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Advances in Chemistry
Volume 2016, Article ID 6080343, 8 pages
http://dx.doi.org/10.1155/2016/6080343
Research Article

Density Functional Investigation of the Inclusion of Gold Clusters on a CH3S Self-Assembled Lattice on Au(111)

1College of Science and Mathematics, University of the Virgin Islands, St. Thomas, VI, USA
2Department of Science, BMCC/CUNY, New York, NY 10007, USA

Received 27 May 2016; Accepted 28 July 2016

Academic Editor: Abhishek K. Mishra

Copyright © 2016 Darnel J. Allen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We employ first-principles density functional theoretical calculations to address the inclusion of gold (Au) clusters in a well-packed CH3S self-assembled lattice. We compute CH3S adsorption energies to quantify the energetic stability of the self-assembly and gold adsorption and dissolution energies to characterize the structural stability of a series of Au clusters adsorbed at the SAM-Au interface. Our results indicate that the inclusion of Au clusters with less than four Au atoms in the SAM-Au interface enhances the binding of CH3S species. In contrast, larger Au clusters destabilize the self-assembly. We attribute this effect to the low-coordinated gold atoms in the cluster. For small clusters, these low-coordinated sites have significantly different electronic properties compared to larger islands, which makes the binding with the self-assembly energetically more favorable. Our results further indicate that Au clusters in the SAM-Au interface are thermodynamically unstable and they will tend to dissolve, producing Au adatoms incorporated in the self-assembly in the form of CH3S-Au-SCH3 species. This is due to the strong S-Au bond which stabilizes single Au adatoms in the self-assembly. Our results provide solid insight into the impact of adatom islands at the CH3S-Au interface.

1. Introduction

Self-assembled monolayers (SAMs) have been examined in a huge variety of applications in the field of materials chemistry or catalysis [14]. Methyl thiolate (SCH3) SAMs on gold, and especially on the (111) surface of gold, have been regarded as a model system for the study of these two-dimensional structures [57]. SAMs offer the opportunity to tailor surface properties such as adhesion or surface energy, as well as other interfacial characteristics of a metal surface [810]. Despite the remarkable interest in the properties of SAMs, one of the topics widely overseen in the field is the presence of defects and imperfections in the self-assembly, especially when the control of the SAM quality is crucial for many SAM technological applications [11].

Self-assembly is often accompanied by the formation of surface defects such as disordered boundaries between crystalline regions within the SAM and vacancy pits or islands [12]. Such variances in surface structure can influence self-assembly stability, and this is indeed one of the most serious constraints of SAM. On one hand, atomic steps in the gold substrate play an active role during the self-assembly process, and in one of our recent studies we demonstrated that step edges are feasible sources of defects during self-assembly [13]. The presence of both monatomic high gold islands and vacancy pits has been extensively observed during the self-assembly of a large number of molecules on Au(111) [1417]. We recently suggested that one of the roles of vacancy pits is to stabilize the self-assembly, reducing the number of free surface vacancies [13]. The properties of gold islands, on the other hand, have been less studied, and there is little information on the role of those features produced during self-assembly. The self-assembly process on Au(111) produces single gold adatoms [1820]. These gold atoms can incorporate into alkanethiol monolayers forming gold-thiolate species with reduced mobility. Gold adatoms can also be deposited onto a self-assembled monolayer by means of physical vapor deposition. STM experiments have demonstrated that deposited Au atoms penetrate through the self-assembly and preferentially nucleate either at the intersection of different domains or inside domains of less dense striped phase [15, 16].

In this contribution, we present a first-principles, plane wave density functional theory (DFT) study of the inclusion of small gold clusters in the well-packed (√3 × √3)-R30°-CH3S self-assembled lattice. We characterize the self-assembled lattice in the presence of gold clusters of increasing size at the Au-CH3S interface. We use SAM adsorption energies to characterize monolayer stability and gold adsorption and dissolution energies to quantify the structural stability of the gold clusters at the interface. Our results show that the inclusion of small gold clusters, with less than four Au atoms, enhances the binding of CH3S species, hence making the SAM energetically more stable. Larger clusters tend to destabilize the self-assembly, diminishing the CH3S binding. A density of states analysis indicates that the presence of low-coordinated gold atoms is responsible for the stabilizing effect of small clusters. Our results further reveal that clusters located in the SAM-Au interface are thermodynamically unstable towards dissolution, and they will tend to dissolve producing Au adatoms incorporated in the self-assembly. Our results provide solid insight into the impact of adatom islands at the CH3S-Au interface.

2. Theoretical Approach

The metal substrate is modeled by means of periodic slabs separated by a vacuum space of ~1.0 nm containing four (111) atomic planes. The vacuum space was found enough to converge the binding energies within 0.01 eV. The lattice parameter of 4.177 Å has been optimized for bulk Au and has been kept fixed in the slab calculations. The two outermost atomic layers of the substrate were allowed to relax.

We employed a 3(√3 × √3)-R30°-9CH3S unit cell to model the CH3S adsorption onto the Au(111) surface. This is the original adsorption model discovered by means of He diffraction and atomic force microscopy studies [21, 22]. Even when further studies discovered the existence of more complex superlattices [23, 24], for example, c(4 × 2), the original model is still observed in different metals and for different adsorbates and constitutes a convenient model system to systematically characterize the impact of Au clusters on SAM stability, which supports our choice [2527]. It contains nine SCH3 species adsorbed via the sulfur () head group on the bridge position, with a slight shift towards the face-centered-cubic (fcc) hollow site of the Au(111) surface. The atomic coordinates of SCH3 (MT) moieties were allowed to relax without further constraints.

The DFT calculations are carried out using the Vienna Ab initio Simulation Package (VASP) [2831]. The exchange-correlation energy and potential are described using the generalized gradient approach for exchange-correlation functional within the Perdew-Wang (PW91) implementation [32, 33]. The one-electron wave functions have been expanded on a plane wave basis with a cut-off of 400 eV for the kinetic energy. The Brillouin zone sampling is carried out at Γ point, which is a reasonable approach for large enough supercells. The projected augmented wave (PAW) method [34, 35] has been employed to describe the effect of the inner cores of the atoms on the valence electrons. The tolerance used to define self-consistency is 10−4 eV for the single-point total energy and 10−3 eV for the geometry optimization. The energy minimization for a given atomic configuration is carried out using a Davidson-Bloch iteration scheme.

We calculated average SAM adsorption energies () with respect to the SCH3 radical, according to the following equation:where is the total energy of the SAM containing a gold cluster and , , and are the total energy of the Au slab, the number of SCH3 species in the unit cell, and the total energy of the SCH3 radical, respectively.

The calculated average binding energy of the self-assembly in the absence of Au clusters () defined as the energy needed to adsorb the monolayer per adsorbed SCH3 species as compared to gas-phase SCH3 and the gold substrate was found to be −1.96 eV. This value is close to those previously found in the literature [36]. The absorption energy of gold clusters is defined as in the following equation:where is the total energy of the Au slab containing the gold cluster and , , and are the total energy of the Au slab, the number of Au atoms in the cluster, and the total energy of bulk Au, respectively. Finally, the absorption energy of the gold clusters to the self-assembled phase is defined asand the SCH3 vacancy energy is defined aswhere is the total energy of the SAM containing a gold cluster with SCH3 vacancy.

3. Results and Discussion

We study the incorporation of clusters of increasing size in the well-packed (√3 × √3)-R30°-CH3S self-assembled lattice and address (i) the impact of those clusters on the molecular network properties and (ii) the impact of the self-assembly on the properties of the Au clusters. We report geometrical parameters characterizing both the molecular network and the clusters in Table 1 and average SCH3 binding energies in Table 2. The geometries of the Au clusters at the SAM interface are depicted schematically in Figure 2.

Table 1: Calculated geometric parameters characterizing the (√3 × √3)-R30°-CH3S self-assembled lattice containing Au clusters with increasing sizes. Structures are displayed in Figure 2.
Table 2: Calculated energetic parameters characterizing the (√3 × √3)-R30°-CH3S self-assembled lattice containing Au clusters with increasing sizes. A graphical representation of the different binding energies is displayed in Figure 1 and the geometric structures for the clusters at the SAM-Au interface are displayed in Figure 2.
Figure 1: Schematic representation of the different energy descriptors employed in the paper in order to characterize the stability of the self-assembly ( and ) and the stability of the Au clusters in the SAM-Au interface ( and ). Atoms on the Au cluster are highlighted in orange.
Figure 2: Plain view of the self-assembled structures containing Au clusters of increasing size. Au atoms in each cluster are colored white, SCH3 atoms are colored in light grey, and bottom metal layers are colored black with transparent planes representing the surface. On some of the structures (Au3 and Au7), we label different SCH3 adsorption sites on top of the cluster or on the Au(111) terrace.

To begin with, we address the impact of small gold clusters with sizes ranging from Au1 to Au3 on SAM stability, corresponding to Au coverage of 0.11 and 0.33 monolayers (ML), respectively. Gold adatoms (labeled Au1) incorporate into the SCH3-gold interface at the most stable fcc adsorption sites, in which the Au adatom is bonded to two different SCH3 species on top-fcc sites. The average binding energy of the SAM containing a single Au adatom is −1.99 eV. This value is slightly more exothermic than for the Au-free SAM ( = −1.96 V). This indicates that Au adatoms stabilize the self-assembly. The inclusion of gold dimers and trimers (labeled Au2 and Au3) also stabilizes the SAM, and is −1.99 and −1.98 eV, respectively. These values are more exothermic than those for the Au-free SAM. is an average binding energy which includes the binding contribution of all CH3S species in the unit cell and hence the energy changes due to clusters are small. In order to gain a deeper insight into the stabilizing effect of small gold clusters on the SAM, we use the gold substrate containing an Au3 cluster and compute SCH3 vacancy energies , defined as the energy needed to generate a vacancy in the molecular assembly. The lower this energy is, the stronger the Au-SCH3 bond will be. We compute for two different SCH3 sites on the substrate: a site on the Au(111) terrace with of −1.96 eV and a site directly on the Au3 gold cluster with of −2.48 eV. SCH3 species directly attached to the Au3 gold clusters are strongly bonded to the Au substrate. Differently, Au3 cluster has a small impact on the bonding of SCH3 species on the Au(111) terrace, and SCH3 vacancy energy is very similar to the average binding energy for the adatom-free SAM ( = −1.96 V). These results are consistent with a decrease in the lateral coordination of the Au atoms in the Au3 cluster with respect to the Au(111) surface (3 versus 6).

The presence of larger gold clusters with sizes ranging from Au4 to Au7 (0.44 and 0.77 ML, resp.) destabilizes CH3S bond and is more endothermic than that for the Au-free SAM. This energy change is in contrast to smaller clusters, which tend to stabilize the SAM. In order to gain more insight into the destabilizing effect of larger Au cluster, we use the substrate with the Au7 cluster as an example and carefully analyze the binding properties of the CH3S species on the structure by means of CH3S vacancy energies. This substrate contains three distinct adsorption sites: a top site on the island (labeled island-top site), an edge site of the island (labeled island-edge site), and the sites on the Au(111) terrace (labeled terrace site). The average binding energy of the self-assembly to a gold substrate containing Au7 island is −1.82 eV. Our results indicate that CH3S species located on the island step-edge are more strongly bonded to the gold substrate ( V) than CH3S species located on island-top sites ( V) or the Au(111) terrace ( V). Our results further indicate that the gold cluster also impacts the geometry of the self-assembly, lifting the SCH3 molecular network, increasing the average height of S from 2.25 to 2.85 Å, as reported in Table 1.

We now turn to analyze geometric and electronic properties of the Au clusters in the self-assembly. In order to do this, we compute binding energies for the adsorption of the Au clusters on the SAM-free Au(111) substrate, , which quantify the stabilizing impact of the Au substrate on the cluster. We also compute binding energies for the adsorption of the Au clusters on the SAM-covered Au(111) substrate, ; these quantify the stabilizing contribution of the SAM on the gold cluster. Both and values are displayed in Figure 3(b). Our results indicate that the energy needed to include a single adatom in the self-assembly ( eV) is more exothermic than the energy needed to adsorb the adatom on the bare Au(111) surface ( eV). We found similar results for Au2 and Au3 clusters, indicating that the SAM also stabilizes these clusters. Differently, we found an opposite trend for clusters larger than Au3. For these clusters, becomes more exothermic than . As an example, for Au7 (i.e., the largest gold cluster we considered), is 0.43 eV, with this value being larger than  eV. This indicates that an Au7 cluster is more stable on the bare Au(111) surface than on the SAM interface. The gold clusters suffer in general minor geometrical changes in the interface and the average height of Au is unaffected by the presence of any SAM (see results from Table 1).

Figure 3: (a) Binding energy values, , in eV, for the adsorption of SCH3 SAM to Au(111) substrate containing gold clusters of increasing size. The horizontal line represents the adsorption energy value of the self-assembly to the cluster-free Au(111) surface ( = −1.96 V), whereas the shaded region below the line indicates the energy values lower than . (b) Calculated values for the adsorption energy of gold clusters to the clean Au(111) surface (solid line, squares) and to the SAM-covered substrate (dashed line, diamonds) in eV. The shaded region indicates the lowest energy values for each cluster size.

We further carried out a density of states (DOS) analysis in order to gain insight into the electronic structure differences for gold clusters of increasing size included in the self-assembly. We display the DOS plots projected on the CH3S species in Figure 4 (top inset) and on the Au(111) surface in Figure 4 (bottom inset). We also display a DOS plot projected on the Au clusters for the SAM structures containing Au1, Au4, and Au7 clusters in the central panel. The results indicate that the states of the Au clusters progressively shift towards positive energies for increasing cluster sizes. This shift correlates with a decrease in the hybridization energy between the Au clusters and the CH3S species and an increase in hybridization energy between the Au clusters and the Au(111) surface and indicates that the Au-CH3S bonds weaken, while the Au-Au(111) bonds strengthen. These observations explain the different trends found between and with increasing cluster size: increases and decreases when the Au cluster size increases (Figure 3(b)). A similar effect has been found for Pd nanoparticles with increasing particle size [37].

Figure 4: Density of states (DOS) plots projected on the CH3S species (top panel) and on the Au(111) surface (bottom panel). DOS plots projected on the Au clusters of increasing size are further displayed at the central panel. The energy values were scaled with the Fermi energy (). See Figure 2 for more details on the structures.

Finally, we evaluate the stability of Au clusters 1–7 towards dissolution and compute each dissolution energy , which is defined as the energy needed to dissolve SAM-covered Au cluster and produce SAM-covered gold adatoms (see Figure 5(a), bottom panel). We display values for different cluster sizes in Figure 5(a) (top panel) and the numerical values in Table 3. The computed values are exothermic, which indicates that aggregated Au islands are in general energetically less favored than structures containing separate Au adatoms in the self-assembly. This suggests that Au clusters will tend to dissolve in the self-assembled phase, forming Au adatoms that will integrate in the SAM. These results are consistent with previous experimental observations finding that Au adatoms deposited on a packed SAM dissolve and nucleate preferentially only at the intersections of different self-assembled domains. In order to provide further information of the energy contributions involved in the cluster dissolution process, we break down for some selected cluster sizes in two different terms, + . The first represents the energy needed to dissociate an Au cluster, producing Au adatoms homogeneously distributed in the SAM, and the second, , represents the energy needed to dilute the adatoms in the SAM (see Figure 5(b)). We schematically represent the two contributions to in Figure 5(a) (bottom panel), whereas in Table 3 we report the numerical values. The results displayed in Figure 5(a) (bottom panel) indicate that , the dissociative contribution to , is exothermic and larger than the dilution energy , making exothermic for all cluster sizes considered here. Our results are consistent with the experimental observations finding island nucleation rarely within densely packed SAM [15].

Table 3: Calculated dissolution energies of the Au clusters adsorbed in the Au-SAM interface to produce gold adatoms. For some selected clusters, we break down the dissolution energies in two different energy contributions needed to dissociate the cluster and dilute the gold adatoms. Figure 5(b) provides a graphical representation of the dissolution, dissociation, and dilution processes.
Figure 5: (a) Dissolution energy, , in meV, for the dissolution of gold clusters of increasing sizes in the SAM. The lower plot indicates the two different contributions involved in the cluster dissolution energy: the dissociation energy in meV and the dilution energy in meV. (b) A schematic representation for Au cluster dissolution process, displaying the energy contribution and structures for the dissolution of a trimmer inside the SAM.

4. Conclusion

Periodic density functional calculations have been carried out to gain insight into the inclusion of gold clusters on the (√3 × √3)-R30°-CH3S self-assembled lattice on Au(111). Our results have demonstrated that the inclusion of gold clusters with less than four Au atoms enhances the binding of CH3S species in the self-assembled lattice. In contrast, larger gold clusters destabilize the self-assembly. We attributed this effect to the presence of low-coordinated gold atoms with significantly different electronic properties compared with larger clusters, which makes the binding energetically more favored. Our results further indicate that all gold clusters are thermodynamically unstable at the SAM-Au interface and that they will tend to dissolve, producing Au adatoms. This was consistent with experimental evidence from the literature. Our results provide solid insight into the impact of adatom islands at the CH3S-Au interface.

Competing Interests

The authors declare that there are no competing interests regarding the publication of this paper.

Acknowledgments

This research was supported, in part, by a grant of computer time from the City University of New York High Performance Computing Center under NSF Grants CNS-0855217, CNS-0958379, and ACI-1126113. This research also used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract no. DE-AC02-05CH11231. Support for this project was provided to Daniel Torres in part by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and the City University of New York and by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Visiting Faculty Program (VFP). Wayne E. Archibald wishes to acknowledge startup funding from the University of the Virgin Islands support of an energy development grant.

References

  1. J. J. Gooding, F. Mearns, W. Yang, and J. Liu, “Self-assembled monolayers into the 21st century: recent advances and applications,” Electroanalysis, vol. 15, no. 2, pp. 81–96, 2003. View at Publisher · View at Google Scholar · View at Scopus
  2. R. Otero, J. M. Gallego, A. L. V. de Parga, N. Martín, and R. Miranda, “Molecular self-assembly at solid surfaces,” Advanced Materials, vol. 23, no. 44, pp. 5148–5176, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Kumar, H. A. Biebuyck, and G. M. Whitesides, “Patterning self-assembled monolayers: applications in materials science,” Langmuir, vol. 10, no. 5, pp. 1498–1511, 1994. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Ulman, “Formation and structure of self-assembled monolayers,” Chemical Reviews, vol. 96, no. 4, pp. 1533–1554, 1996. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Yu, N. Bovet, C. J. Satterley et al., “True nature of an archetypal self-assembly system: mobile Au-thiolate species on Au(111),” Physical Review Letters, vol. 97, no. 16, Article ID 166102, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Häkkinen, “The gold-sulfur interface at the nanoscale,” Nature Chemistry, vol. 4, no. 6, pp. 443–455, 2012. View at Publisher · View at Google Scholar · View at Scopus
  7. C. Vericat, M. E. Vela, G. Benitez, P. Carro, and R. C. Salvarezza, “Self-assembled monolayers of thiols and dithiols on gold: new challenges for a well-known system,” Chemical Society Reviews, vol. 39, no. 5, pp. 1805–1834, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. R. Maboudian, W. R. Ashurst, and C. Carraro, “Self-assembled monolayers as anti-stiction coatings for MEMS: characteristics and recent developments,” Sensors and Actuators A: Physical, vol. 82, no. 1, pp. 219–223, 2000. View at Publisher · View at Google Scholar · View at Scopus
  9. C. E. D. Chidsey and D. N. Loiacono, “Chemical functionality in self-assembled monolayers: structural and electrochemical properties,” Langmuir, vol. 6, no. 3, pp. 682–691, 1990. View at Publisher · View at Google Scholar · View at Scopus
  10. I. H. Campbell, S. Rubin, T. A. Zawodzinski et al., “Tailoring SAM-on-SAM formation,” The Journal of Physical Chemistry Letters, vol. 2, no. 24, pp. 3124–3129, 2011. View at Publisher · View at Google Scholar
  11. B. A. Parviz, D. Ryan, and G. M. Whitesides, “Using self-assembly for the fabrication of nano-scale electronic and photonic devices,” IEEE Transactions on Advanced Packaging, vol. 26, no. 3, pp. 233–241, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. G. E. Poirier, “Mechanism of formation of Au vacancy islands in alkanethiol monolayers on Au (111),” Langmuir, vol. 13, no. 7, pp. 2019–2026, 1997. View at Publisher · View at Google Scholar · View at Scopus
  13. P. Carro, D. Torres, R. Diaz, R. C. Salvarezza, and F. Illas, “Mechanisms of defect generation and clustering in CH3S Self-assembled monolayers on Au (111),” Journal of Physical Chemistry Letters, vol. 3, no. 16, pp. 2159–2163, 2012. View at Publisher · View at Google Scholar · View at Scopus
  14. G. Yang and G. Y. Liu, “New insights for self-assembled monolayers of organothiols on Au (111) revealed by scanning tunneling microscopy,” Journal of Physical Chemistry B, vol. 107, no. 34, p. 8746, 2003. View at Google Scholar
  15. F. Li, L. Tang, W. Zhou, and Q. Guo, “Single layer gold islands at the interface between a self-assembled monolayer and the Au(111) substrate: a high-resolution STM study,” Surface Science, vol. 605, no. 11-12, pp. 1016–1020, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Ohgi, H.-Y. Sheng, Z.-C. Dong, and H. Nejoh, “Observation of Au deposited self-assembled monolayers of octanethiol by scanning tunneling microscopy,” Surface Science, vol. 442, no. 2, pp. 277–282, 1999. View at Publisher · View at Google Scholar · View at Scopus
  17. W. Azzam, A. Bashir, P. Ulrich Biedermann, and M. Rohwerder, “Formation of highly ordered and orientated gold islands: effect of immersion time on the molecular adlayer structure of pentafluorobenzenethiols (PFBT) SAMs on Au(111),” Langmuir, vol. 28, no. 27, pp. 10192–10208, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. P. Maksymovych, O. Voznyy, D. B. Dougherty, D. C. Sorescu, and J. T. Yates Jr., “Gold adatom as a key structural component in self-assembled monolayers of organosulfur molecules on Au(1 1 1),” Progress in Surface Science, vol. 85, no. 5–8, pp. 206–240, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. N. A. Kautz and S. A. Kandel, “Alkanethiol monolayers contain gold adatoms, and adatom coverage is independent of chain length,” Journal of Physical Chemistry C, vol. 113, no. 44, pp. 19286–19291, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. N. A. Kautz and S. A. Kandel, “Alkanethiol/Au(111) self-assembled monolayers contain gold adatoms: scanning tunneling microscopy before and after reaction with atomic hydrogen,” Journal of the American Chemical Society, vol. 130, no. 22, pp. 6908–6909, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. C. E. D. Chidsey, G.-Y. Liu, P. Rowntree, and G. Scoles, “Molecular order at the surface of an organic monolayer studied by low energy helium diffraction,” The Journal of Chemical Physics, vol. 91, no. 7, pp. 4421–4423, 1989. View at Publisher · View at Google Scholar · View at Scopus
  22. C. A. Alves, E. L. Smith, and M. D. Porter, “Atomic scale imaging of alkanethiolate monolayers at gold surfaces with atomic force microscopy,” Journal of the American Chemical Society, vol. 114, no. 4, pp. 1222–1227, 1992. View at Publisher · View at Google Scholar · View at Scopus
  23. R. Mazzarello, A. Cossaro, A. Verdini et al., “Structure of a CH3S monolayer on Au(111) solved by the interplay between molecular dynamics calculations and diffraction measurements,” Physical Review Letters, vol. 98, no. 1, Article ID 016102, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. P. Fenter, F. Schreiber, L. Berman, G. Scoles, P. Eisenberger, and M. J. Bedzyk, “On the structure and evolution of the buried S/Au interface in self-assembled monolayers: X-ray standing wave results,” Surface Science, vol. 412-413, pp. 213–235, 1998. View at Publisher · View at Google Scholar · View at Scopus
  25. X. Torrelles, C. Vericat, M. E. Vela et al., “Two-site adsorption model for the (3×3)-R30° dodecanethiolate lattice on Au(111) surfaces,” Journal of Physical Chemistry B, vol. 110, no. 11, pp. 5586–5594, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Cahangirov, V. O. Özçelik, L. Xian et al., “Atomic structure of the 3 ×  3 phase of silicene on Ag (111),” Physical Review B, vol. 90, no. 3, Article ID 035448, 2014. View at Publisher · View at Google Scholar
  27. H. Huang, H. Over, S. Y. Tong, J. Quinn, and F. Jona, “Atomic geometry of Ge (111)  3 ×  3 R30°-Ag determined by low-energy electron diffraction,” Physical Review B, vol. 49, no. 19, p. 13483, 1994. View at Google Scholar
  28. G. Kresse and J. Hafner, “Ab initio molecular dynamics for liquid metals,” Physical Review B, vol. 47, no. 1, pp. 558–561, 1993. View at Publisher · View at Google Scholar · View at Scopus
  29. G. Kresse and J. Hafner, “Ab initio molecular-dynamics simulation of the liquid-metalamorphous- semiconductor transition in germanium,” Physical Review B, vol. 49, no. 20, pp. 14251–14269, 1994. View at Publisher · View at Google Scholar · View at Scopus
  30. G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Computational Materials Science, vol. 6, no. 1, pp. 15–50, 1996. View at Publisher · View at Google Scholar · View at Scopus
  31. G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Physical Review B, vol. 54, no. 16, pp. 11169–11186, 1996. View at Publisher · View at Google Scholar · View at Scopus
  32. J. P. Perdew, J. A. Chevary, S. H. Vosko et al., “Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation,” Physical Review B, vol. 46, no. 11, pp. 6671–6687, 1992. View at Publisher · View at Google Scholar · View at Scopus
  33. J. P. Perdew, J. A. Chevary, S. H. Vosko et al., “Erratum: atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation,” Physical Review B, vol. 48, no. 7, p. 4978, 1993. View at Publisher · View at Google Scholar
  34. P. E. Blöchl, “Projector augmented-wave method,” Physical Review B, vol. 50, no. 24, pp. 17953–17979, 1994. View at Publisher · View at Google Scholar · View at Scopus
  35. G. Kresse and D. Joubert, “From ultrasoft pseudopotentials to the projector augmented-wave method,” Physical Review B, vol. 59, no. 3, pp. 1758–1775, 1999. View at Publisher · View at Google Scholar · View at Scopus
  36. F. P. Cometto, P. Paredes-Olivera, V. A. Macagno, and E. M. Patrito, “Density functional theory study of the adsorption of alkanethiols on Cu(111), Ag(111), and Au(111) in the low and high coverage regimes,” Journal of Physical Chemistry B, vol. 109, no. 46, pp. 21737–21748, 2005. View at Publisher · View at Google Scholar · View at Scopus
  37. F. Viñes, F. Illas, and K. M. Neyman, “Density functional calculations of Pd nanoparticles using a plane-wave method,” Journal of Physical Chemistry A, vol. 112, no. 38, pp. 8911–8915, 2008. View at Publisher · View at Google Scholar · View at Scopus