrumentation, including microwavecoupled scanning probe microscopy.

are enhanced above the step riser and ∼5 Å beyond the step edge onto the lower terrace. This compensates for the change in coordination of the surface atoms at the step edge and is known as the Smoluchowski effect.42 Benzene acts as a weak nucleophile (electron donor) and is thus attracted to the increased empty state density on the top of (and just below) the steps.28-31,68 On Pt{111}, STM images indicate that motion of low coverage, terrace-adsorbed benzene molecules is frozen out at 4 K.27,40 However, even at coverages of 0.9 ML, benzene appears mobile on Au{111} terraces, indicating that Au/benzene has a weaker surface-adsorbate bond or a more weakly corrugated adsorbate-substrate potential interaction than does Pt/benzene. This motion is most likely induced by the STM.43 On Pt{111}, benzene can adsorb at hcp 3-fold hollow, fcc 3-fold hollow, or defect-stabilized atop sites.27,44 Some of these binding sites revealed that the adsorbate depleted the local density of states (LDOS) in a three-lobed geometry of the metal substrate up to 10 Å from the center of the molecule.27 These electrondepleted regions enhance the adsorption for further benzene molecules in these regions at higher surface coverages, much

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Zachary Donhauser is an assistant professor of chemistry at Vassar College in Poughkeepsie, NY. He is a 1998 graduate of Providence College and received his Ph.D. in chemistry from The Pennsylvania State University in 2003. His current research interests involve the study of cytoskeletal elements using scanning probe microscopy.

Vin Crespi is a professor of physics and materials science and engineering at The Pennsylvania State University. He received his Ph.D. in Physics at UC Berkeley and joined the faculty at Penn State in 1997. Crespi is currently the associate director of the Penn State Materials Research Science and Engineering Center. His research covers a broad range of condensed matter theory, from simple analytical models to large-scale computation. Topics of research include carbon nanostructures, photonic materials, superconductivity, surface science, semiconductor alloys, magnetic frustration, molecular and catalytic motors, phyllotaxis, and self-assembly. Crespi is also active in public outreach and has contributed to the development of several cart-based museum shows on materials. His name appears on a blackboard in the movie Fat Man and Little Boy, if you know where to look.

like the enhanced empty states at step edges. On Cu{111}, benzene molecules were found to have a similar effect at the step edges. In this case, the formation of a row of benzene molecules along a step edge perturbs the surface LDOS, enhancing the ability for a second row of molecules to form, thereby perturbing the substrate and enabling a third row of benzene molecules to adsorb.30,40,45 We did not observe multiple rows of benzene molecules along step edges for Au{111} at low coverage.43 The surface stress inherent to a Au{111} surface induces a (23 × x3) herringbone reconstruction with an average compression of 4.5% along one of the three [1h10] directions,46-48 as seen in the inset image of Figure 1. The reconstructed surface contains three distinct regions: 0.3 Å protrusions that constitute the soliton walls (displayed as bright lines), narrow regions between soliton walls that have a hexagonal close-packed (hcp) structure (ABA stacking), and wider regions between sets of soliton walls that have a fcc structure (ABC stacking). The only difference between the fcc and hcp regions is the registration

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Paul S. Weiss is a distinguished professor of chemistry and physics at The Pennsylvania State University. He received his S.B. and S.M. from MIT in chemistry in 1980 and his Ph.D. in chemistry from UC Berkeley in 1986. After postdoctoral appointments at AT&T Bell Laboratories and IBM Almaden Research Center, he began his academic career at The Pennsylvania State University in 1989. His interdisciplinary research group includes chemists, physicists, biologists, materials scientists, electrical and mechanical engineers, and computer scientists. Their work focuses on the atomic-scale chemical, physical, optical, mechanical, and electronic properties of surfaces and supramolecular assemblies. He and his students have developed new techniques to expand the applicability and chemical specificity of scanning probe microscopies. They have applied these and other tools to the study of catalysis, self- and directed assembly, physical models of biological systems, and molecular and nanoscale electronics. They work to advance nanofabrication down to ever smaller scales and greater chemical specificity in order to connect, to operate, and to test molecular devices. Weiss was recently named Editor-in-Chief of a new ACS journal focusing on nanoscience, ACS Nano.

of the top three layers of atoms; however, this difference in registration is enough to affect the electronic structure of the surface.49 Various experimental and theoretical works have derived the potential for surface-state electrons at the Fermi energy for each region of the surface. It was found that the surface-state electrons are less strongly bound to the fcc region than the hcp region.46,49 The spacing of these three regions allows the simultaneous imaging and characterization of adsorbates interacting with three different surface potentials. These different interactions are manifested in properties such as the region-dependent packing structures (Figure 1). At a coverage of ca. 0.9 ML, the benzene molecules form a 2D solid on the terraces and selectively occupy the hcp and fcc regions (Figure 1). At the tunneling conditions used in Figure 1, the benzene molecules appear as 0.6 ( 0.1 Å protrusions that are spaced 7.0 ( 0.1 Å apart. Due to the selective adsorption of the benzene molecules in the hcp and fcc regions, the soliton walls appear as lower (dark) regions. Both the fcc and hcp regions have long-range commensurate overlayer structures.38 For the fcc region, we assigned a (x133 × x133)R17.5° overlayer structure with p6 symmetry (top of Figure 2), and for the hcp region, we assigned a close-packed (x52 × x52)R13.9° overlayer structure (bottom of Figure 2). Since the gas-like soliton wall absorbate regions isolate the crystalline stripes of pinwheel and closed-packed structures from each other, each soliton stripe forms a quasi-1D system. Such a 1D system with short-range interactions cannot sustain long-range translational order along its axis, and it is not surprising that perturbations arising from fluctuations in the atomic structure of the soliton walls can induce substantial local shifts and rearrangements of the pinwheel structure. Our proposed structures for the hcp and fcc regions place molecules in 3-fold hollow, atop, and near-bridge sites, all of


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Figure 1. Scanning tunneling microscope image of 0.9 ML of benzene on Au{111} (180 Å × 180 Å, sample bias of 200 mV, tunneling current of 10 pA). Each round protrusion in the image corresponds to a single benzene molecule.43 The image shows that the benzene overlayer structure at this coverage is different for the hexagonally close-packed (hcp) and face-centered cubic (fcc) regions. The circle highlights a pinwheel structure in the fcc region, and the white square highlights the region where the time-resolved series of images was acquired. The inset shows an STM image of the clean Au{111}-(23 × x3) surface (600 Å × 600 Å, sample bias of 100 mV, tunneling current of 100 pA). The horizontal streaks near the top of the image indicate monatomic step edges; the pairs of lines are the 0.3 Å protrusions of the Au{111} herringbone reconstruction. The narrow regions between two soliton walls (the pairs of protruding rows in the inset) have hcp packing and the larger regions between soliton walls have fcc packing.

which have been observed for benzene on Pt{111}, Pd{111}, or Rh{111}.27,50-52 For clarity, the 3-fold hollow and atop adsorbed molecules are highlighted with cyan and white circles, respectively, in Figure 2. For both overlayers, there is a hexagonal ring of six benzene molecules around the 3-fold hollow and atop adsorbed molecules. In the hcp region, this ring is shared between the 3-fold hollow and atop molecules, whereas each 3-fold hollow and atop molecule has its own set of six surrounding benzene molecules in the fcc region. For this reason, we refer to the fcc overlayer at near-monolayer coverage as a pinwheel structure, where molecules that have six nearest neighbors, in this case the 3-fold hollow and atop molecules, are called “pinwheel centers”. The surrounding six benzene molecules at near-atop sites are the “wheel” molecules. An example of this pinwheel structure is highlighted by the circle in Figure 1. The center-to-center distance of a pinwheel center molecule to a wheel molecule is 1.5% longer than the close-packed molecules in the hcp region. The nearest neighbor distances for hcp and fcc regions are 6.92 and 7.04 Å, respectively. The coverages are 2.40 and 2.01 molecules/nm2 for hcp and fcc regions, respectively. Similar pinwheel structures have been observed for the linear molecules N2O on graphite (0001)53 and N2 theoretically modeled on a triangular lattice.54 An important feature of Figure 1 is the apparent noise or streakiness in the soliton regions. Scanning tunneling microscopy is an inherently slow technique, usually limited by the bandwidth of the current preamplifier and feedback loop electronics (typically 1-3 kHz). If a molecule diffuses under the tip on a time scale faster than imaging (1-10 ms per pixel), it will cause a topographic noise spike in the image. Thus, the apparent noise and partial imaging of some molecules in the soliton region

Figure 2. Benzene overlayer structures for the fcc (top) and hcp (bottom) regions of Au{111}. The cyan and white circles denote benzene molecules that are adsorbed at 3-fold hollow or atop sites, respectively. The white parallelograms denote the (x133 × x133)R17.5° overlayer for the fcc region (top) and (x52 × x52)R13.9° overlayer for the hcp region (bottom). The magenta parallelogram represents the unit cell of the Au surface. The radius of the atoms in the benzene molecules has been reduced to allow for the visualization of the adsorption sites; however, bond lengths are drawn to scale. The rotational alignment of the benzene molecules is not resolved using STM and is arbitrarily drawn here.

indicates the presence of a (laterally confined) 2D gas where some molecules are transiently adsorbed or actively diffusing (or being swept about by the tip).16,38,55 Similar transient adsorption of benzene was observed for the Cu{111} surface and attributed to substrate-mediated interactions.30,40,45 This phenomenon has also been observed for benzene on Cu{111} and for CS2 on Au{111}; transient features of the same amplitude as the apparent-height of the molecules indicated interaction of the mobile molecules with the surface state.29,30,56 The time scales given above correspond to constant-current mode imaging, and constant-height images can acquire images at significantly faster rates, from 20 to 30 frames/s, though this

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J. Phys. Chem. C, Vol. 111, No. 17, 2007 6171 The next task was to identify the locations of all of the molecules in each frame of the image sequence. The raw image, Figure 4A, contains too much noise to identify single molecules directly. A cross-correlation technique similar to the registration algorithm can be used to identify features in an image.63 Instead of correlating two full images, an image is correlated with a simulated molecule (the feature to be identified); thus, the resulting correlation image exhibits a peak at the site of each molecule. The simulated molecule, shown in Figure 4B, is a 2D Gaussian peak with the same dimensions (height and width) as a benzene molecule, centered in an image the same dimensions as the STM image. The cross-correlation image, Figure 4C, is calculated by63

Figure 3. Perspective display of an STM image of benzene molecules at high coverage (0.99 ML) on the herringbone-reconstructed Au{111} surface. The image is of a 180 Å × 180 Å area acquired with a sample bias of -1 V and tunneling current of 10 pA. At this coverage, the overlayer is continuous over the entire surface, completing the (x52 × x52)R13.9° structure of the hcp region. The lower (dark) areas are single benzene vacancies, located mostly over the soliton walls.

mode places constraints on image acquisition, such as a smaller field of view and higher instrument stability.14,57 As the coverage was increased to almost a monolayer (0.99 ML), all regions of the overlayer assumed the hexagonal (x52 × x52)R13.9° structure of the hcp region, as shown in Figure 3. Benzene vacancy sites were primarily located over the soliton walls. The remaining protrusions on the soliton walls indicate that the adsorbate-substrate bond is not strong enough to lift the herringbone reconstruction, unlike that observed for Au-S bonds in self-assembled monolayers58 or K and Na overlayers, which reconstruct the surface to Au{111}-(1 × 1).59,60 At a coverage of 0.9 ML, there is an equilibrium between the 2D gas phase and the 2D solid-phase that manifests itself as various types of motion on the surface. To observe and to quantify the dynamics of this system, a series of 600 time-lapse images of an 81 Å × 81 Å area were acquired over 41 h (∼4.07 min/frame). The region where this series of images was acquired, highlighted by the white box in Figure 1, includes hcp, fcc, and soliton regions. This series of images is included as a movie in the Supporting Information. Using digital image processing, each molecule was identified and sequential images were analyzed to track the motion of each molecule. A thorough analysis of these data has revealed three types of motion: (1) the desorption of a molecule into the 2D gas phase between subsequent images, (2) the uncorrelated readsorption of a molecule from the 2D gas phase, and (3) multiple molecules simultaneously moving (2.4 ( 0.6 Å) in the same direction (cascade motion). Each type of motion will be discussed in detail. 3. Digital Image Processing The data set presented here requires several types of image processing and analyses, including drift compensation, molecule identification, and detection of changes in the overlayer from image to image.61 Through the course of acquiring these data, the tip laterally drifted ∼27 Å across the sample. For this analysis, the location of each molecule must be known from the first frame through to the last. To accomplish this, we used a Fourier-transform-based cross-correlation image analysis to calculate the registration of each frame relative to the first frame.62 The resulting drift track enables the registration of the location of each molecule throughout the course of the image sequence.

C(x,y) ) F

-1

[F (A(x,y))F(B(x,y))*]

(1)

where C is the cross-correlation image, F -1 is the inverse Fourier-transform, F is the Fourier-transform, A is the original image, B is the simulated image, and * denotes the complex conjugate. After cross-correlation, the next step is to “threshold” the correlation image to locate each molecule. Rather than a cross-correlation intensity-based threshold, we detect the regional maxima of the cross-correlation images to locate the molecules. This results in each molecule being represented by a single pixel with a value of one, and the remainder of the image being set to zero, yielding the binary image shown in Figure 4D. The ones in the binary image (white) directly correspond to the locations of benzene molecules in the initial image, as seen in Figure 4E, where each red circle represents a one in the binary image drawn over the raw data. One of the more common errors encounted by this technique is incorrectly locating the center of each molecule; an example of this type of error is shown by the rightmost white circle in Figure 4E. This is caused by the local environments of the molecules; for example, the molecules next to soliton walls are often detected as being farther away from the soliton walls than they actually are. Another type of error is not locating a molecule, either by false detection (i.e., detecting a molecule that is not in the image) or by missing it altogether (i.e., not identifying a molecule that is in the image). These types of errors are caused by noise in the raw images, such as those marked by the two leftmost white circles in Figure 4E. These detection errors can be avoided by processing the raw data with low pass or median filtering before cross-correlation. Instances where molecules were improperly detected were corrected by hand. Through the described image processing, 78,000 molecules were located in the 600-frame sequence (about 120 molecules per frame). In addition to providing the location of each benzene molecule, the binary image (Figure 4D) can be used to calculate the number of nearest neighbors for each molecule, and also to detect any changes in the overlayer such as 2D adsorption, 2D desorption, or small motion of any molecule. To determine the number of nearest neighbors for each molecule, the distance between every molecule is calculated, and molecules closer than 8 Å are counted as nearest neighbors; this threshold value for nearest neighbor distance was selected by the radial distribution function (RDF) results, discussed below. The adsorption region for each of the molecules is determined by its location on the surface, corresponding to the hcp, fcc, or soliton regions. Each of these properties are individually marked in Figure 5, where colored outlined shapes denote the region of adsorption for benzene molecules. The molecules marked with black diamonds were detected but not used in the desorption analysis (discussed below) because their complete sets of local neighbors were not imaged. The numbers indicate the number of nearest neighbors.


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Figure 4. Using digital image processing, each of the stable benzene molecules in an image is located. A is an unfiltered image from the image sequence. B is the simulated image of a single benzene molecule represented by a 2D Gaussian peak. Cross-correlating (eq 1) image A and B results in image C. Using a regional maximum detection algorithm, image C is transformed into a binary image containing ones (white) at the locations of local maxima and zeros (black) elsewhere. The single pixels were enlarged by dilation for enhanced visualization in this image. This binary image is used to label (red circles) the raw data (benzene molecules) as shown in E. F illustrates the detection algorithm to identify motion on the surface, as discussed in the text. The black background represents zeros, the white regions represent two dilated images (Di and Di+1), the red regions represent the logical AND (Ai) of the two dilated images (eq 4). The white circles highlight the three scenarios observed from this calculation: white regions containing a red region denote a molecule did not move, a single white region denotes a molecule 2D desorbed or 2D adsorbed from the site, or a set of two white regions in close proximity denotes a small displacement of a molecule.

Detecting motion in the overlayer requires several types of digital image processing techniques, most of which are binary morphological (e.g., dilation) or logical (e.g., AND) operations. Since each benzene molecule is represented by a single pixel in the binary image, any analysis would require an exact alignment of benzene molecules from frame to frame. This alignment is further complicated by the errors associated with locating both the center of a molecule and the drift between frames, as discussed above. To minimize the need for exact alignment, the binary image is dilated.64 Dilating (x) the binary image Fi with the structuring element B, as given by

[ ] 1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

(2)

yields the dilated image, Di. The dilation operation has transformed the single pixels that represent each benzene molecule into a 5 × 5 array of ones. To detect motion in the overlayer, several logical operations are required. The logical OR (∨) of two frames, Ri, is given by

Ri(x,y) ) Di(x,y) ∨ Di+1(x,y).

Ai(x,y) ) Di(x,y) ∧ Di+1(x,y).

(3)

The image Ri thus contains the dilated version of all of the

(4)

The red regions in Figure 4F represent the logical AND image, Ai. The set Si of any elements in Ri that does not have a corresponding element in Ai is

Si ) {r|r ∪ a ) L, for r ∈ Ri, a ∈ Ai}.

Di ) Fi x B 1 1 B) 1 1 1

molecules in frames i and i + 1, as depicted by the white regions in Figure 4F. If a molecule does not undergo some type of motion between frames, there will be overlap between the dilated images. This overlap is detected using the logical AND (∧) of the dilated images, as given by

(5)

corresponding to molecules that exhibited some type of motion. The resulting image, Si, contains the dilated version of the molecule location. The last step is to relate the image Si back to the single pixels (benzene molecules) in Fi or Fi+1 using a logical AND operator. This procedure not only returns the location of the benzene molecule that has moved but also reveals the type of motion. The 2D desorption events, Sdi, are obtained by

Sdi(x,y) ) Si(x,y) ∧ Fi(x,y)

(6)

and the 2D adsorption events, Sai, are obtained by

Sai(x,y) ) Si(x,y) ∧ Fi+1(x,y).

(7)

These 2D adsorption/desorption events are marked in Figure 5

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Figure 6. Radial distribution functions (RDF) for the fcc and hcp regions for 0.9 ML coverage of benzene on Au{111}. The red lines denote the radial distribution function calculated using the data from the binary images. The blue lines represent the RDF predicted for the proposed overlayer structures. The colored circles on the left of each graph represent the overlayer structure for that region; like colors correspond to molecules that are the same distance from the center molecule. The corresponding distance is marked in the graph with the same color. For the fcc graph, the cyan and magenta lines correspond to the distances that generate the peaks between the first and second nearest-neighbor distances. Figure 5. Results obtained from image processing. Each molecule is located and marked according to its region of adsorption (hcp, fcc, soliton) by colored outlined shapes, as identified in the legend. Motion events are marked, according to type, by colored dots. The numbers in white represent the number of nearest neighbors for each molecule.

with yellow and green dots, respectively. With this information, we correlate the motion of various regions of the surface with properties such as the number of nearest neighbors to calculate interaction energies. It is important to distinguish small displacements and 2D desorption. These small motions are characterized by two closely spaced motion events (the molecules’ locations before and after movement), as illustrated by the white circle in the middle of Figure 4F. Using a technique identical to the motion detection algorithm just described, these small motions can be identified and isolated from the 2D adsorption/desorption events. This is accomplished by substituting Si (motion events image) for Fi (the binary image corresponding to molecule location) in eqs 2-5, mutatis mutandis. In this case, it takes two iterations of dilation (eq 2) to generate the required overlap and thus identify the small motion. This process generates upper and lower bounds on the distance a molecule travels to be identified as part of a cascade event; the frame-to-frame distance for a molecule must be a minimum of 1.25 Å away (four pixels here) but not more than 3.15 Å (ten pixels here), as determined by the size of the structuring element (B) and number of iterations of dilation. After all of the small motion events are identified, they are removed from the Sdi and Sai images, and independently analyzed. Both in the Supporting Information and in Figure 5, these events are marked with blue and red dots that correspond to the initial and final location of each benzene molecule, respectively. Using digital image processing, we have located each molecule, the region on which each molecule is adsorbed, calculated the number of nearest neighbors, and detected various types of motion in the overlayer. All of this information can be visualized in relation to the raw STM data, as seen in Figure 5. With each molecule digitally located, the measured and proposed overlayer structures can be compared using a radial

distribution function, g(r). A radial distribution function is a measure of the local structure of the overlayer as defined by

g(r) ) (NF)-1

ni(r, dr) . i)1 2πr dr N

∑

(8)

where r is the center-to-center distance between molecules, N is the total number of molecules, F is the density of molecules, ni(r,dr) is the number of molecules that are in the annulus r ( dr away from molecule ni. Using every molecule identified in the 600-frame sequence of images, g(r) was calculated and compared to the proposed overlayer structures using dr ) 0.25 Å (Figure 6). For comparison between the measured data and the proposed structures, g(r) for the proposed structure was normalized such that the first nearest neighbor peaks at 7.0 Å are the same intensity. There is a strong correlation of peak location and intensity with that predicted for our proposed overlayer structures. The width of the peaks results from the accuracy with which each molecule is detected and thus the detection errors discussed earlier contribute to peak width. The first peak that occurs at 7.0 Å corresponds to molecules that are nearest neighbors. Therefore, g(r) is used to determine the distance threshold to calculate the number of nearest neighbors, n, for each molecule. From Figure 6, a value of 8.0 Å was selected as the maximum distance between molecules to be considered a nearest neighbor. 4. Two-Dimensional Desorption/Adsorption of Single Molecules Even with the observed 2D adsorption and 2D desorption, the apparent coverage of benzene molecules undergoes only small fluctuations about a dynamic equilibrium between a highly mobile 2D gas phase and a 2D solid phase; the 600 image data set included 1,149 2D desorption events and 1,147 2D adsorption events, shown in Table 1. Similar 2D gas/solid coexistence has been seen for benzene on Cu{111},30 and sub-phthalocyanine molecules on Ag{111}.39 Benzene undergoes similar long jump diffusion events on Si{111}.65


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TABLE 1: Data for Motion Events as a Function of Number of Nearest Neighbors (n) and Regiona n

fcc

hcp

soliton

1 2 3 4 5 6

19/25/138 79/93/1279 93/110/3125 96/86/7252 45/31/13307 4/2/2026

1/8/53 18/32/401 49/54/2317 56/32/5208 16/12/4937 2/9/3510

35/92/275 148/186/771 238/228/1414 151/116/1144 37/18/234 3/0/3

a The numbers represent 2D adsorption events/2D desorption events/ number of molecules detected. The 2D desorption events and number of molecules detected correspond to the sum of M and C over all frames as described in eq 10.

In any system that uses a scanning probe to monitor motion, it is important to determine if the probe causes or influences the motion. For our specific system, it is difficult to monitor the influence of the tip. Attempts were made to image this system under different tunneling currents and voltages to elucidate the perturbative effect of the tip. However, this proved difficult because when either the tunneling current was raised (>30 pA), or the bias voltage was decreased ( 0). The resulting trend (Figure 7) shows an exponential relationship between the probability of desorption and the number of nearest neighbors. Using eq 9, the slope of the log of P(n) versus n yields ∆ESMI ) 0.54 ( 0.05 kJ mol-1 molecule-1, and the intercept yields ∆Etip ) 0.51 ( 0.06 kJ mol-1.70 The hcp and fcc regions were independently analyzed. However, it was found that the values for both regions are not statistically different; thus, we present the average of the two regions.43 It would be informative if these experiments could be carried out over a range of temperatures, though, as previously mentioned, the temperature is not easily varied in the instrument used. Adsorbates can interact with one another through several types of direct (through-space) interactions such as electrostatic, dipole-dipole, or van der Waals (VDW) interactions. However, as VDW interactions decay as 1/d6 the interaction between benzene molecules at 6.95 Å experiences a 50-fold decrease in interaction energy as compared to the 3.6 Å spacing observed elsewhere.66 When an adsorbate bonds to the substrate, it can perturb the lattice or electronic structure of the substrate.71,72 These perturbations change the local properties of the substrate

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Figure 8. Spatial histograms indicating the locations of 2D adsorption or 2D desorption events. Background images of frames 1 and 600 (displaced to compensate for drift) are displayed for reference. Bright dots (see color scale on the left) indicate where 2D adsorption events occurred (A), B indicates where 2D desorption events occurred. C shows the shortest distance from each point in the fcc and hcp region to the soliton wall; this is used to calculate the data for Figures 9 and 10.

and thus influence how other adsorbates interact with the substrate, referred to as a substrate-mediated interaction. Substrate-mediated interactions can act by scattering surface state electrons, analogous to Freidel oscillations, or they can act by perturbing the local substrate LDOS. We and others have previously observed how these SMIs can influence adsorbates on surfaces.29-31,68,72 Surface electronic perturbations can result from surface strain in the substrate.73 High surface strain is responsible for the herringbone reconstruction of the Au{111} surface.47 However, even after reconstruction, there is still strain in the overlayer. The herringbone reconstruction is not lifted by the benzene molecules, indicating that the presence of the adsorbate-surface interaction does not substantially change the surface stress of the substrate. Like other fcc{111} noble metal surfaces, Au{111} has an s-p derived surface state whose electrons behave as a nearly free 2D gas.49,74-78 These electrons can scatter from substrate defects or adsorbates and create quantum interference patterns,74,79,80 generating favorable and unfavorable adsorption sites.29,40,68,81 It has been shown that these surface-state interference patterns are responsible for long-range adsorbate interactions15,74,81 and can influence adsorption sites for a variety of atoms and molecules.14,15,22,56,71,74,81 Most often, these molecules interact with the electrons at or near the Fermi energy of the substrate; thus, the interference patterns on the surface reflect the Fermi wavelength, kF ) 1.7 nm-1 for Au{111}.74,82 Unfortunately, we are unable to probe the surface electron density oscillations directly, due to the near-monolayer coverage of benzene molecules. However, at low coverage, we have observed that benzene molecules can perturb the electronic structure of the Au{111} surface,43 and in Pt{111} benzene can deplete the LDOS up to 10 Å away.44,83 Thus, we postulate that the mechanism for this SMI involves the adsorbed benzene molecule donating charge to the surface, creating image charges at distances 5-10 Å from the molecule. These perturbations of the electronic structure of the surrounding surface create both favorable and possibly unfavorable sites for the adsorption of other benzene molecules and are responsible for the enhanced stability of molecules with more nearest neighbors. Further modeling of this system is required to confirm this mechanism. In addition to characterizing 2D desorption as a function of nearest neighbors, we have also characterized the system as a function of the locations from (to) which benzene molecules desorbed (adsorbed). By correlating the location of adsorbing and desorbing molecules, we constructed a spatial histogram

Figure 9. Multidimensional histograms for the fcc region that represent A, 2D adsorption events; B, 2D desorption events; and C, number of molecules (indicated by color) as a function of distance from the soliton wall (x axis) and number of nearest neighbors n (y axis). White regions in these plots indicate “no data”.

(Figure 8) that highlights the most active sites. The majority of adsorption and desorption events were located in the soliton region; however, there was also motion in the fcc and hcp regions. This distribution is not surprising as we have observed that soliton regions are the last to be occupied by benzene molecules, apparently due to the different substrate electronic structure.43 To determine if all of the 2D adsorption and 2D desorption was limited to the 2D gas-solid interface, we calculated the distance of these events from the soliton-fcc/hcp interface. Figure 8C shows the shortest distance from the soliton interface for both the hcp and fcc regions. By correlating the distance from the soliton interface with adsorption and desorption events, we determined the extent to which this interface plays a role in the 2D adsorption and desorption. Figures 9 and 10 are multidimensional histograms for the fcc and hcp regions, respectively, of 2D adsorption (A), 2D desorption (B), and number of molecules (C) as a function of distance from the soliton interface and number of nearest


Mantooth et al. 5. Cascades

Figure 10. Multidimensional histograms for the hcp region that represent A, adsorption events; B, desorption events; and C, number of molecules (indicated by color) as a function of distance from the soliton wall (x axis) and number of nearest neighbors n (y axis). White regions in these plots indicate “no data”.

neighbors. Histograms in Figures 9C and 10C show that, because the soliton wall region was the last region to be occupied by the adsorbed molecules, molecules near the soliton interface had fewer nearest neighbors; molecules with higher coordination were most likely to be found some distance away from this interface. For both the hcp and fcc regions, adsorption primarily occurred near the soliton interface; however, it should be noted that there were a minority of adsorption and desorption instances that occurred throughout these regions (Figure 9B). If the minority 2D desorption events that did not occur along the soliton interface are normalized by dividing by the number of molecules at a given distance, the result is a relatively equal probability of 2D desorption as a function of distance from the interface (not shown).

Some molecules undergo concerted displacements of 2.4 ( 0.6 Å, which are significantly smaller than the overlayer lattice spacing (7.0 Å). Chains of up to 12 molecules simultaneously undergo such small displacements, as seen in Figure 11. We use the term “cascade” to describe this concerted motion of molecules within or between two consecutive frames.38,84 Due to the time scale of imaging for STM (in this case, 4 min to acquire each image), we cannot directly observe each step of the cascade motion, only the initial and final locations of the molecules. Therefore, we cannot track the identity of any specific benzene molecule, only that a benzene molecule resides in a different site in a subsequent image. In some instances, we observed the cascade during the acquisition of the image, as marked by the arrow in Figure 11I, where some molecules appear “stretched” across two locations. We assert that cascades are the result of multiple benzene molecules being displaced; each set of blue and red dots in Figure 11 corresponds to the initial and final positions of the same benzene molecule. Because we have observed chains of up to 12 molecules display this motion, it is not statistically probable that cascade motion is the result of multiple desorption and adsorption events.38 Similar to the energy/thermal contribution from the tip (∆Etip) associated with the 2D desorption, it is possible that these cascade events are initiated by the STM tip. However, due to the relatively slow motion of the tip, we believe that the tip only initiates the motion. The number of molecules involved and the geometry of the cascade is determined by the structure (i.e., configuration) of the overlayer.38 There are a limited number of systems that have shown significant correlated motions, such as polymer systems near their glass transition temperature,85-88 the diffusion of metal clusters across metallic surfaces,89-91 and concerted jumps of atomic adsorbates.92 Briner et al. have observed that CO clusters diffuse faster than individual CO molecules on a Cu{110} surface.93 C60 molecules move in clusters on Au{111} due to van der Waals interactions and the presence of two types of binding sites, where one site is more stable than the other,10 similar to the multiple adsorption sites observed for benzene in this work. In the case of benzene on Au{111}, there are only significant interactions of the benzene with the Au surface and

Figure 11. Images A-I depict examples of cascade events. Blue dots represent the locations of benzene molecules that will undergo small displacements in the subsequent image. Red dots show where the benzene molecules will reside in the next frame. Green and yellow dots indicate 2D desorption and 2D adsorption of benzene molecules, respectively. Images C and E show cascade movement in the hcp region. The most commonly observed cascades are shown in images F-H. Image I shows a vertical cascade that occurred during the acquisition of the image, the arrow denotes where/when the cascade occurred. The yellow circle indicates the molecule that adsorbed during the image that likely caused the cascade.

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Figure 12. This spatial histogram highlights the locations of cascade events. The grayscale background images of frames 1 and 600 (displaced to compensate for drift) are displayed for reference. Brightness indicates the number of cascade events at that site. The white circles correspond to the 3-fold hollow or atop adsorbed molecules, as marked in Figure 2.

via substrate-mediated interactions; thus, we believe that these molecules interact predominantly via SMIs. Similar to Figure 8, a spatial histogram registering the location of all cascade motion events is shown in Figure 12. The white circles in Figure 12 indicate atop and 3-fold-hollow-adsorbed molecules. That there are very few cascade events at these sites corroborates our proposed (x133 × x133)R17.5° overlayer structure and indicates that molecules at these 3-fold hollow and atop sites are bound more strongly to the Au surface. The closely spaced pairs of spots in Figure 12 correspond to the sites between which benzene molecules oscillate, as

J. Phys. Chem. C, Vol. 111, No. 17, 2007 6177 highlighted by the colored circles in Figure 13. Surprisingly, the molecules in Figure 13 adsorbed at sites labeled in blue, henceforth referred to as Rβ cascades, tend to move in the same direction at the same time as indicated by the blue traces in Figure 13A. It was unexpected that three “independent” rows of molecules, each separated by a row of molecules, could influence one another to move in the same direction at the same time. There is a second set of molecules labeled in red, referred to as Rγ cascades, which also move in the same direction at the same time. To elucidate the mechanism for this type of motion, the sites a molecule occupies are treated as the configuration state for any given molecule; three configurations are assigned: R, β, and γ. Rβ cascade molecules occupy a different site in state β than in state R, and Rγ cascade molecules occupy a different site in state γ than in state R. For visualization in a state diagram (Figure 13), these configurations are assigned values. The Rβ cascades are marked with blue traces where R has a value of zero and β has a value of one. Similarly, Rγ cascades are marked with red traces where R has a value of zero and γ has a value of one. Although the cascade motion occurs in many directions, there is always one site that is more to the left (in our display) than the other site. For Rβ cascades, state β is the leftmost site; for Rγ cascades, state γ is the rightmost site. The unusual geometry and long-range correlations of these cascade motions can be revealed by looking at the structures of the overlayer before and after cascade events (see the movie in the Supporting Information). As evidenced by the amount of cascade movement in the fcc region, the proposed pinwheel structure is an equilibrium structure. When a cascade occurs, one of the wheel molecules becomes the pinwheel center molecule, as depicted in Figure 14. The result of an Rβ or Rγ cascade is a translation of the pinwheel structure. The assigned states R, β, and γ represent the three locations that pinwheel center molecules can be located. The black dots in Figure 14B represent the pinwheel structure when the pinwheel center molecules are located on the 3-fold hollow and atop molecules (state R); for clarity, some of the pinwheel center molecules

Figure 13. State diagram for molecules that undergo cascade motion. A, Cascade state for each site, as defined in B. The state of a molecule is determined by its location on the surface, as described in the legend and in the text. B, Spatial histogram of cascade events; the circles depict the region within which one molecule moves between sites. Rβ cascades are highlighted in blue, Rγ cascades in red. C, Overall configuration of the overlayer as a function of time. Note that sites X-AA were not in the field-of-view until after frame 300 (hour 21).


Mantooth et al.

Figure 15. Histogram of the lifetimes of cascade states for both configurations for Rβ and Rγ cascades. The lifetime is binned in 1 frame intervals (4.07 min). Each trace is vertically offset by 200 occurrences for clarity. The lifetime (τ) is given in units of time and frames since the tip-driven motion is dependent on scanning frequency.

molecules in this case), there is an equivalent site before and after translation. Figure 14E shows the sites for the secondary cascades where the pinwheel center molecule is on the opposite side from the β configuration. Because multiple rows of molecules simultaneously change states, we consider the overall configuration of the overlayer (Figure 13C). Due to the equivalent sites, some molecules in the overlayer may be in the β configuration, although the Rγ molecules are detected in their R sites (and the same for Rβ cascade molecules and γ site). To remove the “spatial degeneracy” of the β and R configurations for Rγ cascade molecules, the state of all molecules is monitored to determine the configuration of the overlayer; that is, both Rβ and Rγ molecules must be in the R state for the overlayer to be in the R configuration. From these observations, we can treat the cascades as a dynamic equilibrium between configurations as described by K1

K2

β y\z R y\z γ. Figure 14. Top row of images depicts three of the configurations for the fcc region structure as a result of overlayer translation; colored dots show the locations of the centers of benzene molecules for the β, R, and γ configurations. Some pinwheel center molecules are highlighted with stars for clarity. The backgrounds for these images are the spatial histograms for cascade motion presented in Figure 9. The Rβ cascade sites result from translation from the R to the β configuration (D); Rγ cascades sites result from translation from the R to the γ configuration (E). As seen in F, the R configuration places all wheel molecules at near bridge sites, the β and γ configurations have wheel molecules at 3-fold hollow, atop, bridge, and various other sites.

are marked with stars. Translating the pinwheel structure by one nearest neighbor distance, such that the pinwheel center molecules are now located on the blue stars, shifts the overlayer to sites marked by blue dots in Figure 14A (state β). Translation of the overlayer generates both equivalent and nonequivalent sites; for any translation, some molecules reside in the same location (i.e., no translation) and some molecules reside in a slightly offset location, as illustrated by the superposition of the R and β configurations in Figure 14D. The offset sites correspond to the sites that undergo cascade motion. The black and blue dots overlap with the Rβ cascade sites, showing how this translation would affect every other row of molecules. For the molecules that do not move (the Rγ cascade

(11)

This equation represents configurations of the overlayer, not products and reactants. Using the cascade state diagram (Figure 13C), equilibrium constants and lifetimes are calculated for each of these configurations. Considering the configuration of the entire overlayer (Figure 13C), the overlayer is in the β configuration 41.3% of the time (K1 ) 1.214), the R configuration 50.2% of the time, and in the γ configuration 8.5% of the time (K2 ) 0.169). This indicates that the overlayer is more stable when the pinwheel center molecules are adsorbed at 3-fold hollow and atop sites. Figure 15 shows the “lifetimes” for all of the configurations. Each distribution is fit to a single exponential, occurrences(t) ) A exp(-t/τ), where t is time and the time constant (τ) yields the apparent lifetime of a given state. Similar to the equilibrium data, the lifetimes show that the R state is the most stable, followed by the β and γ states, respectively. The term lifetime may be misleading for this system. If cascades are tip-driven, the molecule only has a chance to cascade in the few milliseconds that the tip is in close proximity to the molecule. However, the relatiVe values of the lifetimes are still meaningful. There are several observations that we make regarding this motion. First, the 3-fold hollow and atop adsorbed molecules

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Figure 16. State diagram for the occupation states of adsorbate sites along the soliton region. The image on the right is a spatial histogram of all types of motion (2D adsorption/desorption, and cascade motion). Sites marked with yellow circles indicate the locations where molecules adsorb/ desorb in the soliton region. The graph on the left indicates when each site was occupied (high state) or unoccupied (low state).

for both Rβ and Rγ molecules never (or very rarely) moved. This corroborates the proposed overlayer structure in that these molecules seem to have a stronger bond to the Au surface. Additionally, the molecules that became the pinwheel centers after a cascade did not move to become pinwheel center molecules (though this molecule may display motion at other times), it is only the surrounding wheel molecules that exhibit motion. When a cascade occurs, the cascade molecules change types of adsorption sites (e.g., from bridge to atop). For the R configuration, all of the wheel molecules occupy near-bridge sites (black dots in Figure 14F). For the β and γ sites, wheel molecules occupy 3-fold hollow, atop, and bridge sites (blue dots in Figure 14F). The relative stability of the R configuration could be the result of the imperfect alignment and multiple adsorption sites occupied in the β and γ configurations. Second, there are sites indicated by pairs of dots resulting from overlayer translation that did not correspond to cascade motion; for example, compare the first row of primary cascades in Figure 14D with the spatial histogram of cascade motion in Figure 12. It is possible that the lack of cascade motion at these sites is the result of proximity to an elbow of the herringbone reconstruction. As seen in Figure 1, packing in the fcc region changes from the pinwheel overlayer to a close-packed structure when near the elbow. This change in overlayer structure could inhibit cascade motion for Rβ cascades. One of the remaining questions is how cascade events can be correlated between many molecules over such long distances. We have shown that it is statistically improbable that cascade motion is the result of multiple simultaneous random events.38 Therefore, cascades result from adsorbate-adsorbate or adsorbate-substrate interactions. We have shown that the structure of the pinwheel overlayer plays a vital role in cascade motion. Additionally, as seen by 2D desorption, substratemediated interactions play a role in the adsorbate-substrate and adsorbate-adsorbate interactions and, thus, likely play a role in the overlayer structure. There is a strong correlation with 2D adsorption/desorption events occurring at the fcc-soliton interface that could initiate (or be the result of) the change in pinwheel structure that causes cascade motion. For example, in Figure 11, nearly all of the cascade events are concurrent with 2D adsorption/desorption events. Due to the time scale of imaging, it is not possible to tell if the 2D adsorption/desorption events caused the cascades or if the cascades created stabilized/ destabilized sites inducing molecules to adsorb or to desorb.

This is illustrated by Figure 11I, where a cascade event occurred along the scan line indicated by the white arrow. For this image, the yellow dot is drawn as a circle to show the 2D adsorption of the molecule, as indicated by a rapid transition from vacant (dark) to occupied (bright) one scan line before the cascade event is observed. To investigate the correlation between adsorption in the soliton region and cascade motion, we identified the occupation state of specific sites, identified by numbers, in the soliton region (Figure 16). Soliton sites were assigned one of two states: occupied (high state) or unoccupied (low state). To determine the relationship between various types of motion on the surface, correlation coefficients were calculated for the state data between each of the cascade sites. The correlation coefficient equals 1 if the two traces are identical, 0 if there is no correlation, or -1 if there is anticorrelation (i.e., the state data are exactly opposite). Figure 17A shows the correlation coefficients for the cascade sites (Figure 13); red regions indicate correlation, and blue regions indicate anti-correlation. All Rβ molecules show positive correlation with other Rβ molecules (the same is true for Rγ molecules); this further illustrates the observation that multiple rows of molecules often behave in the same manner. The blue regions in Figure 17A indicate that Rβ and Rγ cascades are anticorrelated, as expected, because the β and γ sites cannot be simultaneously occupied. However, both the Rβ molecules and the Rγ molecules can simultaneously occupy R sites (this is required for the R configuration). Figure 17B plots the correlation coefficients for the state data of the occupation of sites along the soliton wall (Figure 16). Although most soliton sites show little correlation, a few sites are strongly correlated. Sites 3 and 5 show significant anticorrelation; if site 3 is occupied, site 5 is not. Similarly, sites 5 and 9 show anticorrelation, and sites 3 and 9 show positive correlation. If the pinwheel structure is extended onto the soliton regions, sites 3 and 9 are either 3-fold hollow or atop sites. Other sites showing significant anti-correlation are sites 11 and 13, which correspond to wheel molecule sites for the R configuration. Correlation between soliton sites can be understood in relation to cascade events. Figure 18 plots the correlation coefficients for cascade states relative to the occupation of the soliton sites. From this, we relate the occupation of a soliton site with the configuration of the fcc region. The top graph in Figure 18 relates the overall configuration of the fcc region (Figure 13C) to the occupation of each soliton site,


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Figure 18. Correlation coefficients for cascade states and soliton site occupation. Color indicates the value of the correlation coefficient. Cascade sites are indicated by letters (defined in Figure 13), and soliton sites are indicated by numbers (defined in Figure 16). The correlation coefficients at the top correspond to the configuration of the overlayer as shown in Figure 13C.

Figure 17. A, Correlation coefficients for cascade states, and B, occupation of sites in the soliton region. Color indicates the value of the correlation coefficient. Cascade sites are indicated by letters (defined in Figure 13); soliton sites are indicated by numbers (defined in Figure 16).

whereas the bottom graph shows the relationship of each cascade site to each soliton site. These graphs indicate that soliton sites 3, 5, 9, 11, and 13 show significant correlation (or anticorrelation) with the configuration of the overlayer. However, other sites (e.g., sites 7, 8, 10, and 12) show no correlation with overlayer configuration. Thus, we infer that occupation of specific soliton sites influences, mediates, or enables cascade motion. When soliton sites 3, 6, and 9 are occupied, the overlayer is typically in the R configuration. These sites correspond to the pinwheel center molecules in the R configuration. Site 13 corresponds to a pinwheel center molecule for the γ configuration, and when occupied, the overlayer is typically in the γ configuration. From the correlation of soliton sites 3, 6, 9, and 13, we posit that, if a soliton site is the pinwheel center for a configuration and the site is occupied, the overlayer will translate/cascade to the configuration where the molecule is the pinwheel center. We have focused our analyses on the transitions between these states as a configuration of the complete overlayer. However, there are instances where only one row of molecules

exhibits cascade motion (e.g., cascade sites Y-AA near hour 35 in Figure 13). This indicates that the entire overlayer does not have to translate simultaneously. Clusters of molecules, such as those seen in Figure 11, panels B, D, and E, exhibit cascade motion and do not conform to a simple translation of the pinwheel structure. Cascade motion was also observed in the hcp region (e.g., Figure 11E), which usually modified the packing from pinwheel-like to close-packed structures. Although the entire overlayer does not always change structure at the same time, the majority of cascade events involved several rows of molecules simultaneously moving. This implies that changes in the overlayer configuration cause changes in the SMI significant enough to cause changes in structure two nearest neighbor distances (∼14 Å) away and strong enough to propagate across multiple rows of molecules. Thus far, we have discussed only three configurations of the overlayer as the result of the translation of the overlayer structure in two directions. However, there are four other wheel molecules that could be pinwheel center molecules and, thus, four other configurations of the overlayer. In a few rare cases, we observed these configurations (e.g., Figure 11, panels A and I). The Rβ and Rγ translations are more likely to occur than any other. The observation of three configurations and the number of times specific molecules cascade are a result of the geometry of the fcc region. Rβ cascades may be more active because there are more β configuration pinwheel center molecules along the soliton wall than γ configuration pinwheel center molecules. From these results, we propose a mechanism for cascade motion. Because the overlayer configuration shows strong correlation with 2D adsorption/desorption, it is likely that the overlayer is stable until a 2D adsorption/desorption event occurs. The presence of the 2D gas of benzene molecules along the soliton wall provides an interface where benzene molecules are highly mobile, thus enabling the observed 2D adsorption/ desorption. The soliton sites that induce most cascades cor-

Feature Article respond to pinwheel center sites. When a molecule moves to/ from these pinwheel center sites, it changes the SMIs of the nearest neighbor molecules, causing the molecules to move. The translation of the cascading molecules induces changes in other SMIs of the overlayer until reaching the opposite side of the fcc region. The SMIs are propagated over long distances, inducing other rows of molecules to rearrange into the new configuration. The observation of only single rows of molecules cascading can be related to a molecule not occupying a stabilizing site or not moving from a destabilized site in the soliton region. 6. Conclusions Automated digital image processing enables the identification, extraction, and distillation of large quantities of data. Only through such large volumes of data can statistically relevant analyses of single molecule processes be performed. The combination of scanning tunneling microscopy and these digital image processing techniques enabled the quantification and ultimately the elucidation of detailed mechanisms and structural changes for benzene on Au{111}. We have been able to determine and to quantify the structural changes due to single molecule motion, and to correlate this motion to substratemediated interactions. We have observed and quantified 2D adsorption/desorption as a function of the number of nearest neighbors. Using an Arrhenius-like over-barrier model, we were able to calculate an attractive substrate-mediated interaction energy of 0.48 kJ mol-1 molecule-1 and found that our STM contributed an equivalent of 0.54 ( 0.01 kJ mol-1 (∼45 K) of energy to the system. We also characterized molecular cascade motion in which molecules move in a concerted manner across the surface as the result of the translation of the overlayer structure. The cascade motion is dependent on the occupation of benzene molecules at specific sites along the soliton wall. The quantification of these SMIs and the observation of cascade motion are measurable only by this type of single molecule analysis of many molecules. Acknowledgment. The authors gratefully acknowledge financial support of the Army Research Office, the National Science Foundation, and the Office of Naval Research. We thank Profs. Kristen Fichthorn and Luis Ferna´ndez-Torres for helpful discussions. B.A.M. is grateful for a fellowship from the ACS Division of Analytical Chemistry sponsored by GlaxoSmithKline. Supporting Information Available: A set of 600 timeresolved STM images illustrating the motion of benzene on Au{111} at 4 K are included as a movie. Each image is of an 81 Å × 81 Å area acquired with a sample bias of 1 V and a tunneling current of 20 pA. Motion is identified by colored dots following the legend for Figure 5. Several of the 3-fold hollow and atop adsorbed molecules are highlighted with white circles. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Tsong, T. T. Rep. Prog. Phys. 1988, 51, 759. (2) Tsong, T. T. Mater. Sci. Eng. A 2003, 353, 1. (3) Gomer, R. Rep. Prog. Phys. 1990, 53, 917. (4) Ho, W. J. Chem. Phys. 2002, 117, 11033. (5) Lauhon, L. J.; Ho, W. Phys. ReV. Lett. 2002, 89, 79901. (6) Pohl, D. W.; Moller, R. ReV. Sci. Instrum. 1988, 59, 840. (7) Swartzentruber, B. S. Phys. ReV. Lett. 1996, 76, 459. (8) Dunphy, J. C.; Sautet, P.; Ogletree, D. F.; Dabbousi, O.; Salmeron, M. B. Phys. ReV. B 1993, 47, 2320.

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Analyzing the Motion of Benzene on Au{111}: Single Molecule

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