Electron Attachment Leads to Unidirectional In-Plane Molecular

Jul 9, 2019 - (8) Riedel et al. observed the isotropic in-plane rotation of biphenyl(9) and Schofield et al. the out-of-plane rotation of acetophenone...
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Electron Attachment Leads to Unidirectional In-Plane Molecular Rotation of Para-Chlorostyrene on Si(100) Si Yue Guo, Matthew J. Timm, Kai Huang,† and John C. Polanyi* Lash Miller Chemical Laboratories, Department of Chemistry and Institute for Optical Sciences, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada

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S Supporting Information *

ABSTRACT: We report the observation of electron-induced unidirectional planar molecular rotation of para-chlorostyrene on Si(100), studied by scanning tunneling microscopy (STM) at room temperature and by ab initio theory. This bifunctional molecule is shown to be favorable to the electroninduced rotation since the phenyl group acts as a pivot and the vinyl as a lever arm. In the initial configuration, both phenyl and vinyl are attached to silicon dimers along the same row of the substrate. The first electron from the STM tip is observed to induce a lateral shift of the vinyl to “state 1” in which the vinyl is bound asymmetrically to one side of a silicon dimer. The second electron is found to give rise to a ∼60° rotation to “state 2”, a configuration in which the vinyl has swung around the phenyl to an adjacent dimer row. The impulsive two-state (I2S) model was employed to explain the conversion of the initial state to state 1 and the conversion of state 1 to state 2. These two successive impulses were computed by the I2S model to be the result of excitation to different configurations in an anionic excited state. Following addition of the second electron, the repulsion between the asymmetric vinyl and the surface was shown to give rise to a torque with the magnitude and direction required to explain the observed rotation.

1. INTRODUCTION The miniaturization of machines requires exploration of the dynamics of molecular motions at the atomic level.1−3 For molecules adsorbed on surfaces, scanning tunneling microscopy permits examination of the reagents and the products of reactions, as well as revealing the source of excitation that drives reaction due to the injected charge.4 Molecules on a variety of substrates behave analogously to molecular machines. Examples include switches,5 a molecular latch with an anchor and movable part,6 or a molecular ballbearing with a rotor and stator.7 These dynamics were the result of the selective adsorption and reaction of the different functional groups within an intact molecule.8 Riedel et al. observed the isotropic in-plane rotation of biphenyl9 and Schofield et al. the out-of-plane rotation of acetophenone,10 both on silicon. Reactions in each case were initiated by phenyl detachment. Recently, workers in this laboratory reported the dynamics of iodophenyl pivoting around a chemical bond on copper, the rotation being driven by successive iodine−metal attractions.11 Here, we report the case of a bifunctional molecule adsorbed on silicon, the surface most-widely used for electronic applications. Para-chlorostyrene, pClSty, was induced by electron attachment from a scanning tunneling microscopy (STM) tip to rotate in the plane of the Si(100) surface (see Figure 1 for a schematic of the surface and the molecule). The rotation was a two-electron process, in which the vinyl acted as a lever arm and the chlorophenyl as a pivot. We shall describe the role of the functional groups in the unidirectional rotation, © XXXX American Chemical Society

Figure 1. (a) Schematic of the Si(100)-c(4×2) surface showing silicon dimer rows. Each dimer is buckled as a result of charge transfer from the down-Si (in orange) to the up-Si (in red). (b) Parachlorostyrene.

as determined by experiment and by quantum mechanical modeling. The electron-induced migration of benzene and ethylene (related to the phenyl and vinyl in this study) has been the subject of detailed study in earlier work.12−14 Styrene has been the subject of extensive STM experiments on Si(100).15−18 Notably, injection of holes by the STM tip produced molecular rearrangement and desorption but no in-plane adsorbate rotation. In order for the functional groups to play a part in the electron-induced dynamics of pClSty, both groups must interact with the surface. However, styrene attaches to the surface through only the vinyl. To also bring the phenyl ring Received: April 30, 2019 Revised: June 25, 2019 Published: July 9, 2019 A

DOI: 10.1021/acs.jpcc.9b04076 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C into contact with the surface, we added a Cl atom in the para position. Our computation shows that the Cl withdraws charge from the phenyl, thereby making it more electrophilic. In addition, the interaction of Cl with a down silicon atom, δ+ charge, brings the phenyl ring close to the surface. This results in the phenyl group of chlorostyrene forming an additional two sigma bonds with the surface in what is known as the “butterfly” configuration12,14 (see Figures S3 and S4 in the Supporting Information).

The dynamics on the anionic upper pes were modeled in Gaussian 0931 since this allowed addition of an electron. We used the B3LYP hybrid functional and the 6-31g(d) and 631+g(d) basis sets for neutral and charged calculations, respectively. The Si(100) surface was modeled by three clusters of increasing size: “small” Si15H16, “medium” Si29H28, and “large” Si53H44.32 The small and medium clusters have two silicon dimers, whereas the large has four dimers. Only the top two layers of the cluster were allowed to relax during the optimization calculations. To test for convergence, identical calculations were performed on all three clusters, and the results were compared. We found that the bond lengths were consistent to within 0.05 Å and forces on atoms were comparable in direction, diminishing in magnitude with increasing cluster size. Since an added electron is distributed over all of the atoms, the smallest cluster allows for the best representation of a molecular anion, simulating localization of the negative charge. Below, we report the results for the smallest cluster, Si15H16. See Figure S10 and Table S3 in the Supporting Information for details of the clusters and results for the medium- and large-size clusters.

2. METHODS 2.1. Experiment. The experiments were carried out at room temperature in ultrahigh vacuum on an Omicron variable-temperature scanning tunneling microscope (VTSTM). Silicon(100) samples were cut from n-type, phosphorus-doped single-crystal wafers obtained from Virginia Semiconductors (0.02 Ω cm) and cleaned by repeatedly flashing to 1400 K.19 Imaging was carried out in constant-current mode using a tungsten tip etched in 3 M NaOH. Para-chlorostyrene (97% purity) and styrene (≥99% purity) were obtained from Sigma-Aldrich and dried using molecular sieves, then degassed using approx. eight cycles of freeze−pump−thaw. Before dosing, we checked the clean silicon surface for less than 0.2% defects. Chlorostyrene (pClSty) or styrene (Sty) was then introduced into the vacuum chamber by background dosing via a leak valve on the preparation chamber, at a pressure of 1 × 10−10 Torr for approximately 60 s. This corresponds to an average dose of 0.006 L (1 L = 1 × 10−6 Torr s), as indicated by an ion gauge in the STM chamber. The base pressure in the chamber was approximately 4 × 10−11 Torr. Electron-induced reaction was obtained by two methods, pulsing and scanning. In the pulsing mode, individual molecules were induced to react by applying a pulse with the tip over the adsorbate, with the feedback loop still engaged. The bias was ramped up linearly over 5 ms and then held for a few seconds before returning to the normal scanning bias. In the scanning mode, we studied multiple adsorbate molecules at a time by scanning a small region of the surface (∼10 × 10 nm2) at the excitation biases and comparing the images before and after the scan. Approximate threshold voltages for the reaction were determined by altering the bias by 0.1−0.2 V increments. Reaction yields were obtained using the method described by Sloan and Palmer20 and are detailed in the Supporting Information (SI, Section 3). 2.2. Theory. To examine the potential-energy surface (pes) and the dynamics of the reaction, approximate quantum calculations were performed on neutral and anionic moleculeplus-surface systems. We used the Vienna Ab initio Software Package (VASP)21,22 to calculate adsorption geometries and projected densities of state (PDOS). The Si(100)-c(4×2) surface was represented by a 7-layer slab, Si112H32 (15.36 × 15.36 × 30 Å3), terminated by H-atoms. The H-atoms and the bottom two layers were frozen during the calculations. We used the revised Perdew−Burke−Ernzerhof (RPBE) functional23,24 and the generalized-gradient approximation and projector-augmented wave method25 with an energy cutoff of 450 eV and a force criterion of 0.01 eV Å−1. Calculations made use of the semiempirical DFT-D2 van der Waals correction.26 We employed visual molecular dynamics27 and VESTA28 to visualize calculation results. STM images were simulated by the software HIVE v.1.5 using the Tersoff−Hamann model.29,30

3. RESULTS AND DISCUSSION 3.1. Observed Rotation. As a bifunctional molecule, pchlorostyrene (pClSty) can initially adsorb in several configurations that involve bonding of vinyl or phenyl or both to the surface. After dosing pClSty, we observed three major adsorption configurations: “on-dimer” 27 ± 2%, “interrow” 41 ± 3%, and “tight-bridge” 31 ± 2% (calculated from a total of 557 counts). (See Figure S1 in the Supporting Information for STM images and calculated adsorption geometries of these configurations.) On-dimer was the initial state that gave electron-induced rotation. The complete rotation observed is shown in Figure 2. For this rotation, with Cl initially in the top-right position, the molecule invariably (74 cases) rotated 90° in a clockwise direction around a surface silicon atom. The rotation proceeded from the initial state through a stable intermediate state 1, then through a metastable state 2, to the final state. This was a sequential two-electron process, exhibiting a threshold energy of 3.3 eV for the first electron and approximately 0.3 eV for the second electron, followed by thermal reaction from state 2 to the final state. As the tip voltage and current were increased, so did the rate, with the result that the probability of observing the intermediate state 1 decreased (see Figure S8). In the figure, all of the images are aligned as observed on the surface. The black vertical tick marks show the center of the initial dimer row. All of the stable chemisorption geometries were computed in VASP. These geometries were then simulated from their partial charge densities and compared with the experimental images to identify a match. The Cl atom, labeled on the STM images, provided a useful “marker” since it imaged as higher (brighter) than the rest of the molecule due to the greater density of states. This effect was most marked at biases below ±1 V. In the initial state, the molecule chemisorbed on two silicon dimers along a dimer row forming four C−Si sigma bonds. The adsorption consisted of a [4 + 2] cycloaddition involving the phenyl as an on-dimer butterfly configuration and a [2 + 2] cycloaddition for the vinyl and the next dimer (see the schematic in Figure S4). The adsorption energy was calculated to be 1.85 eV. B

DOI: 10.1021/acs.jpcc.9b04076 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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STM image of the vinyl on one side of the silicon row. In the computed adsorption geometry for state 1, the vinyl C−C bond shortened as compared with the initial state (see Table S1, SI). This indicated a change in hybridization from sp3 to sp2 associated with the formation of a pi-complex. The adsorption energy for this state was calculated to be ∼1.5 eV. After the addition of a second electron, state 1 converted into state 2, which reacted thermally to form the final state. The final state was identical to the inter-row adsorption geometry present after dosing. Experimentally, we measured an upper limit on the threshold energy of approximately 0.3 eV for the attachment of the second electron. Below this bias, imaging on the semiconductor surface became unstable. The reaction yield was approximately 1 × 10−10 events/electron. State 2 was observed to be short-lived at room temperature, with a half-life of approximately 2 min on the surface before reacting thermally to form the final state. By tracking this thermal reaction over time, we derived an energy barrier of 0.91 ± 0.01 eV, assuming first-order Arrhenius behavior and a prefactor of 1013±2 s−1 (see Section 2.3, SI, for details). To exclude a decomposition process in the final state, we looked for the fragments, vinyl, Cl, and H, after electron attachment on the product up to 4.5 V and found none. By examining the STM images for state 2 and the final state in Figure 2, the adsorption geometries were deduced from the positions of the bright Cl atom and those of the silicon dangling bonds, one on the left dimer row and two on the right row. As illustrated in the schematic, in both of these states, the molecule spanned two adjacent dimer rows, with the phenyl attached as an inter-dimer butterfly and the vinyl forming one sigma bond to the next row. The difference between state 2 and the final state lies in the points of attachment of the molecule to the surface such that the axes of the molecule as defined by the C−Cl bond are ∼30° apart. In state 2, the Cl atom rests above a nucleophilic up-Si (δ−), an energetically unfavorable state.34 Significantly, pClSty in the final state has rotated by approx. 90° with respect to its position in the initial state, as the green arrows indicate (Figure 2c). The adsorption energy for state 2 was calculated to be 1.33 eV and that of the final state was 1.46 eV. Although the final state was computed to be 0.4 eV less stable than the initial state, examination of the products showed no reversion to the initial state over a period of 24 h. The final state is similar to the well-established adsorption geometry for phenylacetylene, which resembles styrene.35−38 To rule out any thermal rotation reaction at 300 K, we compared the coverage and relative population of initial-state and final-state adsorbates over 24 h during which the surface was not scanned, and found no change within statistical error. Additionally, after having induced the first step, we found no thermal reaction of molecules in state 1 at 300 K within an hour of reaction. State 1 molecules survived for 30 min at the surface and did not change until scanned at the minimum scanning bias of 0.3 V. Withdrawal of an electron (hole attachment) did not give rise to rotation. 3.2. Theory and Dynamics. Ab initio calculations were performed to investigate the source of the unidirectional inplane rotation of pClSty through the two stages of reaction, initial to state 1 and state 1 to state 2. The calculations were based on density functional theory (DFT) and involved two complementary approximations, a slab calculation in VASP and a cluster calculation in Gaussian. The slab model gave the

Figure 2. STM images and their simulations for the electron-induced rotation: initial state (on-dimer), state 1, state 2, and final state (interrow). The reaction occurs from electrons with threshold voltages of ca. 3.3 and 0.3 V, followed by thermal reaction at 300 K. For each state, (a) the STM image is shown and compared to (b) the simulated image (both at positive surface bias) and (c) the calculated adsorption geometry. Four successive C−Cl bond directions are labeled (horizontal scale bar = 5 Å). The silicon atom around which rotation occurred is indicated by a red dotted circle. (Additional details of the pClSty rotation can be found in Section 2 of the Supporting Information.)

The Cl atom attached to the phenyl appeared clearly, supporting the notion that the entire molecule was bound to the surface, rather than being attached only at the vinyl group. Despite the challenges of simulating images at semiconductors,33 the simulated structures in Figure 2 are in satisfactory agreement with the STM images. With a sharp STM tip, two variants of the initial state pClSty could be discerned: one with the Cl atom over a down-Si and the other with Cl over an up-Si (this conclusion was based on the pinning of the silicon dimers at the Cl). The configuration over the electrophilic down-Si was more commonly observed; it was calculated to be 5 meV more stable than that over an upSi (−1.853 vs −1.848 eV). The in-plane rotation was similar for both these variants of the initial state. (See Figure S2, SI, for STM images of the two variants.) A first electron of 3.3 V converted a pClSty in the initial state into state 1. At the threshold voltage, the reaction yield was 1 × 10−10 events/electron. This state was most readily observed at near-threshold voltages and low currents. (See Section 3, SI, for a plot of the yield as a function of the voltage for the first electron.) The phenyl group in state 1 remained above the same silicon dimer as in the initial state. It was determined by calculation to be a butterfly with two sigma bonds binding it to one silicon dimer. The electronic excitation caused the di-sigma-bound vinyl to convert to a weakly bound pi-complex attached to one silicon of another dimer. This change in configuration manifested itself as an increase in the measured height in the C

DOI: 10.1021/acs.jpcc.9b04076 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The second step of the rotation, in which state 1 gave state 2, experimentally occurred at 0.3 eV and was also ascribed to electronic excitation, E → E, since the 0.3 eV energy of the electron matched the calculated electronically excited state at 0.33 eV (panel b of Figure 3). The vinyl−silicon interaction in this lowest unoccupied molecular orbital was bonding in character (see the inset). Although vibrational excitation cannot be ruled out, E → E was supported by the theoretical evidence of an electronically excited state of the required energy. The rotation reaction described in this paper did not give evidence of any field effect within the range of current 0.2−0.6 nA; there was no detectable alteration in threshold voltage over this range of current. We employed the impulsive two-state (I2S) model14,40,41 computed in Gaussian to understand the dynamics of rotation due to the attachment of two electrons. Figure 4 gives a

potential energy and charge distributions at the surface but was unable to model electron attachment and the ensuing repulsion in C−Si bonds. Accordingly, we first performed neutral ground-state slab calculations in VASP, then transferred the optimized structures onto a cluster in Gaussian for the anionic potential-energy calculations. The two approaches were shown to be consistent through examination of the shape of the frontier orbitals of a neutral and anionic gas-phase molecule, in both VASP and Gaussian (See Figure S9, SI, and ref 39). Figure 3 plots the projected density of states (PDOS) of pClSty in the initial state and state 1 of the rotation, computed

Figure 4. Schematic of the potential energy for the two trips to the anionic state. The first electron (shown in red) brings the initial state to a repulsive anionic state and thereafter to state 1. The second electron (shown in green) excites the state 1 to an attractive part of the anionic potential; upon its return, it rotates to the final state via state 2.

schematic representation of the neutral and anionic potentialenergy surfaces (pes), showing the evolution of the system through the two stages of electron attachment. Each of the two electrons, as shown by the red and green arrows, gave rise to a vertical transition from the neutral ground state to the excited anionic state. To understand the resultant rotation, we examined the forces experienced by the molecule as it relaxed in the excited anionic state and the forces following reversion to the neutral state. The first electron impinging on the initial state excited the system into the antibonding anionic state. The predominant force on the anionic pClSty was a repulsion between the vinyl and its underlying silicon dimer, based on our Gaussian calculations. The molecule remained anchored to the surface by its two phenyl−silicon bonds. The repulsive forces on the anionic pes produced most of the change in configuration toward state 1. This resulted in the extension of the vinyl− silicon bonds and a shift of the vinyl to one side of the silicon dimer. In the ground state, the vinyl became asymmetrically pibound with one silicon atom of the dimer, constituting state 1. As a result of the trip to the anionic pes, the system gained ∼0.5 eV of energy, which propelled it across the ground pes. The addition of the second electron to state 1 resulted in an attraction between the molecule and the surface in the asymmetric vinyl pi-complex. On returning to the ground state, the molecule was repelled by the surface unidirectionally. The repulsion was strongest (∼1 eV Å−1) in the vinyl−silicon

Figure 3. PDOS for pClSty in the (a) initial state and (b) state 1, showing the relative energy of an unoccupied molecular orbital with respect to the Fermi level, calculated in VASP. The inset above each plot shows a slice of the partial charge-density isosurface (0.04 e− Å−3) of the vinyl and silicon dimer calculated at the labeled energy (side view). In (a), the dashed white lines show a nodal plane between the C in vinyl and the Si atoms; in (b), the circle shows bonding.

in VASP, and identifies the peak corresponding to an unoccupied molecular orbital for each of the two impulsive steps. For the initial state, the partial charge density in the inset of panel (a) reveals the antibonding character of the vinyl− silicon bonds (nodal plane) at 3.3 eV. The calculated antibonding electronically-excited state at 3.3 eV accords with our experimental finding of a 3.3 eV threshold for electron attachment to pClSty (see Figure S7, Supporting Information), indicating that the first step was an electronic excitation (E → E). Vibrational excitation, which would involve multiple steps, would not be expected to exhibit a single 3.3 eV threshold and would not lead to the antibonding configuration, which was implicated in the repulsion leading to rotation from the initial state to state 1 (see the I2S calculations below). The result of the first electron attachment was an asymmetric vinyl picomplex attached to silicon. D

DOI: 10.1021/acs.jpcc.9b04076 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C bonds and C−Si bonds ortho to Cl. The ring center remained above the same Si atom that constitutes the pivot point. The forces on state 1 after returning from the anionic state contained a significant component parallel to the surface such that the molecule rotated in the plane of the surface. In Figure 5 are plotted the in-plane components of the force vectors on

Figure 6. Initial states calculated in VASP for (a) styrene, involving only vinyl attachment by two C−Si sigma bonds, and (b) chlorostyrene, involving phenyl and vinyl attachment to silicon by four C−Si sigma bonds. The tick marks indicate the dimer row direction. The total electron density of the gas-phase molecules is shown above, as obtained from Gaussian (same color scale for both molecules, −3.0 × 10−2 to 3.0 × 10−2 eV Å−1).

Figure 5. In-plane forces (straight arrows, ∼1 eV Å−1) on the atoms of the adsorbate in state 1 upon its return to the ground state, as calculated in Gaussian on a Si15H16 cluster. The molecule experiences a torque from the vinyl lever arm around the pivot (labeled), leading to clockwise in-plane rotation (shown by the curved arrow).

pClSty since it provided the pivot around which rotation could occur.

each atom of pClSty upon its return to the neutral pes. On arrival to the ground potential, the molecule experiences a net 3 eV torque around the pivot, resulting in a 60° in-plane rotation in ∼0.3 ps in the direction of the observed rotation to state 2. This time was similar to that previously calculated for rotational periods of ethylene on silicon.42 (See Section 5, SI, for details of the calculation.) In state 2, the Cl is above an up-Si, as determined from examination of the adjacent surface buckling. This configuration is a short-lived intermediate since halogen atoms move to δ+ down-Si atoms.34,43 The nearest available down-Si is one-lattice-spacing away along the dimer row (Figure 2). At room temperature, the molecule can readily overcome the 0.91 eV energy barrier to convert to this position, thermally continuing the rotation. The result is pClSty in the final state, which is 0.13 eV more stable than state 2. Rotation in the reverse direction (anticlockwise) is energetically unfavorable and was never observed. 3.3. Electron Addition to Styrene as Compared to Chlorostyrene. Experimentally, our numerous attempts over a range of biases up to 5 V failed to give any cases of electroninduced rotation in styrene. For styrene, here and elsewhere,18 only decomposition or desorption was observed. The failure to observe rotation in styrene is attributed to the differing initial adsorption geometries between styrene and chlorostyrene, as described below. The initial states for the two molecules were calculated in VASP and are shown in Figure 6. They differ in the number of C−Si sigma bonds formed between the molecule and the surface: two for styrene and four for pClSty. For styrene, the initial adsorption geometry involved only vinyl attachment to a silicon dimer at the surface.15,17,18,44 For pClSty, the addition of a Cl-substituent withdrew charge from the phenyl ring, altering the adsorption geometry (see Figure 6). This charge withdrawal rendered the phenyl more electrophilic and hence more strongly attached to the surface. The pClSty structure was calculated to be 50 meV more stable than that of styrene. The phenyl attachment favored the observed rotation in

4. CONCLUSIONS We have studied the electron-induced reaction of pchlorostyrene on Si(100) by scanning tunneling microscopy at room temperature. In the initial state, pClSty attached to silicon via both phenyl and vinyl, each forming two sigma bonds with Si atoms of an adjacent pair of dimers in a row. Electron irradiation of pClSty at 3.3 V produced a change in the bonding of the vinyl to the surface, from two sigma bonds to a pi-complex, resulting in the intermediate state 1. Subsequently, a second electron attachment at 0.3 V resulted in a rotational conversion of state 1 to the metastable state 2, which thereafter thermally rotated to the observed final state. The experimental evidence, supported by calculated adsorption geometries, showed that the reaction was a two-step unidirectional rotation of the molecule in which pClSty pivoted in the plane of the surface around the phenyl ring. Adsorption geometries, energies, and projected densities of state were calculated for the ground pes by density functional theory (DFT) using a slab for the surface. The mechanics of re-bonding and rotation as a result of electron attachment were obtained from the impulsive two-state method applied to a cluster model. The first electron attached to an antibonding orbital of the vinyl−silicon bonds in the initial state. This resulted in the re-bonding of the molecule with vinyl attached as a pi-complex to one side of a silicon dimer, as state 1. The second electron excited this pi-complex, producing an asymmetric repulsion with the surface, resulting in a unidirectional torque around the phenyl. This torque was sufficient to account for the observed 60° rotation. The role of the Cl atom substituent was to bond the aromatic ring to the surface, creating a pivot for rotation at the surface.



ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b04076. E

DOI: 10.1021/acs.jpcc.9b04076 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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STM images showing the adsorption geometries; experimental details of the rotation; determination of the experimental yield; and VASP and Gaussian calculations (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Kai Huang: 0000-0001-8907-4441 John C. Polanyi: 0000-0002-4401-7758 Present Address †

Guangdong Technion Israel Institute of Technology, 241 Daxue Road, Shantou, Guangdong Province 515603, P. R. China Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the University of Toronto NSERC General Research Fund. Computations were performed on the SciNet supercomputer, funded by the Canada Foundation for Innovation under Compute Canada, the Government of Ontario, Ontario Research Fund, and the University of Toronto. We thank Harjeet Soor and Prof. Andrei Yudin for assistance with sample preparation.



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