Cooperative Chiral Adsorption of Styrene Molecules on the Si(001)-c

ARTICLE pubs.acs.org/JPCC

Cooperative Chiral Adsorption of Styrene Molecules on the Si(001)c(2 4) Surface: First-Principles Investigation of Reaction Mechanisms Noboru Takeuchi* Department of Physics and Astronomy, Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio 45701, United States, and Centro de Nanociencias y Nanotecnologia, Universidad Nacional Autonoma de Mexico, Apartado Postal 2681, Ensenada, Baja California, 22800, Mexico

Yosuke Kanai Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, Livermore, California, United States, and Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina, United States

bS Supporting Information ABSTRACT: Detailed reaction mechanisms for the chiral adsorption of styrene molecules on the reconstructed Si(001)-c(2 4) surface are investigated using first principles calculations based on density functional theory. The most stable configuration corresponds to the R chirality on the so-called “on-top” site, where the molecule is adsorbed on a single silicon dimer. The on-top styrene adsorption does not encounter reaction barriers, but there is a small energy barrier following an intermediate metastable state associated with the styrene adsorption on bridge sites between two Si dimers (the “singleend-bridge” site, or SEB). Our calculations show that when the first styrene molecule is adsorbed in the SEB configuration, there is no energy barrier associated with the adsorption of the second molecule. This cooperative effect leads to the experimentally observed “paired end-bridge” configuration.

1. INTRODUCTION The organic functionalization of semiconductor surfaces, especially of silicon, has attracted considerable interest in the past decade. Combining diverse organic functionalities with conventional silicon technology may indeed lead to applications in various fields, such as chemical/biosensing, surface passivation, and molecular electronics. Some exciting experiments have already begun to emerge in the field for such technological applications, including the direct measurement of transport properties through single molecules (styrene, TEMPO) adsorbed at a Si(001).1 19 An important advancement in the field toward technological applications is having controllable fabrication methods for organic molecular layers on semiconductor surfaces. One of the most promising approaches starts with a hydrogen-terminated silicon surface in the so-called “radical chain reaction mechanism” to form a well-ordered organic monolayer. The mechanism consists of a series of self-propagating sequential adsorption of terminally conjugated organic molecules at a dangling bond site in the surface.1 Alternatively, organic molecules can be straightforwardly adsorbed on clean silicon surfaces to form organic monolayers at the r 2011 American Chemical Society

surface. However, it is important to note that such adsorption processes are not sequential, as mentioned above for the radical chain reaction mechanism on hydrogen-terminated surfaces, but the adsorptions are correlated events on clean surfaces. Acetylene and ethylene molecules have been particularly popular for developing fundamental understanding for this class of silicon surface reactions with organic molecules.20 28 Early experiments have indicated that these molecules adsorb on top of a single Si dimer by forming two σ bonds between the C and Si atoms in a configuration termed “on top (OT)” or di-σ structure (see Figure 1); however, scanning tunneling microscopy (STM) experiments have revealed that the acetylene Si(001) interaction is actually quite complicated, with at least three different configurations for the adsorption of acetylene on the Si(001).27,28 In addition to the OT structure, the so-called “single end-bridge (SEB)” structure, in which an acetylene molecule adsorbs between two adjacent dimers of the same dimer row, has been also observed. The most complicated image is believed to correspond to the Received: March 15, 2011 Revised: June 3, 2011 Published: June 08, 2011 14213

dx.doi.org/10.1021/jp202469q | J. Phys. Chem. C 2011, 115, 14213–14218

The Journal of Physical Chemistry C

ARTICLE

In this work, we investigated reaction mechanisms to understand how the structurally more complex PEB configuration (two styrene molecules adsorbed on two silicon dimers) appears in addition to the OT configuration using first-principles electronic structure calculations. Kinetics and energetics of various reaction mechanisms are characterized, expanding on existing theoretical works in literature in which the styrene adsorption on Si(001) was investigated.32,33

Figure 1. Possible bonding configurations of styrene chemisorbed on the Si(001)-c(2 4) surface. (a) S on top; (b) R on top; (c) S SEB (I), with the phenyl group on top of the dimer row; (d) R SEB (I), with the phenyl group on top of the dimer row; (e) S SEB (II), with the pheyl group in the trench between two dimer rows; (f) R SEB (II), with the pheyl group in the trench between two dimer rows; (g) S,S trans-PEB; (h) R,R trans-PEB; (i) R,S cis-PEB. For a e we have used a (4 4) unit cell; for h I, we have used a (4 6) unit cell.

“paired end bridge (PEB)” structure, in which two acetylene molecules adsorb at opposite ends of the same two adjacent dimers. First-principles calculations have shown that for both aceytlene and ethylene, the OT structure is energetically more favorable than the SEB structure, and the formation of the PEB structure is favored over the formation of two separate OT structures.20 26 Among many organic molecules suitable for adsorption at the Si(001) surface, styrene is of great interest because it contains a highly conjugated phenyl group. There are two distinct features observed in the STM images of the adsorption of styrene on Si(001): the first one appears on a single dimer row but shifted slightly to one side, whereas the second is centered between two dimer rows.29 Taking into account the statistics of several images, the first feature is dominant, and the second corresponds to less than 10% of the adsorbates. Infrared spectroscopy showed that the styrene molecules attach almost exclusively through the vinyl group, with the phenyl ring left unperturbed.29 A first-principles calculation supported the OT configuration, explaining the observed STM feature.29 An STM experiment of the styrene adsorption on Ge(001) has found that styrene absorbs in the OT and PEB configurations at room temperature.30 The authors of this work also suggested that the images of styrene molecules on Si(001) in ref 29 show features similar to the paired end-bridge configuration seen for Ge(001). Moreover, recent STM experiments of styrene molecules on Ge(001) show that among the PEB configurations, trans-PEB configuration is more prevalent than cis-PEB configuration at the initial coverage because of adsorbate-induced surface reconstruction.31

2. METHOD First-principles electronic structure calculations based on density functional theory (DFT) have been performed within the Car Parrinello approach34,35 using the gradient corrected approximation of Perdew, Burke, and Enzerholf (PBE) for the exchange and correlation effects.36 Electron ion interactions are described using the Troullier Martin37 pseudopotential for Si atom and ultrasoft pseudopotentials38 for C and H atoms. The electronic states are expanded in plane waves with kinetic energy cutoffs of 25 and 200 Ry for the wave function and charge density, respectively. In our periodic supercell approach, the surface is modeled as a slab of five (001) layers with 16 silicon atoms per layer and c(2 4) symmetry. Some calculations were performed with a larger cell with 24 atoms/layer. Due to the large size of our unit cells, only the electronic states at Γ have been included. This corresponds to a sampling of 16 and 24 k points in the surface Brillouin zone.39 When the energy differences of the calculated configurations were very small, we performed additional calculations using a (2 2 1) Monkhorst Pack mesh to sample the Brillouin zone. Molecules are adsorbed on the upper surface with a c(2 4) reconstruction. On the slab’s bottom surface, all Si dangling bonds are saturated with H atoms. The four topmost Si layers of the slab as well as the adsorbed molecules are fully relaxed, whereas the lowest Si layer and the saturating H atoms are held fixed at the ideal positions to simulate a bulklike environment (the Si H distance was previously optimized). In the geometry optimizations, the residual forces on all mobile atoms are smaller than 10 4 atomic units. Our recent diffusion quantum Monte Carlo study of the styrene adsorption on a hydrogenated Si(001) surface has shown that DFT with the GGA exchange-correlation functional gives a qualitatively correct description of surface reactions, although the absolute energy barriers and adsorption energies still need to be improved toward the “chemical accuracy”.40 To characterize the reaction pathways, we employ the string method41 as implemented in the context of the Car Parrinello molecular dynamics.42 The string method allows us to determine the minimum energy pathway (MEP) of a reaction in which both the initial and final states are known. This method has been successfully applied to the study of the adsorption of alkynes and alkenes on hydrogenated Si(111) and (001) surfaces.12 16 3. ADSORPTION OF A SINGLE STYRENE MOLECULE We first consider the two primary structures of a single styrene molecule adsorbed on the Si(001)-c(2 4) surface: the OT and the SEB configurations. The fully relaxed structures using a (4 4) unit cell are shown in Figure 1, and the calculated adsorption energies for these configurations are summarized in column 2 of Table 1, where they are compared with similar theoretical works for C2H2 and C2H4 adsorptions using DFT with a GGA approximation. All possible adsorption configurations in a c(2 4) reconstruction have been considered. The styrene results follow the same trend 14214

dx.doi.org/10.1021/jp202469q |J. Phys. Chem. C 2011, 115, 14213–14218


ARTICLE

Table 1. Calculated Binding Energies (in eV) Per Molecule on Si(001) for Various Molecules in Different Adsorption Configurationsa styrene reference

C2H2

this work

22

23

2.71, 2.49 (0.125, 1)

2.63, 2.63 (0.5, 1)

C2H4 20

26

20

On Top S on top R on top

1.66 1.77

2.74, 2.76 (0.5, 1)

2.74, 2.70 (0.125, 1)

1.94, 1.91 (0.5, 1)

2.61 (0.5)

2.38, 2.51 (0.125, 0.5)

1.82 (0.5)

2.82, 2.82 (0.25, 1)

2.01 (1)

Single End Bridge S SEB (I)

1.24

R SEB (I)

1.44

S SEB (II)

1.43

R SEB (II)

1.48

S,S trans-PEB

1.79

R,R trans-PEB R,S cis-PEB

1.83 1.78

2.45 (0.125)

2.53 (0.5)

2.93 (1)

2.79 (1)

Paired End Bridge

a

2.88 (1)

Coverage is in parentheses.

as the case of acetylene and ethylene: the OT structure is energetically more favorable than the SEB. It is important to note that each configuration of OT and SEB can be further divided into either R or S chirality because of the tilted silicon dimers on the c(2 4) reconstructed surface. The most favorable configuration the R OT.43 In the S OT configuration, the phenyl group is close to an up atom of the Si dimer, and steric effects cause this configuration to be less stable. The adsorption energies for styrene are generally smaller than that for acetylene and ethylene. In the R OT configuration, the styrene molecule is adsorbed on top of a single Si dimer, as shown schematically in Figure 1a. The two C atoms of the vinyl group bond with the Si atoms of the dimer, forming two σ bonds. Upon adsorption, the Si dimer becomes essentially symmetric, and its silicon bond length is elongated from 2.34 to 2.36 Å, indicating a weakening of the bond. The styrene adsorption also breaks the Si Si π bond and produces two σ bonds between the Si dimer atoms and the C atoms. Si C bond lengths are 1.96 and 1.99 Å. Notice that in this geometry, no dangling bonds are left on the Si dimer. For styrene adsorption in the SEB configurations, the geometry with the phenyl group in the trenches between two dimer rows (type II) is more stable than the one with the phenyl group over a single dimer row (type I), as shown in Figure 1. In addition, the R chirality is more stable than the S chirality.44 In the S chirality, the phenyl group is much closer to the up atom of the Si dimer, and it results in the reversed tilting of the dimer. The initial c(2 4) arrangement of the surface is therefore altered. In the most stable SEB type II configuration of the R chirality, the styrene molecule is adsorbed across the ends of two adjacent dimers in a slightly asymmetric manner: atoms Si2 and Si4 occupy similar vertical positions (Figure 1f). In contrast, atom Si3 is at higher vertical position with respect to Si4 by 0.35 Å, and Si1 is lower than Si2 by 0.53 Å. Upon the styrene adsorption, the Si1 Si2 and Si3 Si4 bond lengths are elongated. Dimer Si1 Si2's bond length is 2.41 Å, and dimer Si3 Si4's bond length is 2.47 Å. This asymmetric behavior has been previously observed in the adsorption of SiH245 and GeH246 on Si(001) surfaces. The distortion of the end-bridge structure is generally of Jahn Teller type, enhancing the stability by the symmetry breaking, causing the dimer to be nonmetallic.

4. REACTION MECHANISM OF A SINGLE STYRENE ADSORPTION In this section, we discuss the reaction mechanism at the molecular level by locating and investigating the minimum energy pathways (MEPs) for the adsorption of styrene on the Si(001)-c(2 4) surface. 4.1. On-Top Structure. Two separate and sequential string calculations were performed to locate the MPE for investigating the reaction mechanism. The first string calculation was performed with 10 replicas, where the initial state was a configuration with the styrene molecule 5 Å above the Si(001) surface. At this distance, the interaction between the molecule and the surface is essentially negligible. The molecular plane is oriented parallel to the surface so that the molecular π bonds interact directly with the surface dangling bond as they approach each other. The final state corresponds to the on-top configuration in the calculation. This initial string calculation did not show any energy barrier along the located MEP. We then performed another string calculation with an improved resolution along the pathway to be sure of our finding. From the MEP determined in this first string calculation, we have taken a replica where the molecule is closer (∼2.5 Å) to the surface, but not chemically attached, as the initial state of the second string calculation with 15 replicas. The overall results, shown in Figure 2, show clearly no adsorption barrier. A similar result (no barrier) has been found for acetylene on Si(001) in refs 20 and 26. A [2 + 2] cyclo-addition reaction is generally considered “symmetry-forbidden” by the Woodward Hoffmann symmetry rule that dictates that the reaction cannot occur without significant activation energy. Close examination of the MEP at the atomistic level in the intermediate state (inset b of Figure 2) reveals that the attachment of the styrene molecule to the Si dimer is asymmetric, indicating that the Woodward Hoffmann rule is not violated in this particular reaction. 4.2. End-Bridge (SEB) Structure. The adsorbed configuration with the phenyl group in the trenches between two Si dimer rows is more stable than the ones with the phenyl group over a single dimer row (Figure.1c f). Furthermore, the latter configuration cannot lead to the stable PEB, configurations as observed in 14215



Figure 2. Potential energy profile along the MEP for the reaction of styrene with Si(001)-c(2 4) surface. The zero of energy corresponds to the noninteracting surface + molecule system, and the final state is the on-top geometry.

ARTICLE

Figure 4. Potential energy profile along the MEP for the change in the relative vertical position of the Si atoms of the dimers, where the molecule is attached.

Figure 3. Potential energy profile along the MEP for the reaction of styrene with the Si(001)-c(2 4) surface. The zero of energy corresponds to the noninteracting surface + molecule system. In the black line trajectory, the final state is the S end bridge configuration, whereas in the red line trajectory, the final state is the R end bridge configuration.

SEB structures of S or R chirality, respectively. The energy barrier to reach the S chirality is very small (0.17 eV), and the TS is shown in Figure 3c. On the other hand, the barrier to the R SEB is considerably larger (0.45 eV), since it involves breaking of a Si C bond. As seen in Table 1, configuration R SEB is slightly more stable than S SEB by around 0.05 eV. We can observe that the only difference between the S and R configurations is the relative buckling of the Si dimer atoms not bonded to the molecule. At room temperature, switching between the two end-bridge adsorptions of the R and S types is rapid, because the energy barrier is only 0.15 eV, as shown in Figure 4. This means that to get into the R SEB configuration, it will first pass through the S SEB configuration. Although the OT adsorption does not encounter any adsorption barriers (as discussed in Section 4.1), unlike the end-bridge (SEB) adsorption, this does not necessarily mean that the on-top configuration is kinetically favored. Forming the intermediate state for the end-bridge configuration does not encounter any energy barrier either, and molecular desorption from this resulting intermediate state is significant (0.65 eV) compared with the energy barrier of 0.18 eV for reaching the end-bridge adsorption. Therefore, a majority of the intermediate states eventually lead to the end-bridge configuration instead of desorbing away from the surface.

experiments.31 Therefore, we considered here only the former case for investigating the reaction mechanism by locating the MEP for which the phenyl group is in the trenches. An intermediate metastable state was located as shown in inset b of Figure 3, as the CR atom forms a chemical bond with the Si down atom of the dimer. The adsorption energy of this configuration is 0.65 eV. The MEP was determined by performing two separate string calculations, each involving 10 replicas, one from the initial to the intermediate state, and the other from the intermediate to the final state (Figure 3). In the initial state, the styrene molecule is placed 5 Å above the Si(001) surface, as in the case discussed above for the on-top configuration. The MEP shows no adsorption barrier for the initial attachment of the molecule to the surface forming the intermediate state. From this intermediate state, the adsorbed molecule could form another Si C bond in two different ways by sliding forward (Figure 1e and Figure 3e) or backward (Figure 1f and Figure 3f), resulting in

5. COOPERATIVE ADSORPTION OF STYRENE MOLECULES In this section, we discuss the adsorption of two styrene molecules forming the PEB configuration. For these calculations, we use a (4 6) unit cell. In this case, the phenyl rings are in the trenches between two adjacent Si dimer rows. The PEB configurations can be classified into two types depending on the orientation of the phenyl groups of the two adsorbed styrene molecules: cis-PEB and trans-PEB, as shown in Figure 1g i. The R,R trans-PEB configuration (Figure 1h) is found to be the most stable geometry as listed in Table 1. However, we note here that all the PEB configurations are very close in energy, and at room temperature, the differences are rather insignificant. The S,S PEB and R,R PEB configurations are different by the buckling of the dimers in neighboring chains, but at room temperature, the dimers are flipping rather rapidly.47 14216



ARTICLE

and its formation is barrier-free, the end-bridge configurations are also plausible in experiments (as in the case of acetylene on Si(001)27,28). Our calculations further show that a subsequent end-bridge adsorption of another styrene molecule does not encounter any energy barrier once the first one is adsorbed in the end-bridge configuration on the Si(100)-c(2 4) surface. This cooperative effect of the first adsorbate on the second styrene adsorption explains the experimental observation of the paired end-bridge configurations. The most stable paired end-bridge configuration corresponds to the R,R trans-PEB as observed in the experiment. In this arrangement, the original c(2 4) orientation of all Si dimers is retained.

’ ASSOCIATED CONTENT Figure 5. Potential energy profile along the MEP for the reaction of a second styrene molecule with the Si(001)-c(2 4) surface with a styrene molecule forming the S SEB structure. The zero of energy corresponds to the noninteracting S SEB structure + molecule system. The final state is the S,S paired end bridge configuration.

In the R,R trans-PBE arrangement, the phenyl rings are close to a down Si atom of the nearest neighbor dimer, and the original c(2 4) orientation of all Si dimers is maintained. The two Si dimers become almost symmetric. Upon styrene adsorption, the Si Si bond lengths of the dimers involved in the adsorption are stretched to 2.43 Å, indicating a weakening of the Si Si bonds. No dangling bonds are left on those dimers. In Table 1, we also compare our results of the OT, SEB, and PEB configurations to published results for acetylene and ethylene adsorption in the literature.20,22,23,26 The results for the styrene molecule follow the same trend of acetylene and ethylene: the paired end-bridge structures are the most stable. Turning to the formation of a PEB configuration, we consider the subsequent adsorption of the second styrene molecule after the adsorption of the first molecule in the end-bridge geometry. Only the type II end-bridge configuration can lead to a PEB configuration upon the adsorption of the second styrene molecule. For convenience, we took the S chirality as the starting point. Our string calculations with a total of 28 images (separated in two calculations) showed no energy barriers for the subsequent adsorption of the second styrene molecule, as shown in Figure 5. The nonexistence of the energy barrier for the second molecule stems from the fact that the first styrene adsorption forces the two adjacent silicon dimers at the surface to exhibit a single dangling bond each. They are highly reactive as they act as the radical atoms seen in many silicon surface reactions (e.g., surface radical chain reaction).12

6. CONCLUSIONS In this paper, we investigated the cooperative chiral adsorption of styrene molecules on reconstructed Si(100)-c(2 4) surfaces using density functional calculations. Our calculations show that the most stable structure for a single molecule is the on top configuration, as in the case of acetylene and ethylene molecules. We have further investigated the reaction mechanism for those adsorption configurations and found that the on-top mechanism does not encounter any energy barriers. For the case of the end-bridge mechanism, there exists an intermediate chemisorption state, followed by a small energy barrier of 0.14 eV. Given that the intermediate state is quite stable

bS

Supporting Information. Atomic positions of relevant stable and transition states. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The calculations were performed at the DGSCA-UNAM supercomputer center. N.T. was supported in part by DGAPA project IN101809. Y.K. thanks the Defense Advanced Research Projects Agency. Part of this work was performed under the auspices of the U.S. Department of Energy at Lawrence Livermore National Laboratory under Contract No. DE-AC5207NA27344. ’ REFERENCES (1) Lopinsky, G .P.; Wayner, D. D. M; Wolkow, R. A. Nature 2000, 406, 48–51. (2) Wayner, D. D. M.; Wolkow, R. A. J. Chem. Soc., Perkin Trans. 2002, 2, 23–34. (3) Buriak, J. M. Chem. Rev. 2002, 102, 1271–1308. (4) Bent, S. F. Surf. Sci. 2002, 500, 879–903. (5) Hamers, R. J.; Coulter, S. K.; Ellison, M. D.; Hovis, J. S.; Padowitz, D. F.; Schwartz, M. P.; Greenlief, C. M.; Russell, J. N., Jr. Acc. Chem. Res. 2000, 33, 617–624. (6) Wolkow, R. A. Annu. Rev. Phys. Chem. 1999, 50, 413. (7) Moller, S.; Pelov, C.; Jackson, W.; Taussig, C.; Forrest, S. R. Nature 2003, 426, 166–169. (8) Linford, M. R.; Chidsey, C. E. D. J. Am. Chem. Soc. 1993, 115, 12631–12632. Linford, M. R.; Fenter, P.; Eisenberger, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc. 1995, 117, 3145–3155. (9) Cicero, R. L.; Lindord, M. R.; Chidsey, C. E. D. Langmuir 2000, 16, 5688–5695. (10) Cicero, R. L.; Chidsey, C. E. D.; Lopinsky, G. P.; Wayner, D. D. M.; Wolkow, R. A. Langmuir 2002, 18, 305–307. (11) Tong, X.; DiLabio, G. A.; Wolkow, R. A. Nano Lett. 2004, 4, 979–983. (12) Takeuchi, N.; Kanai, Y.; Selloni, A. J. Am. Chem. Soc. 2004, 126, 15890–15896. (13) Takeuchi, N.; Selloni, A. J. Phys. Chem. B 2005, 109, 11967–11972. (14) Kanai, Y.; Takeuchi, N.; Car, R.; Selloni, A. J. Phys. Chem. B 2005, 109, 18889–18894. (15) Kanai, Y.; Selloni, A. J. Am. Chem. Soc. 2006, 128, 3892–3893. 14217



ARTICLE

(16) Martinez-Guerra, E.; Takeuchi, N. Phys. Rev. B 2007, 75, 205338. (17) Sieval, A. B.; van den Hout, B.; Zuihof, H.; Sudholter, E. J. R. Langmuir 2000, 16, 2987–2990. (18) Guisinger, N. P.; Yoder, N.L.; Hersam, M. C. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 8838. (19) Guisinger, N. P.; Green, M. E.; Basu, R.; Bluch, A. S.; Hersam, M. C. Nano Lett. 2004, 4, 55. (20) Cho, J.-H.; Oh, D.-H.; Kleinman, L. Phys. Rev. B 2002, 65, 081310 (R). (21) Liu, Q.; Hoffmann, R. J. Am. Chem. Soc. 1995, 117, 4082–4092. (22) Sorescu, D. C.; Jordan, K. D. J. Phys. Chem. B 2000, 104, 8259–8267. (23) Morikawa, Y. Phys. Rev. B 2001, 63, 033405. (24) Miotto, R.; Ferraz, A. C.; Srivastava, G. P. Phys. Rev. B 2002, 65, 075401. (25) Silvestrelli, P. L.; Pulci, O.; Palummo, M.; Sole, R. D.; Ancilotto, F. Phys. Rev. B 2003, 68, 235306. (26) Takeuchi, N. Surf. Sci. 2007, 60, 3361. (27) Mezhenny, S.; Lyubinetsky, I.; Choyke, W. J.; Wolkow, R. A.; Yates, J. T., Jr. Chem. Phys. Lett. 2001, 344, 7–12. (28) Kim, W.; Kim, H.; Lee, G.; Hong, Y. K.; Lee, K.; Hwang, C.; Kim, D. H.; Koo, J. Y. Phys. Rev. B 2001, 64, 193313. (29) Schwartz, M. P.; Ellison, M. D.; Coulter, S. K.; Hovis, J. S.; Hamers, R. J. J. Am. Chem. Soc. 2000, 122, 8529–8538. (30) Hwang, Y. J.; Kim, A.; Hwang, E. Y.; Kim, S. J. Am. Chem. Soc. 2005, 127, 5016–5017. (31) Hwang, Y. J.; Hwang, E.; Kim, D. H.; Kim, A.; Hong, S.; Kim, S. J. Phys. Chem. C 2009, 113, 1426–1432. (32) Calzolari, A.; Ruini, A.; Molinari, E.; Caldas, M. J. Phys. Rev. B 2006, 73, 125420. (33) Zhang, Q. J.; Liu, Z. F. J. Phys. Chem. C 2009, 113, 5263–5273. (34) Car, R.; Parrinello, M. Phys. Rev. Lett. 1985, 55, 2471–2474. (35) Laasonen, K.; Pasquarello, A.; Car, R.; Lee, C.; Vanderbilt, D. Phys. Rev. B 1993, 47, 10142–10153. (36) Perdew, J. P.; Burke, K.; Ernzerholf, M. Phys. Rev. Lett. 1996, 77, 3865–3868. (37) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993–2006. (38) Vanderbilt, D. Phys. Rev. B 1990, 41, 7892–7895. (39) Previous calculations by Ramstad, Brocks, and Kelly have tested the convergence of the energy difference between the p(2 2) and c(2 4) reconstructions with respect to the number of k points. They found that this difference is slightly changed by ∼3 meV/dimer, increasing the number of k points in a (2 2) cell from 4 to 64 (see Figure 11 of this reference). Our 16 k point in a 1 1 cell is equivalent to 4 k point in a (2 2) cell. Ramstad, A.; Brock, G.; Kelly, P. J. Phys. Rev. B 1995, 51, 14504–14523. (40) Kanai, Y.; Takeuchi, N. J. Chem. Phys. 2009, 131, 214708. (41) Ren, E. W.; Vanden-Eijnden, W. E. Phys. Rev. B 2002, 66, 052301. (42) Kanai, Y.; Tilocca, A.; Selloni, A.; Car, R. J. Chem. Phys. 2004, 121, 3359–3367. (43) The 0.11 eV difference between the R and S configurations is only slightly changed to 0.10 eV when using the more accurate k point sampling. (44) The 0.05 eV difference between the R and S configurations is only slightly changed to 0.03 eV when using the more accurate k point sampling. (45) Takeuchi, N Phys. Status Solidi B 2003, 239, 345–352. (46) Sanchez-Castillo, A.; Cocoletzi, G. H.; Takeuchi, N. Surf. Sci. 2003, 547, 9–18. (47) Fu, C. C.; Weissmann, M.; Saul, A. Surf. Sci. 2001, 494, 119–130.

14218


Cooperative Chiral Adsorption of Styrene Molecules on the Si(001)-c

Recommend Documents