Self-Assembled Monolayers on Au(111): Structure, Energetics, and

Article pubs.acs.org/JPCC

Self-Assembled Monolayers on Au(111): Structure, Energetics, and Mechanism of Reconstruction Lifting Yongduo Liu and Vidvuds Ozolins* Department of Materials Science and Engineering, University of California, Los Angeles, California 90095-1595, United States ABSTRACT: Density-functional theory calculations are used to compare competing structural models for SH molecules on Au(111) and to explain the effect of the adsorbed molecules on the energetics of surface reconstruction. Our results indicate that dumbbells, formed by binding two SH molecules to an adatom, are energetically stable structures at low and intermediate coverages, while the recently proposed c(4 × 2) structure with partial occupancies for adatom and vacancy sites [A. Cossaro et al., Science 2008, 321, 943] is preferred at full coverage. Lifting of the Au(111) herringbone reconstruction is attributed to reduction of surface stress due to outward in-plane relaxations of surface Au atoms under the adsorbed species. The smallest reduction of surface stress per molecule occurs when SH molecules are adsorbed in the form of dumbbells, while isolated adatoms and SH molecules have similar effects on the surface stress and reconstruction energy. SH molecules are predicted to energetically favor the fcc region of the reconstruction. We find quantitative correlation between the directly calculated reconstruction energies and changes in surface stress; this relation covers adatoms, SH molecules, and dumbbells on equal footing.

I. INTRODUCTION Thiol-based self-assembled monolayers (SAMs) play a key role in molecular electronic devices, where they are utilized as either passive (e.g., resistive wires, current rectifiers)1 or active (molecular switches)2 components. They are also used in biology, electrochemistry, and materials science for such diverse tasks as attaching cells to surfaces, modifying surface properties of materials, and protecting metals from harsh environments.3 Study of the atomic structure and surface morphology upon chemisorption is key to understanding the self-assembly process and the electronic properties of the resulting SAMs. However, the surface structure of even the most well-studied system, alkanethiol SAMs on Au(111), has been a topic of debate for decades.4−8 Early experiments identified the (√3 × √3) R30° structure with one molecule per unit cell.9 Somewhat later, the c(4 × 2) rectangular superstructure with two inequivalent molecules per supercell was proposed using experimental techniques10,11 (Figure 1). Currently, it is the most widely accepted structure of alkanethiols on Au(111),7 but the origin of the c(4 × 2) structure has been controversial for a long time. Some authors attributed the stability of the c(4 × 2) structure to the different twist angles of the backbones,7 which are related to the 3D structure of the adsorbent molecule, while others claimed a disulfide model in which two thiolate molecules are linked together by the sulfur end groups.6,8 Recent X-ray experiments concluded that alkanethiols tend to absorb on the Au(111) surface as monomers,12 raising doubts about the disulfide model. All these studies assumed an ideal Au(111) surface without any defects on the substrate, while more recent studies point to the importance of adatoms and vacancies. Adsorption with the sulfur headgroup at the top of an adatom sitting on the 3-fold hollow site was proposed based on data obtained using normal incidence X-ray © 2012 American Chemical Society

Figure 1. Types of surface supercells used to represent ideal Au(111). Circles represent surface Au atoms.

standing wave (NIXSW) techniques.13 Novel dumbbell-like structures formed by two thiolates linked with one adatom were discovered using angle-resolved photoelectron diffraction, grazing incidence X-ray diffraction, and first-principles calculations.14,15 Moreover, this dumbbell-like structure was also found on Au nanoparticles coated by thiolate SAMs using X-ray diffraction.16 In addition to the effect of adatoms, the role of surface vacancies has been investigated, and recent findings Received: November 27, 2011 Revised: January 18, 2012 Published: January 20, 2012 4738

dx.doi.org/10.1021/jp211407p | J. Phys. Chem. C 2012, 116, 4738−4747

The Journal of Physical Chemistry C

Article

distances in the slab were fully relaxed, and the in-plane components of the stress tensor were evaluated. To correct for any stress contributions due to small numerical errors in the calculated bulk lattice parameter, stresses for the corresponding 1 × 1 × n bulk supercell were evaluated separately and subtracted from those of the slab to yield the intrinsic surface stress. A dense 36 × 36 k-point mesh was used to sample the surface Brillouin zone, while the bulk calculations were performed using a regular 36 × 36 × 12 k-point mesh. Results of k-point convergence tests are shown in Table 1 using a lower

indicate that the monolayer-covered Au(111) surface reconstructs to have a certain number of adatoms and vacancies.17,18 Wang and Selloni suggested a one-adatom−one-vacancy structure.19 In contrast, based on X-ray diffraction, Cossaro et al. published a novel structure with partial occupancies for possible adatom and vacancy sites in which the sulfur end groups along with adatoms are arranged one after another to form zigzag chains.20 Lifting of the well-known Au(111) herringbone reconstruction21 upon increasing coverage is another key phenomenon caused by surface-adsorbed SAMs. Recent STM studies of the SAM-covered Au(111) surface after reductive reactions indirectly suggested that the lifting of herringbone reconstruction serves as a source of adatoms22 for adatom-stabilized structures, such as dumbbells. Most theoretical investigations assume that the surface reconstruction is lifted by adsorbed molecules and study the energetic stability of various proposed structural models with reference to the ideal Au(111) surface.5,6 On the contrary, STM studies suggest that at a coverage of 0.25 ML and at room temperature decanethiolate adsorption only leads to partial removal of the Au(111) herringbone reconstruction.23 Moreover, a recent study by Nenchev et al.24 revealed that adsorbed methanethiol on the reconstructed Au(111) forms two distinct phases with increasing temperature and/or coverage, among which only the close-packed phase formed via dissociative chemisorption leads to the removal of herringbone reconstruction. Deeper understanding of the mechanism and quantitative evaluation of the threshold coverage for complete removal of herringbone reconstruction are needed to fully understand the interplay between the surface structure and the properties of the adsorbed SAM.25 In this work, we use first-principles density-functional theory (DFT) calculations to compare the energetics of the recently proposed surface models for alkanethiol SAMs on Au(111). Using SH molecules instead of longer-chain alkanethiols, we confirm that the structure recently proposed by Cossaro et al.20 is favored energetically over other previously considered highcoverage SAM structures. We also investigate the reconstruction energy of the Au(111) surface and evolution of surface stress as functions of the SAM coverage. Our results confirm that lifting of surface reconstruction occurs because the adsorbates cause atomic relaxations within the surface layer and thus reduce the intrinsic surface stress. Strong quantitative correlation is found between the directly calculated reconstruction energies and the amount of surface stress reduction.

Table 1. Calculated Values of Surface Energy (Per Surface Atom) and Surface Stress for 24-Layer Slabs of Ideal Au(111) Using a Plane Wave Cutoff Energy Ecut = 225 eV surface k-point mesh

surface energy (eV/atom)

surface stress (N/m)

× × × ×

0.335 0.337 0.336 0.333

−2.23 −1.91 −2.18 −2.33

12 18 24 36

12 18 24 36

plane wave cutoff energy of 225 eV, indicating that the surface stress is converged to approximately 0.1 N/m using the 36 × 36 mesh. These settings gave the following values of surface stress: −2.40 N/m using 12 layers, −2.25 N/m using 18 layers, and −2.33 N/m using 24 layers. Separate convergence tests where we increased the plane wave cutoff energy to 250 eV gave surface stress values of −2.80 and −2.22 N/m for 12- and 18layer slabs, respectively. These values agree well with the earlier calculated values of −2.4 N/m in ref 29 and −2.88 N/m in ref 30. In what follows, we use the value σ = −2.33 N/m for the surface stress of ideal Au(111). In adsorption calculations, the surface was modeled using a six-layer slab and 20 Å thick vacuum. The three bottom layers of the Au slab and the horizontal positions in the third subsurface layer were held fixed, while all other degrees of freedom were relaxed until the residual forces were less than 0.01 eV/Å. Different types of surface supercells were chosen to study the possible adsorption geometries at low and full coverages, as well as surface reconstruction. In the low-coverage regime, (3 × 3)R30°, (4 × 4)R30°, and (6 × 6)R30° cells were used. In the full-coverage regime, we used the c(4 × 2) superstructure. The shapes of these cells are illustrated in Figure 1. k-point meshes of 12 ×12, 9 × 9, and 6 × 6 were used to sample the surface Brillouin zones of the (3 × 3)R30°, (4 × 4)R30°, and (6 × 6)R30° structures, respectively. The surface Brillouin zone of the c(4 × 2) structure was sampled on a 4 × 8 k-point mesh. Convergence tests with sparser k-point meshes showed that the adsorption energies were converged to an accuracy of 30 meV, which was sufficient for comparing the relative stability of different structures in this work. In the study of surface reconstruction, a 22 × √3 supercell was used with two extra atoms in the surface layer. Changes in surface stresses and reconstruction energies due to adsorbed species were derived by comparing adsorption energies on reconstructed and ideal Au(111). The latter were modeled using 11 × n√3 surface supercells to ensure maximum error cancellation in the reconstruction energies. The corresponding k-point mesh and convergence tests are presented in Section III.B.

II. METHODS First-principles calculations based on the density-functional theory (DFT) were carried out using the Vienna Ab-Initio Simulation Package (VASP).26 We used the Perdew−Becke− Ernzerhof (PBE)27 form of the generalized gradient approximation (GGA) for the electronic exchange-correlation functional, and the electron−ion interactions were treated by ultrasoft pseudopotentials.28 The cutoff energy for the planewave basis was fixed to 250 eV, and electronic states were occupied according to the Fermi−Dirac distribution with T = 300 K. The calculated bulk Au lattice parameter, a = 4.18 Å, agreed well with ref 7, where the same functional was used. This value is slightly larger than the experimental Au lattice parameter of 4.08 Å. Surface stress of ideal Au(111) was calculated using a 1 × 1 surface slab consisting of n layers with the in-plane lattice parameter fixed to the calculated bulk value. All interplanar

III. RESULTS The adsorption energy is calculated for the following dissociation reaction: SH2 + Au(111) → SH/Au(111) + 1/2 4739



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Table 2. Calculated Formation Energies of Adatoms and Adsorption Energies of SH Molecules and Dumbbells on Ideal and Reconstructed Au(111) in the Low-Coverage Regimea structure

ΔE(σ) (eV)

adatom in 3 × 3 adatom in 4 × 4 adatom in 6 × 6 adatom in 11 × √3 adatom in 11 × 2√3 2 SH in 3 × 3 SH in 3 × 3 SH in 4 × 4 SH in 6 × 6 2 SH in 11 × √3 [12̅1] SH in 11 × √3 [12̅1] SH in 11 × √3 [112̅] vacancy + SH in 3 × 3 adatom + SH in 3 × 3 dumbbell in 3 × 3 dumbbell in 11 × 2√3

0.62 0.57 0.51 0.54 0.50 −0.18 −0.18 −0.22 −0.29 −0.27 −0.34 −0.23 +0.13 −0.11 −0.36 −0.42

reconstructed 22 × √3 adatom in 22 × √3 fcc adatom in 22 × √3 ridge 1 SH in 22 × √3 fcc [12̅1] 1 SH in 22 × √3 hcp [12̅1] 1 SH in 22 × √3 ridge [12̅1] 1 SH in 22 × √3 fcc [112]̅ 1 SH in 22 × √3 hcp [112̅] 1 SH in 22 × √3 ridge [112̅] 2 SH in 22 × √3 [12̅1] 4 SH in 22 × √3 [12̅1] dumbbell in 22 × 2√3 fcc

−0.40 0.67 0.75 −0.13 −0.08 −0.03 −0.10 −0.06 −0.03 −0.04 −0.04 −0.37

Δσξξ (N/m) 0.63 0.41 0.10 0.36 0.13 1.48 0.80 0.59 0.27 1.06 0.59 0.15

Δσyy (N/m)

A(Δσxx + Δσyy)/2

adatom coverage

SH coverage

5.7 6.6 3.6 6.6 5.3 6.5 7.7 10.2 10.6 8.2 8.5 3.0

8.5 2.2

1/9 1/16 1/36 1/22 1/44 0 0 0 0 0 0 0 −1 1 1/9 1/44

0 0 0 0 0 2/9 1/9 1/16 1/36 1/11 1/22 1/22 1/9 1/9 2/9 1/22

11.4 6.2 1.2 7.7 7.9 3.4 8.3 4.1 1.3 5.8 6.4 9.7

0 1/44 1/44 0 0 0 0 0 0 0 0 1/88

0 0 0 1/44 1/44 1/44 1/44 1/44 1/44 1/22 1/11 1/44

Ideal Au(111) 0.63 0.41 0.10 0.23 0.12 1.69 0.92 0.68 0.32 0.44 0.19 0.12

0.95 0.10

0.93 0.00 Reconstructed Au(111) 0.91 0.13 0.16 0.12 0.02 0.04 0.24 0.11 0.22 0.14 0.07 0.08 0.19 0.19 0.10 0.08 0.01 0.05 0.29 0.24 0.65 0.52 0.12 0.10

a

We also give induced changes in surface stress (in N/m), as well as the product of the area per adsorbed molecule or adatom, A, expressed as the number of surface atoms, and the average stress change, (Δσxx + Δσyy)/2, measuring the “strength” of the stress dipole for each configuration. All energies are defined according to eq 1. For the one vacancy case, there are several options for the site of the vacancy relative to the SH molecule, and we only show the lowest-energy configuration found. Reconstruction energy is given in eV per one half of the 22 × √3 surface cell, and the regions on reconstructed Au(111) are denoted by ″fcc″, ″hcp″, and ″ridge″. Orientation directions of the adsorbed SH molecules are given in standard fcc notation: [111] is perpendicular to the surface, [11̅0] points to the nearest-neighbor Au atoms along the long direction of the 22×√3 unit cell, [112̅] is along the √3 direction, and [12̅1] is at a 30° angle with [11̅0].

attachment rates) play an important role in limiting the availability of Au atoms in many experiments. Here, we present a comprehensive analysis of the underlying thermodynamic tendencies, leaving kinetics for future studies. To compare the energetics of ideal-surface-based structures with those of herringbone-reconstructed configurations, we use a slightly modified form of eq 1 to convert to the units of energy per surface area (eV/Å2) via the following expression

H2. The energetic stability of competing surface structures at different SH coverage levels and with different numbers of surface adatoms and/or vacancies can be compared using the following definition of the adsorption energy per molecule ΔE(σ) = [E(σ) − E(slab) − nSH(σ)ESH − ΔnAu(σ)μAu] /nSH

(1)

where E(slab) is the total energy of the slab representing ideal or reconstructed Au(111), and E(σ) is the total energy of the same slab with the surface structure σ, which has nSH adsorbed molecules. The reference energy for SH molecules is calculated with respect to gas-phase hydrogen sulfide and molecular hydrogen as ESH = E(SH2) − 1/2E(H2). The number of Au atoms that have been added (ΔnAu > 0) or removed (ΔnAu < 0) from the system in the structure σ (not counting those involved in the reconstruction) is given by ΔnAu, and μAu is the chemical potential of Au atoms, taken as the total energy (per atom) of bulk Au. This choice implicitly assumes that these Au atoms are coming from the kinks in the step edges or via the creation of bulk vacancies at thermodynamic equilibrium. It is quite likely that kinetic limitations (e.g., slow diffusion or low detachment/

ΔE′(σ) =

1 [E(σ) − E ideal(slab) − nSH(σ)ESH A(σ) − ΔnAu(σ)μAu]

(2)

where A(σ) and E(σ) are the surface area and energy of configuration σ; Eideal(slab) is the total energy of the slab representing ideal Au(111); and in contrast to eq 1, the number of added/subtracted Au atoms ΔnAu > 0 includes those involved in the surface reconstruction. With the definitions given in eqs 1 and 2, the standard convex hull construction for ΔE′(σ) versus coverage can be used to determine stable ground-state phases at T = 0 K. 4740



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that the relaxation energies for the larger cells are underestimated due to the constraints imposed on the bottom layers of the six-layer slab used in our calculations. B. SH on Unreconstructed Au(111) at Low Coverage. To simulate low coverages, either one or two SH molecules were placed in n × n and 11 × n√3 supercells, and several different types of surface defects were tested: (i) SH on ideal Au(111), (ii) one SH with one vacancy, (iii) one SH with one adatom, and (iv) two SH molecules with one adatom (dumbbell). The relaxed structures for adsorbed SH molecules are shown in Figure 3, and the adsorption energies relative to

We have calculated adsorption energies and changes in surface stress due to adatoms, isolated SH molecules, and more complex structures involving molecules, vacancies, and adatoms, such as dumbbells. The calculated adsorption energies given by eq 1 are summarized in Table 2. We also give in Table 2 the product of the average reduction in stress, (Δσxx+Δσyy)/ 2, and the surface area per adsorbate, A, which measures the strength of the surface stress dipole associated with the adsorbed species. A. Adatoms on Ideal Au(111). Convergence of the adatom formation energy versus the supercell size is shown in Figure 2 for both fully relaxed and unrelaxed configurations; in

Figure 2. Calculated adatom formation energies on ideal Au(111) as functions of supercell size. We show results for 3 × 3 (n = 9), 4 × 4 (n = 16), 11 × √3 (n = 22), 6 × 6 (n = 36), and 11 × 2√3 (n = 44) surface supercells. Unrelaxed energies were obtained by fixing all atoms, including the adsorbed adatom, at the ideal fcc sites.

the latter, all atoms, including the adatom, are fixed at the ideal fcc positions. Whenever possible, we make use of equivalent kpoint meshes to calculate adatom energies (36/n × 36/n for hexagonal n × n surface cells and 2 × 12/n for rectangular 11 × n√3 surface cells), which should ensure a high degree of error cancellation in the adatom formation energies. Figure 2 shows that the adatom energy converges rather slowly with respect to the supercell size. For the unrelaxed configuration, we obtain a decrease from 0.86 eV for the 3 × 3 cell to 0.81 eV for the 6 × 6 cell, while the calculated value using an 11 × 2√3 cell is a further reduction to 0.80 eV. We attribute this variation to adatom-induced Friedel oscillations in the Au substrate, leading to an effective long-range interaction between adatoms. We note here that such effects have been measured experimentally for adatoms on Cu(111) at low temperatures by Knorr et al.31 For relaxed adatom configurations, the energy decreases by almost 0.1 eV when increasing the supercell size from 3 × 3 to 6 × 6, indicating that both relaxation and electronic effects contribute to this phenomenon in a roughly similar degree. We observe changes in the local bonding geometries: the nearestneighbor distance between the Au atoms directly beneath the adatom increases from 3.117 Å in 3 × 3 to 3.235 Å in the 6 × 6 cell, compared with the calculated equilibrium bulk separation of 2.956 Å. These values indicate that each adatom squeezes the surrounding Au substrate and therefore changes surface stress to less tensile values. The induced stresses in Table 2 show that this is indeed the case; i.e., each Au adatom increases the surface stress somewhere between 4 and 6 N/m per unit coverage, depending on the size of the supercell. We also note

Figure 3. Energetically optimized geometries involving one vacancy or one adatom: (A) surface with one vacancy, (B) surface with one adatom, and (C) dumbbell structure. The left and right columns are side and top views, respectively.

SH and 1/2 H2 are given in Table 2. The calculated values of ΔE(σ) [eq 1] show that the one-vacancy and one-adatom configurations are unfavorable with respect to the ideal surface with adsorbed SH molecules, which agrees well with the results presented in ref 17. However, the dumbbell structure is very favorable, in agreement with ref 15. The energy cost of breaking a dumbbell into two SH molecules on ideal Au(111) is 0.18 eV per SH molecule, suggesting that the dumbbells are thermodynamically stable up to very high temperatures. Strong dependence of the adsorption energies on the supercell size is found for SH molecules on ideal Au(111) (see Figure 4). We separate the values for n × n cells from those for the 11 × √3 cell since there appears to be a strong attractive interaction among the adsorbed SH molecules in the former; this will be discussed later. The adsorption energy changes from −0.18 eV/molecule in the 3 × 3 cell to −0.29 eV/molecule in the 6 × 6 cell. This variation is comparable to that calculated for the Au adatom in Figure 2, indicating that here, too, relaxation and electronic structure effects contribute comparably. It is also seen from Figure 4 that the dumbbell configuration is strongly favored over individually adsorbed SH molecules for all supercells considered in this study. 4741



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relaxations and efficient surface stress relief due to the formation of chains of SH molecules on ideal Au(111). C. SH on Au(111) at Full Coverage. In the full-coverage regime, c(4 × 2) rectangular supercells with different kinds of surface defects are investigated: (a) surface without defects; (b) surface with one vacancy; (c) surface with one adatom; (d) surface with one adatom and one vacancy; (e) surface with two adatoms and one vacancy; (f) double-sized c(4 × 2) cell with three adatoms and two vacancies to model the partial occupancy of defects suggested in ref 20. The relaxed configurations are shown in Figure 6, and the formation energies ΔE(σ) defined in eqs 1 and 2 are given in Table 3. It is seen that all other geometries are more favorable than the defect-free surface (a), except the two-adatom−one-vacancy structure (e), which differs from the structure proposed by Cossaro et al.20 by having full occupancy on the Au adatom sites. By decreasing the number of adatoms per cell from 2 to 1.5 [as done in the c(4 × 2) cell-doubled structure in Figure 6(f)], the structure of Cossaro et al.20 becomes lower in energy than all the other full-coverage structures considered here. Moreover, the adatom occupancy of 1.5 agrees very well with the occupancy of 1.6 per c(4 × 2) unit cell suggested by Cossaro et al. The adsorption site of the sulfur end group is geometry-dependent: on the surface without defects, SH molecules adsorb at the bridge site; on defected surfaces, the two SH molecules near the vacancy tend to adsorb at bridge sites and orient slightly toward the vacancy, which agrees with the results in ref 17; the two SH molecules near the adatom are adsorbed either on an atop site of the substrate [Figure 6(d)] or on a bridge site [Figure 6(e),(f)]. It is also important to note that the per-molecule adsorption energy ΔE(σ) of the Cossaro et al.20 structure in Figure 6(f) is 0.1 eV/molecule higher than that of the dumbbell in the low-coverage regime, showing that the former is stable only at high coverages where the interdumbbell repulsion becomes appreciable. Finally, we note that the surface stresses in Figure 6(f) are reduced by Δσxx = 0.61 and Δσyy = 1.68 N/m, suggesting that besides the more favorable bonding configurations for SH molecules the relief of surface stress also plays a role in favoring the formation of surface vacancies and adatoms. D. Reconstruction Energy of Clean Au(111). The (111) surface of Au reconstructs at ambient temperatures21 by laterally contracting the surface layer and incorporating extra Au atoms to maximize the coordination number and reduce the intrinsic surface stress.21 As a result of the reconstruction, the Au(111) surface forms fcc and hcp regions, separated by domain walls that are also sometimes called ridges.21 The Au(111) surface reconstruction can be described by a rectangular unit cell of 22 × √3,32 where the lengths of the two sides are 22 and √3 times the Au−Au nearest-neighbor distance, respectively. The reconstructed surface layer contains two extra atoms in the unit cell (46 atoms in total). To obtain the reconstruction energies, a 22 × √3 × 6-layer slab and a 1 × 12 k-point mesh for surface Brillouin zone sampling were used. We took initial positions from ref 21 and subsequently relaxed the system using DFT to obtain a reconstructed Au(111) (see Figure 7). After full relaxation, the lateral displacement in the [112̅] direction and the vertical corrugation were determined to be 0.85 and 0.14 Å respectively, which are in good agreement with the STM results of 0.9 and 0.12 Å, respectively.29 The data in Table 2 show that reconstruction leads to large, but incomplete, relief of surface stress in the ″long″ [11̅0] direction, while the stress in

Figure 4. Calculated adsorption energies for isolated SH molecules and dumbbells on ideal Au(111). Filled blue triangles show the values obtained for one SH in n × n surface supercells; empty triangles correspond to two SH molecules placed in 3 × 3 and 4 × 4 cells; while filled red circles give the energies in 11 × √3 cells where SH molecules are oriented along [12̅1] and form chains along the √3 direction. Filled black diamonds show the adsorption energy per SH molecule in the dumbbell configuration.

We now turn to analyzing the low-energy configuration of SH in the 11 × √3 cell. Figure 5 shows the local geometry

Figure 5. Comparison of adsorption geometries for SH on ideal Au(111) in 6 × 6 (left) and 11 × √3 (right) surface supercells. All distances are given in Ångströms. The calculated Au−S−Au bond angles between the adsorbed S and the bridging Au atoms are 82.4° and 87.2° in the 6 × 6 and 11 × √3 cells, respectively.

around SH and the corresponding Au−Au bond lengths in the surface layer; 6 × 6 results are shown for comparison. SH molecules are oriented along [12̅1] and form parallel chains along the √3 direction. It is seen that the proximity of the SH molecules favors very large relaxations of surface Au atoms away from the molecule, relieving the intrinsic tensile stress of ideal Au(111) and lowering the surface energy. It is interesting to note that adsorption of SH molecules oriented along the [112̅] direction does not lead to large stress relief and accordingly does not lower the surface energy to a similar degree (see Table 2). To explore the possibility that there might be other low-energy configurations, we have tested four different arrangements of two molecules in the 3 × 3 and 4 × 4 cells (these points are shown as open triangles in Figure 4). None of these cases exhibited the same enhanced relaxation effects as the SH chains in the 11 × √3 cell. Accordingly, the calculated adsorption energies exhibit the same pattern as individually adsorbed SH. Therefore, we conclude that the significant lowering of the adsorption energy in the 11 × √3 configuration shown in Figure 5 is a direct consequence of large 4742



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Figure 6. Adsorption geometries with different kinds of surface defects after relaxation: (a) Surface without defect, (b) surface with a vacancy, (c) surface with an adatom, (d) surface with an adatom and a vacancy, (e) surface with two adatoms and one vacancy, and (f) double-sized c(4 × 2) with three adatoms and two vacancies. The numbers with parentheses on atoms denote the inequivalent adatoms in the corresponding configurations.

Table 3. Formation Energies ΔE(σ) as Defined in Equation 1 for Different Configurations in the Full-Coverage Regimea structure

ΔE(σ) (eV/molecule)

vacancies

adatoms

(a) (b) (c) (d) (e) (f)

−0.25 −0.28 −0.26 −0.31 −0.24 −0.32

0 1 0 1 1 1

0 0 1 1 2 1.5

Figure 7. Top view of the reconstructed Au(111) surface after relaxation. Three layers are contained in this figure to clearly emphasize the fcc and hcp stacking differences. The rectangle outlines the 22 × √3 surface unit cell.

Numbers of vacancies and adatoms are given per c(4 × 2) cell. The structures labeled (a)−(f) are shown in Figure 6.

a

Table 4. Convergence Tests for the Reconstruction Energy of Au(111) with Respect to k-Point Density

the perpendicular ″short″ direction is changed very little. Table 4 shows the convergence tests of the reconstruction energy with respect to the k-point mesh. The reconstruction energy changes by less than 0.01 eV/cell when increasing the density of the k-point mesh from 1 × 8 to 1 × 12, and the 1 × 12 kmesh sampling is used in the subsequent calculations. E. SH Molecules on Reconstructed Au(111). We consider adsorbed SH in the form of isolated molecules and dumbbell structures discussed in Section III.B. To provide a

k-point mesh

1×4

1×6

1×8

1 × 12

ΔErec (eV/cell)

0.397

0.375

0.405

0.399

reference point, we also investigate the effect of adatoms on the reconstruction energy. Table 2 shows that the calculated adsorption energies of SH molecules are significantly lower on the ideal surface than on the reconstructed one. The relaxed adsorption configurations on ideal Au(111) show very large 4743



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relaxations (see Figure 5). In contrast, we do not observe similarly enhanced relaxations on reconstructed Au(111), indicating that the tighter packing of surface Au atoms prevents them from occurring. Adsorbed SH molecules are predicted to favor the fcc region (−0.13 eV/molecule) over the hcp (−0.08 eV/molecule) or the ridge (−0.03 eV/molecule) regions. These results are in qualitative agreement with experiments,23 which show that molecules agglomerate at the fcc elbows of the herringbone. Furthermore, the [121̅ ] orientation (molecule at a 30° angle relative to the long axis of the 22 × √3 unit cell) is slightly preferred over the [112̅] orientation (molecule perpendicular to the long axis) in all cases, except for the ridge region where both orientations have the same energy. This is likely a consequence of slightly more favorable bonding geometries due to the larger Au−Au distance along the √3 direction, as well as more efficient stress relief. We have also tested whether the position of the hydrogen atom relative to the subsurface layer affects the energetics. Since the SH molecule adsorbs with S on the bridge site between two Au, the H atom can point either in the direction of the hcp site (directly above subsurface Au) or to the fcc site (above Au in the second subsurface layer). We find a very small energy lowering of 4 meV when the hydrogen is oriented toward the surface hcp site. This energy difference is negligibly small on the scale of typical adsorption energies, and it can be safely ignored in the following discussion. We now turn to analyzing the effects of adsorbed SH on the surface reconstruction of Au(111). We define the reconstruction energy per surface area with n adsorbed molecules as ΔErec(nSH) =

Figure 8. Calculated reconstruction energy versus coverage for SH molecules (open cirles), adatoms (asterisks), and dumbbells (filled triangle). Line represents a linear fit through the calculated SH energies. Coverage is defined so that the full-coverage configurations in Figure 6 correspond to coverage of one.

our predictions for the critical coverage for reconstruction lifting to higher values. It is also evident from Figure 8 that adatoms and SH molecules induce similar changes in the reconstruction energy. Accordingly, Table 2 shows that the calculated elastic dipole strengths of adatoms are somewhat lower than, but comparable to those of SH, pointing to the importance of stress relief as the driving force for reconstruction lifting. We also note that adatoms placed on the fcc region of reconstructed Au(111) induce approximately the same compressive stress as adatoms on ideal Au(111) [compare the calculated A(Δσxx + Δσyy)/2 values of 6.2 vs 6.6 N/m]. Nevertheless, the formation energies differ by more than 150 meV/adatom (0.7 eV on reconstructed 22 × √3 versus 0.54 eV on ideal 11 × √3), strongly favoring the ideal surface. Since there are no significant differences in local bonding around the adatoms in these cases, we interpret this as a reflection of the fact that the same reduction in tensile surface stress has different effects depending on the initial value of the stress; i.e., it has a greater effect on the energy of the highly stressed ideal surface than on the less-stressed reconstructed surface. F. Dumbbells on Au(111). As demonstrated in Section III.B and in accord with the findings of other studies,33,34 alkanethiol SAMs on Au(111) favor dumbbell structures (RS− Au−SR) in the low-coverage regime. The dumbbell formation is hypothesized as a possible cause of reconstruction lifting due to the significant energy gain relative to ideal Au(111)34 (0.18 eV per SH or 0.36 eV/dumbbell, as shown in Table 2). It is intuitively plausible that Au atoms may be pulled out of the reconstructed surface to form dumbbells, and our data show that this mechanism is energetically favorable. Indeed, consider a process where four adsorbed molecules are converted into two dumbbells and the surface reconstruction is lifted within one 22 × √3 unit cell. The latter step (removal of reconstruction) has an energy cost of approximately 0.4 eV relative to ideal Au(111) (see Table 4), while the formation of two dumbbells corresponds to an energy gain of 0.72 eV. However, direct calculations of the energetics of dumbbells on reconstructed Au(111) are still lacking so that one cannot exclude the possibility that it is thermodynamically favorable to preserve the reconstruction and use the step edges or bulk Au as the primary source of Au adatoms. Therefore, we carry out large-scale DFT calculations for dumbbell-adsorbed surfaces to

1 [E ideal(nSH) − Erec(nSH) + ΔmAuμAu] A (3)

where Eideal(nSH) is the energy of the n-molecule covered ideal surface; Erec(nSH) is the energy of the n-molecule covered reconstructed surface; ΔmAu is the number of extra Au atoms incorporated in the reconstructed surface; and A is the area of the surface supercell. For all adsorbed species shown in Figures 2 and 4 (adatoms, SH molecules, dumbbells), there are significant differences in the calculated energies for different surface supercells. Therefore, care must be taken when calculating adsorption energy differences between ideal and reconstructed Au(111) since the supercell dependence of the adsorption energies is of the same order of magnitude as the adsorption energy differences themselves. In the present study, we use 11 × n√3 surface supercells to calculate the adsorption energies on ideal Au(111); these cells are very similar in shape to 22 × n√3 and permit the use of equivalent k-point meshes. In this way, the supercell size and configuration dependence should mostly cancel out in the calculated reconstruction energies. Reconstruction energy as a function of the SH coverage is shown in Figure 8. SH molecules were placed on the fcc and hcp region in the calculation with two SH molecules and evenly distributed in the calculation with four SH molecules. Our calculations predict that if all SHs are adsorbed in the form of individual molecules and form chains along the √3 direction as shown in Figure 5, the lifting of surface reconstruction will occur at a coverage of ∼0.23 ML (or one SH molecule per 13− 14 surface sites). However, it is evident from Figure 4 that there is a significant configuration dependence of the SH adsorption energies on ideal Au(111). Furthermore, some SH molecules may adsorb in the form of dumbbells. Both effects could shift 4744



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Figure 7), and (iii) the full-coverage structure suggested by Cossaro et al.19 Even though we have not considered dumbbells at coverages between those given by the structures (i) and (ii) above, it is very likely that the dumbbells form stable structures with continuously varying coverage from zero up to a certain maximum coverage, Xdmax. Our results also suggest a two-phase coexistence between dumbbells and the full-coverage phase for coverages between Xdmax and 1. Furthermore, it was shown in Section III.F that it is always favorable for adsorbed SH molecules on reconstructed Au(111) to form dumbbells by pulling out adatom(s) from the reconstruction. However, we stress that the thermodynamically stable structures in the low coverage regime are formed by dumbbells on reconstructed Au(111). Kinetic factors, such as the ease of the removal of Au atoms from the reconstruction as opposed to long-range adatom diffusion from step edges or from the bulk, may play a role in selecting the surface structures observed in STM experiments, and long annealing times and/or elevated temperatures may be needed to achieve thermodynamic equilibrium. H. Elastic Energy Model of Reconstruction Lifting. The detailed mechanism of surface reconstruction lifting is not yet settled, but most of the prevailing theories assume that stress relief plays a major role.35 We now attempt to quantify the relation between the adsorbate-induced surface stress relief and the lowering of the reconstruction energy. We assume that for each surface the elastic energy lowering due to stress relief is proportional to σΔσ, where σ is the initial stress value without adsorbed species. We take into account only the diagonal elements of the surface stress tensor and neglect shear stresses, which are found to be small in our calculations or even zero in symmetric configurations. We propose that the effect of the adsorbed species on the reconstruction energy is proportional to the following quantity

elucidate this issue. Due to the steric repulsion between the dumbbells, the 22 × √3 surface supercell has to be doubled in the short direction, resulting in a total system size of 532 atoms. The reconstruction energy of the surface with one dumbbell as defined by eq 3 is 0.374 eV/cell, which is only slightly lower than the reconstruction energy of molecule-free surfaces (0.399 eV/cell). The corresponding data point is shown as a filled red circle in Figure 8, indicating that the effect of dumbbells on the reconstruction energy is much weaker than that of adatoms and SH molecules. This ordering of reconstruction energies correlates nicely with the calculated elastic dipole strengths on ideal Au(111) in Table 2. Here, it is seen that each dumbbell on ideal Au(111) has A(Δσxx + Δσyy)/2 = 2.2 N/m, significantly smaller than those for both SH (8.6 N/m) and adatoms (6.6 N/m). It is also interesting to note that a dumbbell has a larger effect in relieving the surface stress on reconstructed Au(111) than on ideal Au(111) even though the local environments under the dumbbell are similar in both cases. We note that adsorbed dumbbells sit on the bridge sites and the attached S atoms form bonds both with the adatom and with the Au surface atoms directly beneath them (see Figure 3C). The distance from the S to the surface Au is larger than the bond length between the S and adatom (2.54 versus 2.34 Å). Therefore, the dumbbell is pulled into the Au surface, which is only possible by widening the separation between the two surface Au atoms directly bonded to the bridging adatom. This separation increases from 2.96 to 3.22 Å on ideal Au(111) and from 2.88 to 3.01 Å on reconstructed Au(111); smaller relaxation in the latter case can be explained by shorter Au−Au distances before adsorption and higher induced compressive stresses due to nonlinear soft-core repulsion between the surface Au atoms. G. T = 0 K Phase Diagram. The formation energies ΔE′(σ) [eq 2] of all the configurations considered in this work have been used to construct the T = 0 K convex hull, which is shown in Figure 9. Besides reconstructed Au(111) at zero coverage,

rec ΔΣstress = Aid

2

2

i=1

i=1

∑ σiiidΔσiiid − Arec ∑ σiirecΔσiirec (4)

Figure 9. Calculated formation energies [eq 2] of all configurations considered in this work. Line represents the convex hull connecting thermodynamically stable structures.

where the superscripts “rec” and “id” refer to reconstructed and ideal Au(111), respectively, and A is the corresponding surface area. Equation 4 is derived from the usual harmonic elasticity assuming that the stress relief Δσii is directly proportional to the product of strain and a suitable elastic stiffness constant and using the fact that the change in the elastic energy is given by the product of the stress and strain. Using the stress values listed in Table 2, we obtain the results shown in Figure 10. We see that there is indeed a strong correlation between the reconstruction energy and surface stress relief as measured by rec Δ∑stress . Furthermore, this relation encompasses all adsorbed species considered in the current study (adatoms, SH molecules, and dumbbells), demonstrating that the reduction of surface stress can quantitatively account for the effect on the reconstruction energies. The largest deviation from the linear relationship is seen for the dumbbell. This is not too surprising since our preceding analysis of atomic relaxations under the dumbbell on reconstructed Au(111) suggests that anharmonic effects due to shortened Au−Au distances in the surface layer play an important role.

three calculated structures lie on the vertices of the convex hull: (i) the reconstructed surface with dumbbells at low coverage (represented by a point at 0.08 ML in Figure 7), (ii) the ideal surface with dumbbells at intermediate coverage (0.67 ML in

IV. DISCUSSION Excess tensile surface stress is firmly established as the physical mechanism driving surface reconstruction in 5d metals. It has been suggested that the existence of reconstruction in 5d metals 4745



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light of several interpretations of surface stress, finding that only the covalent bond-strength−bond-order theory of Pauling43 qualitatively agrees with the observed tendencies for O and H adsorption on Pt(111). Subsequent studies44,45 have confirmed Feibelman’s findings, casting doubt on the correlation between the induced charge polarization at the surface and the sign of the adsorbate-induced change in the surface stress. A more complete theory of the energetics of surface reconstruction based on the seminal Frenkel−Kontorova model46 was developed by Mansfield and Needs.47 This theory recognizes that surface stress drives the reconstruction, which is balanced by the energy required to bring an extra atom into the surface layer and the energy penalty on the surface atoms, which are no longer in the minima of the potential wells of the subsurface atoms. Mansfield and Needs proposed a formula which takes into account the surface energies, surface force constants, and the energy penalty due to misregistry between the substrate and the reconstructed surface layer. Their theory was used in conjunction with first-principles calculations by Crljen et al.29 to explain the compressive surface reconstruction in Au and Pt and the absence of reconstruction in Cu. Nevertheless, Crljen et al. also found that the Mansfield−Needs model predicts a weak tendency to reconstruct for Au(111) and a strong tendency for Pt(111), which is at odds with the experimental observations of a strong reconstruction tendency for Au(111) and a very weak one for Pt(111). Thus, while the Mansfield−Needs formula captures the essential physics of surface reconstruction, a detailed account of the reconstruction energetics of Au(111) is still incomplete. Our results confirm that stress relief is the driving force for the removal of the surface reconstruction. While the physical reason for stress relief is difficult to pinpoint unambiguously, our results strongly indicate that local atomic relaxations on the Au surface under the adsorbates play a major role in the surface stress relief. These relaxations occur because the adsorbates are pulled into the surface, which tends to increase Au−Au distances directly beneath the adsorbate and compress the interatomic distances in the surrounding surface region, in accord with the results of ref 30. Other effects, such as charge transfer, direct molecule−molecule interactions for longerchain molecules, and induced dipoles may also contribute to the stress relief, but the associated contributions are difficult to disentangle from those due to atomic relaxations and require careful future work.

Figure 10. Reconstruction energy versus the product of stresses defined in eq 4. Line represents a linear fit through the calculated data rec . points and the origin, ΔErec = kΔ∑stress

(Ir, Pt, Au) and the absence of it in 4d metals (Rh, Pd, and Ag) can be explained by stronger relativistic effects in the former, which produce larger depletion of d charge in the surface layer and hence more tensile surface stresses.36 A different explanation was proposed in a more recent calculation by Kollar et al.,37 who found that the number of surface d electrons is in fact slightly increased, while the number of s and p electrons is decreased relative to the bulk. Kollar et al. argue that since the stress contribution of d electrons is attractive and that of s and p electrons repulsive, the net effect of charge transfer is tensile surface stress. The interpretation of Kollar et al. was later supported by Löwdin population analysis by Srinivasan et al.30 These studies support an early empirical view that surface stresses in transition metals are tensile due to the redistribution of surface charge into bonding orbitals favoring shorter interatomic distances and that charge transfer to bonding orbitals also accounts for the contraction of the interlayer spacing at the surface.35,38 According to this same view, charge transfer to or from the adsorbate is primarily responsible for change in the surface stress and reconstruction tendencies.35 Indeed, electron transfer from the surface to the adsorbate should weaken the bond strength between the surface Au atoms and therefore lead to reduction of tensile stress. Similarly, adsorption of less electronegative species will increase the bonding charge and strengthen the tendency to reconstruct. There are a number of studies in the literature that follow this intuitive picture. For instance, refs 39−41 observed adsorption of S on Au(111) and interpreted the observed reconstruction lifting in terms of charge transfer. Similarly, DFT calculations of ref 30 found a large decrease in the surface stress of ideal Au(111) due to adsorption of alkanethiolates, and the authors attributed it to charge transfer from bonding Au orbitals to the Au−S bond and subsequent outward relaxations of Au atoms. At variance with the conventional explanation, Feibelman42 has argued that the unfilled orbitals on noble metal surfaces are antibonding, and therefore increased electron count should lead to expansion of the interatomic distance and compressive contribution to the surface stress upon absorption of electrondonating molecules (similarly, absorption of electron acceptors should further increase the tensile stress). He also points out a second problem with the conventional explanation, “namely, meager evidence for correlation between outer-layer relaxation and the sign or magnitude of a metal’s surface stress”.42 Feibelman also gives a very clear discussion of his findings in

V. SUMMARY We have conducted a thorough comparison of the energetics of recently proposed structural models for alkanethiol SAMs on Au(111). Our results show that dumbbells formed by two thiols bonding to an adatom and the structure suggested by Cossaro et al.19 are the most favorable structures under low-tointermediate and full coverage regimes, respectively. Our results also show that the surface reconstruction can be lifted locally by pulling out a Au adatom to form a dumbbell structure, but the global energy minimum in the low-coverage regime is achieved by dumbbells on reconstructed Au(111). Kinetic factors, such as the rates of long-range adatom diffusion relative to the ejection rate of surface Au atoms from the reconstruction, may play an important role in selecting between the various surface structures observed in STM experiments. By carrying out a series of self-consistent calculations of total energies and surface stresses, we were able to find a quantitative relation between the surface stress relief induced by the 4746



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adsorbates and the energy required to remove the Au(111) herringbone reconstruction. Our results show that adsorbates induce compressive stresses of comparable magnitude in both ideal and reconstructed Au(111), but the effect on the elastic energy is larger in the highly stressed ideal surface than in the partially stress-relieved reconstructed surface. All adsorbates considered in the present study (SH molecules, dumbbells, adatoms) decrease reconstruction energies and eventually lead to a complete lifting of surface reconstruction upon increasing coverage.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported as part of the Molecularly Engineered Energy Materials (MEEM), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001342. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

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Self-Assembled Monolayers on Au(111): Structure, Energetics, and

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