Surface Radical Chain Reaction Revisited ... - ACS Publications

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J. Phys. Chem. C 2010, 114, 3981–3986

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Surface Radical Chain Reaction Revisited: Comparative Investigation of Styrene and 2,4-Dimethyl-Styrene on Hydrogenated Si(001) Surface from Density Functional Theory Calculations Noboru Takeuchi* Centro de Nanociencias y Nanotecnologı´a, UniVersidad Nacional Auto´noma de Me´xico, Apartado Postal 2681, Ensenada, Baja California, 22800, Me´xico

Yosuke Kanai Berkeley Nanosciences and Nanoengineering Institute UniVersity of California, Berkeley, California, United States of America

Annabella Selloni Department of Chemistry, Princeton UniVersity, Princeton, New Jersey, United States of America ReceiVed: October 10, 2009; ReVised Manuscript ReceiVed: January 15, 2010

We report on periodic Density Functional Theory calculations of the adsorption and desorption of styrene and dimethyl-styrene on the H-terminated Si(001)-2 × 1 surface. Experimentally, the adsorption of these molecules on H-Si(001)-2 × 1 results in the formation of one-dimensional lines parallel to the Si dimer rows. At higher temperature, desorption of the molecules at the end of the lines is observed, leading to a shortening of the lines. The desorption temperature is ∼300 K for dimethyl-styrene and ∼400 K for styrene. To obtain insights into the atomic scale mechanisms of these processes, we have studied the initial steps of the radical chain and inverse chain reactions for the two molecules. Due to the existence of several metastable states, different competing reaction paths exist in both cases. We have found differences between styrene and dimethyl-styrene desorption barriers that are in agreement with experiments. I. Introduction The formation of self-assembled nanostructures on silicon surfaces is an important and intensely investigated area of nanotechnology. In particular, there is a great interest in the design of organic nanostructures that combine the rich functionalities of organic molecules with the well-developed solidstate semiconductor technologies.1-15 One of the most promising approaches for efficiently assembling organic ad-layers is the so-called radical chain reaction mechanism using terminally unsaturated molecules on the hydrogen-terminated Si surface.7-15 Upon creating a dangling bond on the surface, e.g., by means of a scanning tunneling microscope (STM) tip or by UV radiation,7 the reaction proceeds in two steps. First, the molecule readily reacts with the isolated Si dangling bond (hydrogen vacancy) to form a Si-C bond. The resulting intermediate adsorbed state is characterized by the presence of a carbon-centered radical on the molecule. In the second step, the adsorbed molecule abstracts a hydrogen atom from a neighboring Si-H group, creating a new dangling bond (db) at a nearby surface site. This silicon dangling bond can in turn adsorb another molecule, thus leading to a surface chain reaction. This process has been successfully applied to fabricate, for example, one-dimensional (1-D) molecular chains on Si(001)(2 × 1) surfaces in recent years,10-15 and starting from them, one-dimensional organic heterostructures.16 The surface chain reaction could at any time reverse itself, and the probability for such an occurrence would depend on the desorption energy barrier and the temperature. Hosssain, et * Corresponding author. E-mail: [email protected].

al.15 recently reported STM measurements on the H-terminated Si(001)-(2 × 1) surface, in which the reverse chain reaction was observed at 400 and 300 K for styrene and 2-4-dimethylstyrene, respectively. Motivated by these observations, we have carried out first principles DFT calculations where we comparatively investigated the reactions of styrene and 2-4 dimethyl-styrene on H-Si(001)-(2 × 1). Although the basic mechanisms of the chain reaction have been theoretically investigated and understood to a large extent in previous work,9-11 there still exist some discrepancies among different studies, particularly concerning the atomic structures of the intermediate states and the corresponding energetics. In an attempt to overcome these differences, we have performed an exhaustive search of the intermediate energy minima on the complex potential energy surface of the adsorbed molecule/ Si(001) system. This has allowed us to identify several possible reaction intermediates and to accurately compare their relative energetics within the same theoretical/computational framework. II. Method We performed periodic density functional theory (DFT) calculations within the Car-Parrinello approach,17,18 using the Quantum-Espresso code.19 The exchange and correlation effects among electrons are treated at the generalized gradient approximation (GGA) level using the PBE functional.20 Since the systems of interest contain an odd number of electrons (a spin unpaired electron), the spin-unrestricted formalism is used. Troullier-Martin21 and ultrasoft pseudopotentials22 are employed to describe the core-valence electron interaction for Si

10.1021/jp9097183  2010 American Chemical Society Published on Web 02/17/2010

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and C/H, respectively. The electronic states are expanded in plane waves with a kinetic energy cutoff of 25 and 200 Ry for the wave function and charge density, respectively. In this work, we did not consider the effects of van der Waals interactions, which are not included within standard exchangecorrelation functionals, including the PBE functional used here. We note, however, that a recent work on the adsorption of water on Si(111)-H and Si(111)-Cl surfaces has shown that these interactions affect the calculations quantitatively but leave the conclusions substantially unaltered.23 In our periodic supercell approach, the surface is modeled as a slab of five (001) layers with twelve silicon atoms per layer forming a (3 × 4) surface supercell in the (001) plane. The molecules are adsorbed on the top surface of the slab, where H atoms are present to saturate the Si dangling bonds except for one, which is the reactive db site for the adsorption. On the slab’s bottom surface, all Si dbs are saturated by H atoms. The four topmost Si layers of the slab, as well as the H monolayer and the adsorbed molecules are fully relaxed, whereas the lowest Si layer and the saturating H atoms at the bottom are held fixed in their ideal positions in order to simulate a bulk-like environment (the Si-H distance was previously optimized). In the geometry optimizations, the residual forces acting on all mobile atoms are always smaller than 10-4 atomic units. To investigate the reaction pathways and activation energies, we have employed the string method,24 as implemented by Kanai et al.25 in the context of the Car-Parrinello Molecular Dynamics. The string method allows us to optimize the Minimum Energy Pathway (MEP) for a reaction where the starting and ending states have been identified.25 Since the string is discretized into a finite number of images, the accuracy to locate the transition state depends on the number of replicas. For some cases, the string method was repeated as in ref 14 in order to locate the transition state more accurately. III. Results As the adsorption of a terminally unsaturated molecule at an isolated Si dangling bond takes place with no or negligible energy barrier,8,11 in the following we only examine the hydrogen abstraction from the intermediate state to the final state, which represents the rate determining step of the surface chain reaction. 3.1. Styrene: Intermediates and States after Hydrogen Abstraction. In Figure 1, different conformers of the adsorption intermediate of styrene on H-Si(001)-2 × 1 are shown. As shown in detail in a previous study (see, in particular, Figure 2 of ref 8), in the intermediate adsorption state, the cleavage of the π bond between the CR (carbon atom bonded to the surface Si atom) and Cβ atoms results in the transfer of spin-density (density of spin-unpaired electron) from the surface (H-atom vacancy) to the Cβ atom on the adsorbed molecule. We previously reported [11] that styrene adsorbs in a slightly bent geometry. However, upon further investigation we found that there exist at least two nonequivalent configurations. Figure 1 shows these two configurations, G1M and G2M, which differ by the bending direction of the phenyl group with respect to the silicon dimer row. The phenyl ring is bent over the trench between two adjacent silicon dimer rows for configuration G1M while over the silicon dimer row for configuration G2M. For configuration G1M, the CR-Cβ bond length is dC-C ≈ 1.48 Å, a value between a single and a double bond, and the C-Si bond length is 1.97 Å. The phenyl group is tilted such that the CR-Cβ and Cβ-C1 bonds form angles of 23° and 20° with the surface, respectively. Configuration G2M, reported

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Figure 1. Top and side views of intermediate (C-radical containing) adsorption structures of a styrene molecule on the H-Si(001)-(2 × 1) surface. Energies are -0.65, -0.78, -0.63 eV for G1M, G2M, G3M, respectively, relative to the noninteracting molecule + surface system. Large, blue circles correspond to Si atoms; small, gray circles represent H atoms; and red circles are C atoms.

previously in ref 11 has essentially the same CR-Cβ and C-Si bond lengths, 1.47 and 1.97 Å, respectively. The phenyl group is tilted with angles of 28° and 34° between the CR-Cβ and Cβ-C1 (C1 is the carbon in the phenyl group bonded to the Cβ atom) bonds and the surface, respectively. The adsorption energies for configurations G1M and G2M are 0.65 and 0.78 eV, respectively. The slightly larger energy of configuration G2M can be attributed to an electrostatic attraction between the electron-rich phenyl ring and the H atoms at surface. In these configurations, the phenyl groups are optimally positioned close to the abstracting H-atom from the neighboring Si-H unit in the same dimer row. As shown in Figure 1, however, there is also another somewhat different conformer, G3M, in which the phenyl group is oriented perpendicular to the surface, and the plane containing Si-CR-Cβ stands parallel to the Si dimer rows. The CR-Cβ bond length is in this case 1.48 Å, while the adsorption energy is 0.63 eV. We note that this configuration is similar to the one reported by Cho et al. who found an adsorption energy of 0.55 eV.9 Following formation of the intermediate state, Figure 1, the Cβ atom can abstract a H atom from a neighboring Si-H group thus creating a surface dangling bond.11 For the resulting state, there also exist three conformers, Figure 2, each corresponding to one of the intermediate states in Figure 1. Except for the H atom abstracted, the positions of the atoms change only slightly with respect to the positions in the corresponding intermediate structure. In configuration G1F, the CR-Cβ bond length is 1.55

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Figure 3. Final structure of a styrene molecule on the H-Si(001)-(2 × 1) surface, after rotation. The plane of the molecule is now parallel to a Si dimer. (a) is a top view, while (b) and (c) are two different side views. Large, blue circles correspond to Si atoms; small, gray circles represent H atoms; and red circles are C atoms.

TABLE 1: Local Minima, Transition State Energies, and Energy Barriers (in eV) in the Addition Reaction of Styrene to the H-Si(001)-(2 × 1) Surfacea TS

-0.65 -0.78 -0.63

-0.06 0.0 ∼0.5

G1 G2 G3

Figure 2. Adsorption structures after H abstraction of a styrene molecule on the H-Si(001)-(2 × 1) surface. Energies are -0.88, -0.91, -1.00 eV for G1F, G2F, G3F, respectively, relative to the noninteracting molecule + surface system. Large, blue circles correspond to Si atoms; small, gray circles represent H atoms; and red circles are C atoms.

Å, slightly larger than the single carbon-carbon bond length, and the C-Si bond length is 1.92 Å. The phenyl group is tilted such that the CR-Cβ and Cβ-C1 bonds form 28° and 18° angles with the surface, respectively. For configuration G2F, we have essentially the same CR-Cβ bond length of dC-C ≈ 1.54 Å and C-Si bond length of 1.93 Å. The phenyl group is tilted with the CR-Cβ and Cβ-C1 bonds forming angles of 29° and 25° with the surface, respectively. Configurations G1F and G2F are 0.88 and 0.91 eV more stable with respect to the noninteracting molecule + surface system, respectively. In configuration G3F, the CR-Cβ bond length is 1.53 Å and the adsorption energy is 1.00 eV. Therefore, this is the most stable configuration after H-abstraction. In configuration G3F, the styrene molecule is located in close proximity to the newly created dangling bond. As a result, it is very difficult for the subsequently adsorbing molecule to bond with the Si atom and continue the surface chain reaction. For the growth of the 1D lines, the styrene molecule in configuration G3F needs to move the phenyl ring away from the dangling bond by a 90° rotation around the CR-Cβ bond. This rotation results in configuration G4F (see Figure 3). As shown in Table 1, this configuration is slightly less favorable than G3F. This is due to the repulsion between the hydrogen atoms of the styrene molecule and those of the Si surface from the adjacent dimer row. For the 1D line growth, configuration G4F is the final state of each newly added molecule as well as the initial state for the adsorption of a new molecule in the surface chain reaction.

after H final abstraction desorption abstraction G4 barrier barrier

intermediate

-0.88 -0.91 -1.00

-0.94

0.59 0.78 >1.1

0.88 0.94 >1.44

a The energy zero corresponds to the non interacting molecule + surface system. The H-Si bond lengths at the TS are 1.63, 1.67, and >1.61 Å for the G1, G2, and G3 pathways, respectively.

TABLE 2: Local Minima, Transition State Energies, And Energy Barriers (in eV) in the Addition Reaction of 2,4 Dimethyl Styrene to the H-Si(001)-(2 × 1) Surfacea after H final abstraction desorption geometry intermediate TS abstraction G4 barrier barrier G1 G2 G3

-0.83 -0.73 -0.66

-0.10 -0.06 ∼0.4

-0.92 -0.99 -1.03

-0.93

0.73 0.67 ∼1.06

0.83 0.87 ∼1.43

a The energy zero corresponds to the non interacting molecule + surface system. The H-Si bond lengths at the TS are 1.71, 1.70, and 1.71 Å for the G1, G2, and G3 pathways, respectively.

3.2. 2,4-Dimethyl-Styrene: Intermediate and Final States. Configurations similar to those of styrene were found also for 2,4-dimethyl-styrene, see Supporting Information. In the G1M and G2M intermediates, the phenyl group is tilted over a trench between two silicon dimer rows and over the dimer row, respectively. The corresponding adsorption energies are 0.83 and 0.73 eV, respectively. The slightly smaller adsorption energy of structure G2M is due to the electrostatic interaction, in this case repulsive, between the methyl groups and the H atoms at the surface. The adsorption energy for G3M is 0.66 eV. After abstraction of an adsorbed H from the surface, the most stable structure is G3F (adsorption energy of 1.03 eV) followed by G1F (0.92 eV) and G2F (0.99 eV), see Table 2. As in the case of styrene, in the most stable G3F structure the molecule is standing vertically. As shown in Table 2, the rotated configuration G4F shown in Figure 4 is again less favorable than G3F. The difference between the two geometries is larger than in the case of styrene, due to the stronger repulsion between the

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Figure 4. Final structure of a dimethyl styrene molecule on the H-Si(001)-(2 × 1) surface, after rotation. The plane of the molecule is now parallel to a Si dimer. (a) is a top view, whereas (b) and (c) are two different side views. Large, blue circles correspond to Si atoms; small, gray circles represent H atoms; and red circles are C atoms.

Figure 5. Potential energy profile along the MEPs for the H-abstraction reaction of an adsorbed styrene molecule on the H-Si(001)-(2 × 1) surface. The zero of energy corresponds to the non interacting surface + molecule system.

hydrogen atoms of the larger dimethyl-styrene molecule and those of the nearest Si chain. We believe this difference is essential in determining the higher desorption rate of dimethyl styrene seen in experiments. 3.3. Reaction Pathways. In the previous sections, we found that for both styrene and dimethyl-styrene, the most stable final configuration (after H abstraction) is G3F. However, we need to investigate the energy barrier heights to understand which reaction path is preferred at an atomistic level. For this purpose, we employed the string method25 to locate the Minimum Energy Pathways (MEPs) for hydrogen abstraction. The resulting MEPs for each pair of intermediate-final states, i.e., G1M-G1F (G1 path), G2M-G2F (G2 path), and G3M-G3F (G3 path), are reported in Figures 5 and 6 for styrene and dimethyl-styrene, respectively. For some paths, the string method was repeated as in ref 14 in order to locate the transition state more accurately and make a more meaningful comparison. Except for the

Takeuchi et al.

Figure 6. Potential energy profile along the MEPs for the H-abstraction reaction of 2,4 dimethyl styrene adsorbed on the H-Si(001)-(2 × 1) surface. The zero of energy corresponds to the non interacting surface + molecule system.

abstracted H atom, in all paths the atomic positions within the molecule change very little from the intermediate to the final state. The H-Si distances at the transition state are given in the table captions; these values suggest that the H-Si bond is nearly broken at the TS (the ideal calculate Si-H bond length is ∼1.51 Å). As shown in Figure 5 and Table 1, the computed H atom abstraction barriers (the total energy difference between the transition state and the Intermediate state) for styrene are 0.59, 0.78, and >1.1 eV along the G1, G2, and G3 paths, respectively. Along the G1 path, the energy barrier for H abstraction is 0.06 eV smaller than the desorption energy from the intermediate state (this barrier is equal to minus the total energy of the intermediate state, assuming a negligible energy barrier associated with adsorption). Since the abstraction probability is proportional to exp(-∆E/kT), where ∆E is the abstraction barrier, the H abstraction is ∼10× more probable than the desorption of the molecule. The barriers for H abstraction and desorption are practically identical along the G2 path (we recall that the adsorption barrier was found negligible or nonexistent previously8). Alternatively, H abstraction along the G3 pathway has a prohibitively large barrier compared to the desorption energy. To obtain a more complete picture, we also investigated the pathway that goes directly from G1M to G3F. In an earlier work,11 the energy barrier along this path was estimated using a simple interpolation. Here, we obtained the TS (saddle point) by repeating the string method to the accuracy of 0.01 eV/Å for the energy gradient. The computed energy barrier for this G1M-G3F path is 0.65 eV, only 0.06 eV higher than that of the G1 path.26 On the basis of these calculations, we conclude that the H atom abstraction is likely to take place through the G1 path. Once in the G1F state, the molecule can easily rotate to the most stable G3F state, the barrier for this molecular rotation being negligibly small, only 0.10 eV. Rotation from G3F to G4F involves a similarly small energy barrier. Figure 6 shows the potential energy profiles along the G1, G2, and G3 MEPs for 2,4-dimethyl-styrene. The G3 path again shows a very large activation energy (∼1.0 eV), making this path highly improbable (Table 2). For both the G1 and G2 paths,

Surface Radical Chain Reaction Revisited

Figure 7. Adsorption energy per molecule as a function of the number of styrene/dimethyl-styrene molecules forming a 1D line parallel to the dimer rows.

the H atom abstraction energy barrier is smaller than the desorption energy, indicating that both paths are viable. It is interesting to note that while the intermediate state of the G1 path is more stable than that of the G2 path, the TS energies are quite similar along the two paths (Figure 6). Assuming Transition State Theory (the transition probability being proportional to the exponential of the energy barrier) as well as a Boltzmann distribution for G1M and G2M, both paths are likely to contribute to a similar extent. IV. One-Dimensional Line Growth As discussed in the previous section, upon adsorption of one styrene or dimethyl styrene molecule on the H-Si(001)(2 × 1) surface containing a Si dangling bond, a new Si db is formed, which could react with subsequent incoming molecules. We investigated the adsorption of multiple molecules, in order to obtain insights into the growth properties of the organic onedimensional nanostructure. In this case, we modeled the surface with a larger 5 × 4 supercell so that the adsorption of multiple molecules could be studied. The binding energies for a single molecule in the larger supercell are quantitatively very similar to those using a smaller (3 × 4) cell (∼0.02 eV lower), indicating a good convergence with respect to cell size. In Figure 7, we summarize our results for the binding energies of n molecules defined as follows:

Ebinding ) [Eslab - (Evacany + nEmolecule)]/n where Eslab is the total energy of the surface with the adsorbed molecules, Evacany the energy of the hydrogenated surface with a single H vacancy, and Emolecule the energy of an isolated styrene/dimethyl styrene molecule. It appears from the Figure 7 that the binding energy per molecule decreases as the number of molecules along the line increases. To clarify the origin of this effect, in Figure 8a,b we show a side view of the atomic configuration of two styrene (dimethyl styrene) molecules. We can see that in both cases, the molecules are not exactly in the vertical position (Figures 3 and 4), but are slightly tilted, indicating a repulsive interaction between them. In the limiting case of a full one-dimensional line (Figure 8c,d for styrene and dimethyl styrene, respectively), steric effects render the binding energy of dimethyl styrene less

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Figure 8. Side view of the atomic structure of (a) two styrene molecules on the H-Si(001)-(2 × 1) surface (b) two dimethyl styrene molecules on the H-Si(001)-(2 × 1) surface (c) a full line of styrene molecules on the H-Si(001)-(2 × 1) surface, and (d) a full line of dimethyl styrene molecules on the H-Si(001)-(2 × 1) surface. Large, blue circles correspond to Si atoms; small, gray circles represent H atoms; and red circles are C atoms.

favorable than the one of styrene. This difference should make the desorption energy of dimethyl styrene significantly lower than that of styrene, a qualitative conclusion that is not expected to be affected by the introduction of van der Waals interactions. V. Discussion and Conclusions The time-resolved STM studies by Hossain et al.15 show that the length of one-dimensional (1D) styrene lines decreases around 400 K, while for 2-4-dimethyl-styrene such a decrease was observed even at 300 K. The appearance of a dangling bond at the initial dimer site suggests that the molecular detachment occurs through the reverse chain reaction originated in the dangling bond at the end of the 1D line. In such a reverse reaction, there is a transfer of the hydrogen atom in the adsorbed molecule back to the surface dangling bond, followed by the desorption of the molecule (from the intermediate state). Our DFT results indicate that the rate-determining step for the decreasing molecular line length would be the inverse Habstraction step from the final state to the intermediate state. According to our calculations, the energy barrier associated with this process is higher for styrene than for 2-4-dimethyl-styrene, even though only by a small amount, ∼0.05 eV, for the most favorable reverse G1 pathway. The desorption is more favorable for dimethyl styrene than for styrene, consistent with the experimental observation15 that the rate of the desorption is higher for the dimethyl styrene than for the styrene. While our calculations for lines of up to four molecules indicate that for short lines the individual detachment of the molecules depends on the length of the line, this should not be the case for long lines. In the limit of a full one-dimensional line the binding energies of styrene and dimethyl styrene molecules are ∼-0.85 and -0.77 eV respectively, see Figure 7. Assuming that the energy of the transition state of the G1 path does not change, desorption energies for styrene and dimethyl styrene are ∼0.79 and ∼0.67 eV respectively, consistent with the experiment. In conclusion, we have investigated the basic steps of the radical chain reaction for styrene and 2-4-dimethyl-styrene on the H-Si(001)-(2 × 1) surface, using periodic Density Functional Theory (DFT) calculations. The focus of the present work has been to revisit the atomistic details of the proposed

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mechanism by exploring the importance of different conformations of the adsorbed molecules. This was done also to clarify minor but noticeable differences in the results of different DFT calculations in literature. Our calculations reveal the presence of a variety of molecular conformations and pathways, with sizable differences in the energy barrier. Our results show that the adsorbed molecule preferentially bends its phenyl group over the Si surface. This is not only energetically favorable but also helps the subsequent H atom abstraction kinetics even though the most stable conformer after the H abstraction is the one with vertical phenyl group normal to the surface. Acknowledgment. The computations were performed in the DGSCA-UNAM supercomputing center. This work was partially supported by Conacyt under Grant No. 48549, DGAPAUNAM Grant No. IN101809. A.S. acknowledges support from the National Science Foundation MRSEC Program through the Princeton Center for Complex Materials (DMR-0819860). Supporting Information Available: Configurations similar to those of styrene found for 2,4-dimethyl-styrene. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Buriak, J. M. Chem. ReV. 2002, 102, 1271–1308. (2) Bent, S. F. Surf. Sci. 2002, 500, 879–903. (3) Wolkow, R. A. Annu. ReV. Phys. Chem. 1999, 50, 413–41. (4) Reboredo, F. A.; Schwegier, E.; Galli, G. J. Am. Chem. Soc. 2003, 125, 15243. (5) Silvestrelli, P. L.; Pulci, O.; Palummo, M.; Del Sole, R.; Ancilotto, F. Phys. ReV. B 2003, 68, 235306. (6) Calzolari, A.; Ruini, A.; Molinari, E.; Caldas, J. M. Phys. ReV. B, 2006, 73, 125420.

Takeuchi et al. (7) Lopinsky, G. P.; Wayner, D. D. M.; Wolkow, R. A. Nature 2000, 406, 48–51. (8) Takeuchi, N.; Kanai, Y.; Selloni, A. J. Am. Chem. Soc. 2004, 126, 15890–15896. (9) Cho, J. H.; Oh, D. H.; Kleinman, L. Phys. ReV. B 2002, 65, 081310 (R). (10) Tong, X.; DiLabio, G. A.; Wolkow, R. A. NanoLett 2004, 4, 979– 983. (11) Takeuchi, N.; Selloni, A. J. Phys. Chem. B 2005, 109, 11967– 11972. (12) Hosssain, M. Z.; Kato, H. S.; Kawai, M. J. Am. Chem. Soc. 2005, 127, 15030–15031. (13) Hosssain, M. Z.; Kato, H. S.; Kawai, M. J. Phys. Chem. B. 2005, 109, 23129–23133. (14) Martinez-Guerra, E.; Takeuchi, N. Phys. ReV. B 2007, 75, 205338. (15) Hosssain, M. Z.; Kato, H. S.; Kawai, M. J. Am. Chem. Soc. 2007, 129, 3328–3332. (16) Piva, P. G.; Wolkow, R. A.; Kirczenow, G. Phys. ReV. Lett. 2008, 101, 106801. (17) Car, R.; Parrinello, M. Phys. ReV. Lett. 1985, 55, 2471–2474. (18) Laasonen, K.; Pasquarello, A.; Car, R.; Lee, C.; Vanderbilt, D. Phys. ReV. B 1993, 47, 10142–10153. (19) Giannozzi P. http://arxiv.org/abs/0906.2569P. (20) Perdew, J. P.; Burke, K.; Ernzerholf, M. Phys. ReV. Lett. 1996, 77, 3865–3868. (21) Troullier, N.; Martins, J. L. Phys. ReV. B 1991, 43, 1993–2006. (22) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892–7895. (23) Silvestrelli, P. L.; Toigo, F.; Ancilotto, F. J. Phys. Chem. C 2009, 113 (39), 17124–17131. (24) Ren, E. W.; Vanden-Eijnden, W. E. Phys. ReV. B 2002, 66, 052301. (25) Kanai, Y.; Tilocca, A.; Selloni, A.; Car, R. J. Chem. Phys. 2004, 121, 3359–3367. (26) A similar difference was found for the energy barrier for hydrogen abstraction from a dimer in the neighboring row: 1.08 eV going directly from the bent to the vertical phenyl configuration, and 1.03 eV for the case phenyl group remains bent also in the final state. This inter-dimer abstraction of the H atom would result in the molecular line growth perpendicular to the Si dimer rows.

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