ARTICLE pubs.acs.org/JPCA
Development of Interatomic ReaxFF Potentials for AuSCH Systems Tommi T. J€arvi,*,† Adri C. T. van Duin,‡ Kai Nordlund,§ and William A. Goddard, IIIz †
Fraunhofer Institute for Mechanics of Materials IWM, Freiburg, Germany Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, Pennsylvania, United States § Department of Physics, University of Helsinki, Finland z Materials and Process Simulation Center, California Institute of Technology, Pasadena, California, United States ‡
bS Supporting Information ABSTRACT: We present fully reactive interatomic potentials for systems containing gold, sulfur, carbon, and hydrogen, employing the ReaxFF formalism. The potential is designed especially for simulating goldthiol systems and has been used for studying cluster deposition on self-assembled monolayers. Additionally, a large number of density functional theory calculations are reported, including molecules containing the aforementioned elements and adsorption energetics of molecules and atoms on gold.
’ INTRODUCTION Thiol films on gold are the archetypal example of selforganizing metalmolecule contacts, with applications in many areas of nanotechnology.1 Despite this, the true nature of the system has begun to be unveiled surprisingly recently. Thiol gold interface structures have recently been proposed, where the sulfur atoms are bound to gold adatoms2 or as RSAuRS complexes,3 in contrast to the traditional picture, where sulfur head groups directly bind to the Au(111) surface. The first atomic-resolution structural determination of a thiolprotected nanoparticle was published as recently as 2007,4 showing a “staple-like” pattern5 with RSAuRS units attached to surface gold atoms. Since then, also the planar Au(111) surface at saturation coverage was suggested to prefer a structure where the surface is covered with RSAuRS units.6 However, controversy regarding the structure of the planar surface continues.711 Most of the theoretical work on goldthiol interactions has so far relied on density functional theory (DFT), although some attempts at developing simplified potentials for the system have been made. Most attempts (see, for example, refs 1217) employ a simple pair potential, usually Morse, to describe the AuS interaction. In light of the recent discoveries outlined above, this is clearly insufficient as the interfacial structures cannot be reproduced without more complicated functional forms. Another drawback of most previous potentials is that partly nonreactive force fields were used, constraining the application of the potentials. For example, the modeling of nanoparticle fragmentation upon irradiation18 can only be done if all interactions are fully reactive. In the present Article, we present interatomic potentials for the whole set of elements AuSCH, with the aim of enabling r 2011 American Chemical Society
the reactive simulation of goldthiol systems at large lengths and long time scales.
’ METHODS ReaxFF formalism. As the ReaxFF potential formalism and fitting methods have been described in detail before,1921 we give here only a brief summary. The system energy for the presently developed interactions consists of the terms
Esystem ¼ Ebond þ Eover þ Eunder þ Eval þ Etors þ EvdW þ ECoulomb
ð1Þ
which are described in detail in the Supporting Information. Full reactivity is obtained by calculating a bond order for all bonds, and charge effects are taken into account with the EEM approach.22,23 The full range of interactions in the set AuSCH is needed to model goldthiol systems. For CH, the interactions developed in ref 21 are used for the present potential. For elemental gold, a potential was also recently published.24 The rest of the interactions are developed presently. Ab Initio Reference Data. Apart from experimental data, density functional calculations were used to parametrize the potential. Calculations on small molecules in vacuum were produced using Gaussian 0325 with a basis set described in ref 26 (basis III). Slab calculations for molecules adsorbed on the Au surface were done with the Vienna ab initio simulation package (VASP)2730 and the plane-augmented-wave method and Received: February 15, 2011 Revised: July 13, 2011 Published: July 24, 2011 10315
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Table 1. Comparison of B3LYP and PBE Results (Gaussian) with Experimental Data for the Dithiol SS Bond40 and the Au2, S2, and AuS Dimers38a
Table 2. Energies of Atoms in Vacuum with the Present Potential atom
molecule
method
multiplicity
E (eV/at)
~) r (A
Au2
B3LYP
1
0.96
2.57
PBE
1
1.12
2.55
S C
expt.
1
1.17
2.47
H
B3LYP
3
2.05
1.94
PBE expt.
3 3
2.32 2.20
1.95 1.89
B3LYP
4
0.44
2.33
PBE
2
1.36
2.22
S2
AuS
expt.
(SCH3)2
1.31
method
multiplicity
D (eV)
~) r (A
B3LYP
1
2.36
2.10
PBE
1
2.70
2.09
2.8
2.03
expt. a
E denotes the binding energy per atom, and D is the bond dissociation energy. 31,32
pseudopotentials. All calculations were done with the PBE gradient correction33 that has been shown to describe goldthiol interactions accurately. The slab calculations, unless otherwise mentioned, were done with a slab of four layers, the bottom one being kept fixed. The surface consisted of 4 2 two-atom rectangular unit cells so that the lateral dimensions were 11.8 10.2 Å2, the total number of atoms being 64. For a single adsorbed molecule, the coverage was thus ∼6%. An energy cutoff of 520 eV and k-point sampling of 4 4 1 was used. The cohesive energy of Au was found to be 2.98 eV (with the energy given by VASP for a Au atom in vacuum, 0.29 eV, taken into account), and the lattice constant was 4.17 Å. The corresponding values for the Au potential are 3.91 eV and 4.06 Å.24 For calculations of interstitials in Au, a supercell of 108 gold atoms was used, with a k-point sampling of 43. For all VASP calculations, partial occupancies were treated with the smearing method of Methfessel Paxton of order 1 with a width of 0.1 eV.34 For several systems, the energy of the relaxed system was recalculated using the tetrahedron method with Bl€ochl corrections,35 yielding identical results. For all adsorption energies, the energy of the reference molecule in vacuum was also calculated with VASP. By default, we used non-spin-polarized calculations for the slabs and spin-polarized ones for the molecules in vacuum. Many slab cases were subsequently verified with spin-polarized calculations. The effect of zero-point vibrations was ignored in all calculations. The results of the DFT calculations will be given in detail below as the corresponding interactions are discussed. Also, B3LYP36,37 was considered as a source of reference data as it was used in developing the CH interactions on which the present potential is based.21 To compare the two methods, the simplest possible systems, namely, Au2, S2, and AuS dimers, were calculated (see Table 1). It was found that PBE reproduced experimental data better for each system. Also, surprisingly, for AuS, B3LYP gave a different ground-state multiplicity (4) than PBE (2). To our knowledge, there is no experimental data for the state of the dimer, but the dissociation energy has been determined38 and indicates that the PBE result is correct. To cross-check, we
Au
energy (eV) 0 0.04308 0.10831 0
energy (kcal/mol) 0 0.9928 2.4960 0
repeated the B3LYP calculation with Jaguar using the LACV3P** basis set, also obtaining a quartet ground state with a binding energy of 0.40 eV/at and a bond length of 2.35 Å. Note furthermore that a quartet state was also obtained using a post HF-MP2 method with a very low binding energy of 0.14 eV/at.39 This issue clearly deserves greater attention, but for the purpose of the present potential, we have taken the PBE result as reference. B3LYP and PBE were also compared with the dithiol (SCH3)2. While both methods reproduced the SS bond length equally well, the SS bond dissociation energy, experimentally 2.8 eV,40 was better reproduced by PBE (2.70 eV) than B3LYP (2.36 eV).
’ RESULTS AND DISCUSSION We will describe the developed interatomic interactions in four parts. During development, it was found best to first optimize the elemetal sulfur interactions after which SC and SH interactions were added. AuC and AuH interactions were optimized independent of these. Last, the pieces were combined, and the AuS parameters were optimized. Our account below corresponds to this division. We also make some notes on the already-published Au24 and CH21 interactions. It should be noted that when the Eunder term (see Supporting Information) is used in the force field, it is possible that the energy of an atom in vacuum is not equal to 0. This is the case for C and S in the present potential. The vacuum energies are listed in Table 2. The values are taken into account in all binding energies. Note that because gold adatoms and other surface defects exist in the goldthiol interface,6 the surface defect properties of the Au potential are important. These are explored in detail in ref 24. Nonbonded CH2 Interactions. For thiols with larger hydrocarbon chains and other similar structures, the interchain interaction becomes important. As such systems were not reported in ref 21, the subject deserves some comment. As a test system, we took the orthorhombic polyethylene crystal. We determined the cohesive energy of the crystal with respect to a single infinitely long polyethylene molecule, per CH2 unit, and also the lattice parameters and the setting angle, defined as the angle between the longer (a) axis and the intrapolymer carbon plane. The results are shown in Table 3. While there is some discrepancy in the a and b lattice parameters caused by imperfect reproduction of the interchain interactions, the cohesive energy of the crystal agrees perfectly with experiment. Note also that zero-point vibrations, which we ignore, are estimated to account for ∼10 meV/CH2.41 SS Interactions. Our potential is, to our knowledge, the first fully reactive potential for sulfur, where both small molecules and bulk structures are taken into account in the parametrization. Ballone and Jones44 use a bond interchange model together with nonreactive potentials to study polymerization in bulk sulfur. Liang et al.45 have published a bond order potential for MoS, including a SS parametrization emphasizing small molecules. 10316
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Table 3. Properties of an Orthorhombic Polyethylene Crystala property
ReaxFF
Ecoh (meV/CH2)
lit.
85
a (Å) b (Å)
80
6.83 4.66
c (Å)
ref/note 42 (4 K)41,43 (4 K)41,43
7.12 4.85
2.53
Θ (deg.)
43
(4 K)41,43
41
a
The properties are the cohesive energy (Ecoh), lattice parameters (a, b, and c), and the setting angle Θ. All potential properties are at 0 K.
Table 4. Properties of the Sulfur Potentiala property
potential
lit.
ref/note
Figure 1. Binding energy of S2 as a function of separation.
Bulk Properties A16 lattice constants (300 K) a (Å)
10.1
10.5
(300 K)38
b (Å)
12.8
12.9
(300 K)38
c (Å)
24.2
24.5
(300 K)38
phase stability EA16 (eV/at) EA16 ES8 (eV/at)
2.73 0.29
2.86 48 0.10 (0 K)49
Properties of Molecules S2 E (eV/at)
1.69
2.20 38 2.32 PBE
r (Å)
1.90
1.89 38 1.95 PBE
S3 E (eV/at) rSS (Å) — SSS (deg.)
1.52 1.94 117
2.43 PBE 1.98 PBE 119
PBE
S8 E (eV/at)
2.44
2.74 PBE
rSS (Å)
2.03
2.07 38
— SSS (deg.)
∼109
105
38
Bond Dissociation (SCH3)2 DSS (eV)
2.42
2.71 PBE
rSS (Å)
2.06
2.10 PBE
a
All potential properties are at 0 K unless otherwise stated. The binding energy is denoted by E and the dissociation energy by D.
Also, models based on, for example, S8 units exist; see, for example, ref 46. We wanted to reproduce reasonably well the properties of both small sulfur-containing molecules as well as bulk systems. This task is made extremely difficult by the complicated energy landscape of sulfur, there being around 30 well-characterized bulk allotropes.47 The ground state at room temperature has the strukturbericht A16 structure, built of S8 rings with 32 atoms in the primitive unit cell and 128 in the conventional, rectangular one. Another difficulty is obtaining reliable reference data for fitting of the potential. Because A16 is effectively a molecular crystal, the missing description of van der Waals interactions makes DFT
Figure 2. SS Dissociation energy curve of (SCH3)2 as a function of separation.
inherently unreliable for this purpose. While we did use DFT calculations of different bulk phases to get an idea of their relative energies, this information was only used as a qualitative guide in the potential development. The developed potential reproduces roughly the A16 phase with the room-temperature (300 K) lattice constants shown in Table 4. Upon cooling a molten structure slowly from 2000 to 0 K, a structure ∼2 meV/at lower in energy was obtained, containing predominantly two-coordinated S in both ring-like and polymer-like configurations. We did not attempt to completely exclude such phases because excluding all possible lowerenergy phases is likely almost impossible. Other bulk phases exist at energies tens of meV higher than A16, with the metallic sc, bcc, and fcc phases 1.72.2 eV higher. Reproducing the A16 phase in the bulk required some compromise to be made with the SS pair interaction at low coordination. Figures 1 and 2 show the energy versus SS separation of S2 and (SCH3)2. Although the S2 binding energy is somewhat underestimated, the more important bond dissociation energy in (SCH3)2 is roughly correct. Table 4 displays the properties of different sulfur molecules. SC and SH interactions. For the interactions of sulfur with hydrocarbons, the potential was fit to a number of molecules and bond dissociation and angle bending curves. The SC and SH dimer dissociation curves are shown in Figure 3, the correspondence being very good. Table 5 shows more detailed information on bond lengths and angles in different molecules. 10317
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Table 5. Properties of SulfurHydrocarbon Moleculesa property
potential
lit.
ref/note
SC E (eV/at)
3.45
rSC (Å)
1.62
E (eV/at)
1.88
rSH (Å)
1.37
DSH (eV)
3.88
rSH (Å)
1.36
3.75 3.70 1.57 1.53
PBE 38 PBE 38
1.83 1.83 1.38 1.34
PBE 38 PBE 38
3.93 3.95 1.37 1.34 92 92
PBE 38 PBE 38 PBE 38
3.48 3.24 1.85 1.82 3.73 3.79 1.37 1.34 96 97 112 112 106
PBE 38 PBE 38 PBE 38 PBE 38 PBE 38 PBE PBE PBE
3.19 1.86 1.83 3.79 1.37 1.35 109
38 PBE 38 38 PBE 38 PBE
5.90 1.63 1.61 122
PBE PBE 38 PBE
3.41 1.82
PBE PBE
SH
HSH
Figure 3. Binding energy of SH and SC as a function of separation. The density functional reference state is a doublet for SH and a singlet for SC.
AuC and AuH Interactions. In the goldhydrocarbon part of the potential, emphasis was put on adsorption energetics of C and H on Au(111). Slab calculations were done with the adsorbed species on all common adsorption sites, namely, fcc, hcp, top, and bridge sites. Table 6 shows the values given by the potential compared with the DFT results. In cases where a DFT result is not given, the system has relaxed to another structure, such as from a top to a fcc site. All adsorption energies are defined as the energy required to bring an atom from vacuum to the surface and are thus negative. Adsorption of molecular hydrogen on gold is unfavorable in energy.50 Our DFT slab calculation gives an adsorption energy of 0.30 eV when H2 is adsorbed on two adjacent fcc sites on Au(111), the developed potential giving 0.48 eV. (The energies of the H2 molecule were 2.27 and 2.38 eV/at with VASP and the potential, respectively.) The values that we obtained agree very well with the literature.50,51 For the C adatom, we made an interesting discovery while testing the potential by simulating a single C adatom on Au(111). After making a few jumps on the surface, the adatom jumped into a hcp site but slightly below the level of the surface gold atoms, as shown in Figure 4. Upon calculating this configuration with DFT, it was found to be the preferred site. The energy of this configuration is listed in Table 6, marked as hcp2. Table 6 also gives the energies of C and H interstitials in Au. For simplicity these were calculated without volume relaxation for DFT, and thus also for the potential. The simulation box contained 108 gold atoms. The interstitial formation energies were taken in reference to the adatom on the fcc site. Thus, the value clearly shows, whether it is energetically favorable for an impurity on the surface to migrate into the bulk or not. Both tetrahedral and octahedral interstitial configurations were considered. Properties of different small molecules containing gold, carbon, and hydrogen are shown in Table 6. A very good correspondence with reference values was obtained. Also, angular interactions were taken into account in the optimization, Figure 5 showing the energies related to angular distortion in AuCH3 and AuCH2CH3. AuS Interactions. As outlined in the Introduction, a very complicated picture of the interaction between the thiol head group and gold surface has arisen in recent years. Reproducing the correct energy landscape is thus a formidable task for any classical potential. In order to obtain a potential that would behave reasonably in a range of situations, we emphasized the qualitative binding features over exact reproduction of the most
— HSH (deg.)
93
HSCH3 (methanethiol) DSC (eV)
3.62
rSC (Å)
1.85
DSH (eV)
3.70
rSH (Å)
1.38
— CSH (deg.)
95
— SCH1 (deg.) — SCH2 (deg.) — SCH3 (deg.)
110 110 109
HSCH2CH3 (ethanethiol) DSC (eV) rSC (Å)
2.89 1.78
DSH (eV) rSH (Å)
2.88 1.39
— SCC (deg.)
105
SdCH2 (thioformaldehyde) DSdC (eV) rSdC (Å) — SCH (deg.)
5.93 1.67 121
SCH3 DSC (eV) rSC (Å) a
3.69 1.80
All potential properties are at 0 K unless otherwise stated.
likely candidates for the experimental surface structure, which is still under debate. The potential reproduces reasonably well bond lengths and angles in gas-phase molecules containing gold, sulfur, and hydrocarbons, as shown in Table 9. Table 8 shows the adsorption energetics of S and SCH3 on Au(111) at a low coverage of 1 adsorbant per every 16 surface gold atoms, that is, ∼6%. In most cases, we had trouble getting a relaxed configuration for the top site with DFT, that being the reason for the missing values in Table 8. 10318
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Table 6. Properties of the AuC and AuH Interactionsa property
potential
lit.
ref/note
Adsorption on Au(111) C on Au(111) Eads,fcc (eV) Eads,hcp Eads,fcc (eV) Eads,brg Eads,fcc (eV) Eads,top Eads,fcc (eV) Eads,hcp2 Eads,fcc (eV)
3.40 0.033 fhcp 1.40 0.090
4.65 0.035 ffcc ffcc 0.11
PBE PBE PBE PBE PBE (see text)
Eads,fcc (eV) Eads,hcp Eads,fcc (eV) Eads,brg Eads,fcc (eV) Eads,top Eads,fcc (eV)
2.20 0.0090 0.068 0.40
2.14 0.033 0.053 0.24
PBE PBE PBE PBE
0.84 0.92 0.52 0.68
PBE PBE PBE PBE
H on Au(111)
Interstitials in Au C C H H
Etet Eads,fcc (eV) Eoct Eads,fcc (eV) Etet Eads,fcc (eV) Eoct Eads,fcc (eV)
0.55 0.61 0.45 unstable
Figure 5. Energies related to distortion of AuCH and AuCC angles in AuCH3 and AuCH2CH3, respectively. Both molecules are spin singlets.
Table 7. Adsorption Energetics of Methylthiolate on Golda structure
potential
ref 6
1: simple adsorption
0.0
0.0
2: AuSR unit
2.06
1.28
3: (AuSR)polymer
1.37
0.19
5: simple + surface vacancies 6: simple + RSAuSR unit + surface vacancy
0.32 0.19
0.53 0.48
Properties of Molecules AuC E (eV/at) rAuC (Å)
1.54 1.83
1.89
E (eV/at) rAuH (Å)
1.31 1.55
1.70 38 1.56, 1.52 PBE,38
PBE
AuH
AuCH3 DAuC (eV) rAuC (Å) — AuCH (deg.)
2.65 2.10 107
2.87 2.03 108
PBE PBE PBE
rAuC (Å) — AuCC (deg.)
2.10 113
2.05 114
PBE PBE
AuCH2CH3
a
8: RSAuSR unit
0.35
0.78
9: RSAuSR unit
0.33
0.84
The structure numbering refers to the structures in ref 6.
Table 8. Adsorption Energetics of Sulfur and Sulfur-Containing Molecules on Golda
a
All potential properties are at 0 K unless otherwise stated. The binding energy is denoted by E and the dissociation energy by D.
property
potential
lit.
ref/note
Adsorption on Au(111) at Coverage ∼6% S Eads,fcc (eV) Eads,hcp Eads,fcc (eV) Eads,brg Eads,fcc (eV) Eads,top Eads,fcc (eV)
2.43 0.026 fhcp ffcc
3.88 0.22 ffcc
PBE PBE PBE
Eads,fcc (eV) Eads,hcp Eads,fcc (eV) Eads,brg Eads,fcc (eV) Eads,top Eads,fcc (eV)
2.63 0.019 fhcp 0.29
1.82 0.22 ffcc
PBE PBE PBE
5.48 2.14
2.93 3.04
PBE PBE
SCH3 (methanethiolate)
Interstitials in Au Etet Eads,fcc (eV) Eoct Eads,fcc (eV)
Figure 4. The preferred adsorption site for a C adatom on Au(111). a
On clean Au(111) at low coverage, methylthiolate shows preferential adsorption on the fcc site, while at higher coverage, the bridgefcc site is preferred (see, e.g., refs 52 and 53). The potential predicts hcp adsorption at all coverages, the fcc and hcp sites being nearly isoenergetic. At full coverage, our DFT calculation predicts the bridgefcc binding site at an adsorption energy of 1.68 eV per thiol, in agreement with previous results.5355 Although the potential gives the hcp site, the adsorption energy, 1.65 eV, agrees very well with the DFT result.
All potential properties are at 0 K unless otherwise stated.
As for thiol adsorption structures containing gold adatoms and SRAuRS units, structures from DFT calculations in ref 6 were used as reference. The structures are illustrated in Figure 6 (for visualization, we used the VMD package 56), and Table 7 shows the energetics, relative to the simple adsorption case above, as the structures are relaxed at 0 K, compared to the results in ref 6. Although there is some discrepancy with the DFT results, the overall qualitative picture is reproduced. 10319
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Upon annealing at 300 K, most surface structures displayed some evolution and, in some cases, disordering. However, this is to be expected as the structures represent shallow local minima in the complicated methylthiolAu(111) potential energy surface. The stability of the surface structure for dodecanethiols was found to be significantly higher, with no apparent evolution seen for two test cases, the simple adsorption structure, and the one with RSAuRS moieties. It must be emphasized that the results in Table 7 are sensitive to the adatom and vacancy formation energies on Au(111). Because the values of these for the potential and the reference calculation are not the same, care must be taken in interpreting the results. The surface energetics of the present Au potential are reported in detail in ref 24.
Besides the incident deposition energy, (reactive) interactions between all of the components (cluster, SAM, gold substrate) contribute to the process. In order to understand the different interactions during deposition of gold clusters on (dodecanethiol) SAMs, we simulated the process as illustrated in Figure 7. A cluster of 405 atoms was initially placed on top of a SAM (Figure 7a) and given a kinetic energy of 0.3 eV/at toward the substrate. In ref 58, this energy was found to be within the window where the cluster only just becomes bound to the underlying Au(111) surface. Lower energies resulted in noncovalent interaction between the cluster and SAM, whereas higher energies (>∼0.6 eV) allowed full
’ APPLICATION TO CLUSTER DEPOSITION The presented potential has been successfully employed to study the penetration of gold clusters into thiol monolayers on Au(111) surfaces.57,58 Cluster deposition in the presence of a self-assembled monolayer (SAM) is more complex of a process than metal-on-metal59 or even metal-on-graphite60 deposition. Table 9. Properties of GoldSulfurHydrocarbon Moleculesa property
potential
lit.
ref/note
AuS E (eV/at) rAuS (Å)
1.42 2.41
1.36 2.22
PBE PBE
AuSCH3 E (eV/at)
3.64
3.22
PBE
DAuS (eV)
2.96
2.46
PBE
2.28
PBE
rAuS (Å) — AuSC (deg.)
2.43 98
104
PBE
H3CSAuSCH3
a
E (eV/at) DAuS (eV)
3.89 2.08
3.51 2.50
PBE PBE
rAuS (Å)
2.49
2.29
PBE
— SAuS (deg.)
160
180
PBE
— AuSC (deg.)
100
105
PBE
All potential properties are at 0 K unless otherwise stated.
Figure 7. Snapshots of deposition of a gold cluster on a SAM. (a) Initial configuration. (b) Initial reaction with a sulfur atom as the cluster penetrates to the goldSAM interface. (c) Additional reaction with another sulfur atom. (d) Final state, where the sulfurs have formed a SAuS unit with a gold atom pulled out from the cluster.
Figure 6. Thiol adsorption structures as listed in Table 7. 10320
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The Journal of Physical Chemistry A penetration of the SAM and metallic bonding between the cluster and surface gold atoms. As the cluster approaches the surface, it slows down while compressing the thiols under it. The thiols tend to straighten, pushing the cluster back, which prevents the cluster from binding at low energies. At sufficient energy, however, the cluster reaches the layer of sulfur atoms, that is, the goldSAM interface. Even if the deposition energy is not high enough for contact to be made between the cluster and surface gold atoms, covalent bonding may result from reactions between the sulfur layer and the cluster. In the case illustrated in Figure 7, the cluster initially binds to a single sulfur (Figure 7b), which, as the cluster is pushed back by the SAM, pulls out a gold atom from the cluster edge while the cluster is also bound by another sulfur (Figure 7c). While the cluster is pushed back, the two sulfurs form, together with the gold from the cluster, a SAuS unit between the cluster and Au(111), linking the cluster to the surface (Figure 7d). During the entire process, the hydrocarbon chains stay bound to the sulfurs, that is, the dodecanethiol stays intact. Thus, cluster deposition on SAMs turns out as a complex process, requiring accurate, yet reactive, modeling of all interactions present. A more detailed investigation is given in ref 58.
’ CONCLUSIONS We have presented an interatomic potential that allows largescale simulation of systems containing gold, sulfur, carbon, and hydrogen. It is specifically designed for simulating goldthiol systems but is also applicable outside this scope. The present potential enables simulating goldthiol systems unrestricted with respect to reactivity. For example, it was used successfully for modeling gold cluster deposition on self-assembled dodecanethiol molecules. Such simulations, requiring system sizes starting from ten thousand atoms and accurate modeling of reactive processes, have thus far not been possible with atomistic methods. ’ ASSOCIATED CONTENT
bS
Supporting Information. The full ReaxFF potential functions and a potential input file (for the bond order cutoff parameter for angles (cutof2), we used a value of 0.005). This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail: tommi.jarvi@iki.fi.
’ ACKNOWLEDGMENT We would like to thank Dr. Henrik Gr€onbeck for supplying us with structure files for planar thiol interfaces. A part of this work was done within the Finnish Centre of Excellence in Computational Molecular Science (CMS), financed by the Academy of Finland and the University of Helsinki. We also gratefully acknowledge the grants of computer time from CSC, the Finnish IT centre for science. ’ REFERENCES (1) Love, J. C.; Estroff, L. A.; Kriebel, J. K.; Nuzzo, R. G.; Whitesides, G. M. Chem. Rev. 2005, 105, 1103–1169.
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(2) Yu, M.; Bovet, N.; Satterley, C. J.; Bengio, S.; Lovelock, K. R. J.; Milligan, P. K.; Jones, R. G.; Woodruff, D. P.; Dhanak, V. Phys. Rev. Lett. 2006, 97, 166102. (3) Maksymovych, P.; Sorescu, D. C.; John T. Yates, J. Phys. Rev. Lett. 2006, 97, 146103. (4) Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Bushnell, D. A.; Kornberg, R. D. Science 2007, 318, 430–433. (5) Jiang, D.; Tiago, M. L.; Luo, W.; Dai, S. J. Am. Chem. Soc. 2008, 130, 2777–2779. (6) Gr€onbeck, H.; H€akkinen, H.; Whetten, R. L. J. Phys. Chem. C 2008, 112, 15940–15942. (7) Cossaro, A.; Mazzarello, R.; Rousseau, R.; Casalis, L.; Verdini, A.; Kohlmeyer, A.; Floreano, L.; Scandolo, S.; Morgante, A.; Klein, M. L.; Scoles, G. Science 2008, 321, 943–946. (8) Chaudhuri, A.; Lerotholi, T. J.; Jackson, D. C.; Woodruff, D. P. Phys. Rev. Lett. 2009, 102, 126101. (9) Li, F.-S.; Zhou, W.; Guo, Q. Phys. Rev. B 2009, 79, 113412. (10) Voznyy, O.; Dubowski, J. J. Langmuir 2009, 25, 7353–7358. (11) Gr€onbeck, H.; Odelius, M. Phys. Rev. B 2010, 82, 085416. (12) Gerdy, J. J.; Goddard, W. A., III. J. Am. Chem. Soc. 1996, 118, 3233–3236. (13) Beardmore, K. M.; Kress, J. D.; Grønbech-Jensen, N.; Bishop, A. R. Chem. Phys. Lett. 1998, 286, 40–45. (14) Luedtke, W. D.; Landman, U. J. Phys. Chem. B 1998, 102, 6566–6572. (15) Zhang, L.; Goddard, W. A., III; Jiang, S. J. Chem. Phys. 2002, 117, 7342–7349. (16) Jiang, S. Mol. Phys. 2002, 100, 2261–2275. (17) Fartaria, R. P. S.; Freitas, F. F. M.; Fernandes, F. M. S. S. J. Electroanal. Chem. 2005, 574, 321–331. (18) Dass, A.; Dubay, G. R.; Fields-Zinna, C. A.; Murray, R. W. Anal. Chem. 2008, 80, 6845–6849. (19) van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A., III. J. Phys. Chem. A 2001, 105, 9396–9409. (20) Nielson, K. D.; van Duin, A. C. T.; Oxgaard, J.; Deng, W.-Q.; Goddard, W. A., III. J. Phys. Chem. A 2005, 109, 493–499. (21) Chenoweth, K.; van Duin, A. C. T.; Goddard, W. A., III. J. Phys. Chem. A 2008, 112, 1040–1053. (22) Mortier, W. J.; Ghosh, S. K.; Shankar, S. J. Am. Chem. Soc. 1986, 108, 4315–4320. (23) Janssens, G. O. A.; Baekelandt, B. G.; Toufar, H.; Mortier, W. J.; Schoonheydt, R. A. J. Phys. Chem. 1995, 99, 3251–3258. (24) J€arvi, T. T.; Kuronen, A.; Hakala, M.; Nordlund, K.; van Duin, A. C. T.; Goddard, W. A., III; Jacob, T. Eur. Phys. J. B 2008, 66, 75–79. (25) Frisch, M. J. et al. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford CT, 2004. (26) Basch, H.; Ratner, M. A. J. Chem. Phys. 2003, 119, 11926–11942. (27) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558–561. (28) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251–14269. (29) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169–11186. (30) Kresse, G.; Furthm€uller, J. Comput. Mater. Sci. 1996, 6, 15–50. (31) Bl€ochl, P. E. Phys. Rev. B 1994, 50, 17953–17979. (32) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758–1775. (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. (34) Methfessel, M.; Paxton, A. T. Phys. Rev. B 1989, 40, 3616–3621. (35) Bl€ochl, P. E.; Jepsen, O.; Andersen, O. K. Phys. Rev. B 1994, 49, 16223–16233. (36) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (37) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785–789. (38) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, Internet Version, 88th ed.; CRC Press: Boca Raton, FL, 2007. (39) Bravo-Perez, G.; Garz on, I. L. J. Mol. Struct.: THEOCEM 2002, 619, 79–89. (40) Nicovich, J. M.; Kreutter, K. D.; van Dijk, C. A.; Wine, P. H. J. Phys. Chem. 1992, 96, 2518–2528. (41) Kleis, J.; Lundqvist, B. I.; Langreth, D. C.; Schr€oder, E. Phys. Rev. B 2007, 76, 100201(R). 10321
dx.doi.org/10.1021/jp201496x |J. Phys. Chem. A 2011, 115, 10315–10322
The Journal of Physical Chemistry A
ARTICLE
(42) Fred W. Billmeyer, J. J. Appl. Phys. 1957, 28, 1114–1118. (43) Avitable, G.; et al. J. Polym. Sci., Polym. Lett. Ed. 1975, 13, 351. (44) Baletto, F.; Mottet, C.; Ferrando, R. Phys. Rev. Lett. 2003, 90, 135504. (45) Liang, T.; Phillpot, S. R.; Sinnott, S. B. Phys. Rev. B 2009, 79, 245110. (46) Passerone, D.; Ceccarelli, M.; Parrinello, M. J. Chem. Phys. 2003, 118, 2025–2032. (47) Steudel, R.; Eckert, B. Solid Sulfur Allotropes. In Elemental Sulfur and Sulfur-Rich Compounds I; Steudel, R., Ed.; Springer: Berlin/ Heidelberg, Germany, 2003; Vol. 230, pp 179. (48) Kittel, C. Introduction to Solid State Physics; John Wiley & Sons: New York, 1971. (49) Ezzine, M.; Pellegatti, A.; Minot, C.; Pellenq, R. J.-M. J. Phys. Chem. A 1998, 102, 452–460. (50) Hammer, B.; Nørskov, J. K. Nature 1995, 376, 238–240. (51) Strømsnes, H.; Jusuf, S.; Bagatur’yants, A.; Gropen, O.; Wahlgren, U. Theor. Chem. Acc. 2001, 106, 329–338. (52) Vargas, M. C.; Giannozzi, P.; Selloni, A.; Scoles, G. J. Phys. Chem. B 2001, 105, 9509–9513. (53) Gr€onbeck, H.; H€akkinen, H. J. Phys. Chem. B 2007, 111, 3325–3327. (54) Mazzarello, R.; Cossaro, A.; Verdini, A.; Rousseau, R.; Casalis, L.; Danisman, M. F.; Floreano, L.; Scandolo, S.; Morgante, A.; Scoles, G. Phys. Rev. Lett. 2007, 98, 016102. (55) Jeon, B.; Kress, J. D.; Grønbech-Jensen, N. Phys. Rev. B 2007, 76, 155120. (56) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996, 14, 33–38. (57) Lando, A.; Lauwaet, K.; Lievens, P. Phys. Chem. Chem. Phys. 2009, 11, 1521–1525. (58) Costelle, L.; J€arvi, T. T.; R€ais€anen, M. T.; Tuboltsev, V.; R€ais€anen, J. Appl. Phys. Lett. 2011, 98, 043107. (59) J€arvi, T. T.; Kuronen, A.; Meinander, K.; Albe, K.; Nordlund, K. Phys. Rev. B 2007, 75, 115422. (60) Popok, V. N.; Vuckovic, S.; Samela, J.; J€arvi, T. T.; Nordlund, K.; Campbell, E. E. B. Phys. Rev. B 2009, 80, 205419.
10322
dx.doi.org/10.1021/jp201496x |J. Phys. Chem. A 2011, 115, 10315–10322
