Improved ReaxFF Force Field Parameters for AuâSâCâH Systems

Article pubs.acs.org/JPCA

Improved ReaxFF Force Field Parameters for Au−S−C−H Systems Gyun-Tack Bae† and Christine M. Aikens*,‡ †

Department of Chemistry Education, Chungbuk National University, Cheongju 361-763, Korea Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, United States

‡

S Supporting Information *

ABSTRACT: Evaluation and reparameterization of previously reported ReaxFF parameters (Järvi, T. T.; et al. J. Phys. Chem. A 2011, 115, 10315−10322) is carried out for Au−S−C−H systems. Changes in Au−S and Au−Au bond parameters and S− Au−S angle bending parameters yield improvements for bond bending potential energy surfaces. The new ReaxFF parameters lead to good agreement with density functional theory geometries of small clusters and gold−thiolate nanoparticles. The energies of Au38(SCH3)24 clusters are compared, and the new ReaxFF calculations are also in good agreement with PBE calculations for the isomer orderings. In addition, the relative energies of Au40(SCH3)24 nanoparticles and Au-thiolate SAMs are calculated using the updated parameters. These new ReaxFF parameters will enable the study of the geometries and reactivity of larger gold−thiolate nanoparticles.

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shown that −S−Au−S staple motifs are also present at the surface.34−36 In theoretical studies, density functional theory (DFT) can be used to predict structures of thiolate-protected gold clusters in agreement with X-ray crystal structure determination.37 The structures of [Au25(RS)18]q (q = −1, 0, +1) and Au38(SCH3)24 were reported using DFT independently of or in advance of crystal structure determination.37,38 DFT calculations have also been used to predict the structures of Au10(SR)8, Au12(SR)9+, Au20(SR)16, Au44(SR)28−2, and Au144(SR)60.39−46 These clusters have not been determined experimentally. Even though DFT is a powerful tool for prediction of gold−thiolate nanoparticle structures, this method is computationally expensive for larger systems. The reactive force field (ReaxFF) was first developed for hydrocarbons.47 The ReaxFF method allows molecular dynamics (MD) simulations at low computational cost. Thus, it can be used on larger systems for long simulation times. Unlike nonreactive force fields, ReaxFF determines a bond length and bond order relationship and bond orders are updated every MD step. Therefore, ReaxFF can be used to describe chemical reaction steps in complex systems. Previous applications using the ReaxFF force field have studied reactive processes such as combustion,48 nanotube growth,49 hydrogen storage,50 and catalysis.51 In 2008, ReaxFF parameters were developed for gold.52 Recently, fully reactive interatomic potentials for Au−S−C−H systems employing the ReaxFF formalism were also developed.53 DFT calculations with the PBE functional were used to parametrize the potential. In this work, we describe a significant problem with the previous Au− S−C−H ReaxFF parameters and discuss a reparameterization.

INTRODUCTION Gold nanoparticles (NPs) with thiolate ligands have attracted significant interest over the past decade due to their unique optical, electronic, charging, biomedical, and catalytic properties.1−6 The interaction between gold and sulfur is very important for the stabilization of nanoparticles and for their use in drug delivery and medical therapy. Self-assembled monolayers (SAMs) of thiols on planar gold surfaces have been studied for their applications in biology and nanoelectronics. Gold has the third best electrical conductivity of all metals at room temperature and does not form a stable oxide layer under ambient conditions.7 In recent years, many thiolate stabilized gold nanoparticles have been synthesized. Whetten and co-workers generated gold nanoclusters in the range of ∼20−40 Au atoms over 15 years ago.8,9 In 2004 and 2005, Tsukuda and co-workers synthesized and characterized a series of gold clusters from Au10 to Au39 protected by glutathione ligands.10,11 Many experimental groups have performed research on particularly stable gold core structures such as Au25(SR)18−1,12−17 Au38(SR)24,18,19 Au68(SR)34,20 Au144−146(SR)59−60,19 and Au225(SR)75 clusters.21 Larger gold−thiolate nanoparticles of 3−522−27 and 9−10 nm28 have also been studied experimentally. Recently, Jadzinsky et al. successfully crystallized and ascertained the structure of thiolate-protected Au102(pMBA)44 (pMBA = p-mercaptobenzoic acid).29 X-ray crystallography has also been employed to determine the structure of [Au 25 (SCH 2 CH 2 Ph) 18 ] q (q = −1, 0) 14, 16, 30−32 and Au38(SCH2CH2Ph)18.33 The structures of thiolate-protected gold nanoparticles are based on Au(SR)2 and Au2(SR)3 staple motifs which bind to gold cores. The Au25(SR)18 cluster has a central icosahedral Au13 core capped by six extended staple motifs −S−Au−S−Au−S−. The Au102(SR)44 structure has a Au79 core with 19 −S−Au−S− and two −S(AuSR)2 extended staples. Recent experimental and theoretical work on SAMs has © XXXX American Chemical Society

Received: June 17, 2013 Revised: September 11, 2013

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dx.doi.org/10.1021/jp405992m | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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COMPUTATIONAL DETAILS The ReaxFF potential formalism and methods have been published in detail.47−49 We use parameters for Au−S−C−H systems.52,53 The NVE-MD simulations on gold, sulfur, carbon, and hydrogen were relaxed to 0 K with 100 Å × 100 Å × 100 Å periodic boundary conditions. All ReaxFF simulations use the LAMMPS code.54 The Amsterdam Density Functional (ADF) program55 is used for all density functional theory (DFT) calculations. Single point energies and optimized molecular structures employ the Perdew, Burke, and Ernzerhof (PBE) functional.56 A polarized triple-ζ(TZP) basis set is used with a [1s2−4f14] frozen core for gold, a [1s2−2p6] frozen core for sulfur, and a [1s2] frozen core for carbon. The zeroth-order regular approximation (ZORA) is employed in the calculations to account for scalar relativistic effects.57

energies have been modified and are presented here. In ReaxFF, the system energy expression is divided into contributions as shown in eq 1. Esystem = E bond + Eover + Eunder + Eval + Etor + EvdW + Ecoulomb

(1)

The partial contributions in eq 1 include bond energies (Ebond), energy to penalize overcoordination of atoms (Eover), energy to stabilize under-coordination of atoms (Eunder), valence angle energies (Eval), torsion angle energies (Etor), van der Waals (EvdW) interactions, and terms to handle nonbonded Coulomb (Ecoulomb). The energies are described in detail in refs 47, 48, and 53. To improve the S−Au−S PES, we change the Θo,o S−Au−S angle parameter from 20.0000 to 5.0000. We also change roσ (2.1505 → 2.0600) value of Au−S bond parameters. The Θo,o parameter affects the valence angle energy contribution (Eval). The valence angle energies (eqs 2a2c) are calculated using the bond-order (BO)-dependent forms for two bonds.

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RESULTS AND DISCUSSION The linear or nearly linear −S−Au−S- “staple” motif is very important for describing bonding between a gold surface or nanoparticle and the attached thiolate groups. The staple with two S legs attached to the gold surface is favored energetically; it stabilizes systems due to increased HOMO−LUMO gaps compared to clusters without this unit.58 We found that the staple −S−Au−S− unit is not linear or nearly linear using the original Au−S−C−H ReaxFF parameters from ref 53 (denoted “original ReaxFF”). To illustrate this problem, the angle bending (S−Au−S) potential energy surface (PES) of the CH3−S−Au−S−CH3 molecule with original ReaxFF and PBE calculations is shown in Figure 1. We optimized the cluster using PBE and then

Eval = f7 (BOij )f7 (BOjk )f8 (Δj ){pval1 − pval1 exp[ −pval2 (Θo(BO) − Θijk)2 ]}

(2a)

p

f7 (BOij ) = 1 − exp(−pval3 BOijval4 )

(2b)

f8 (Δj ) = pval5 − (pval5 − 1) 2 + exp(pval6 Δangle ) j 1 + exp(pval6 Δangle ) + exp( −pval7 Δangle ) j j

(2c)

σ

The ro parameter is included in a bond order BO′ij which can be calculated between a pair of atoms from the interatomic distances. Bond order calculations are described as sigma bonds, pi-bonds, and double pi bonds. The bond energies are calculated from eq 3. E bond = −Deσ BOijσ exp[pbe1 (1 − (BOijσ ) pbe2 )] − Deπ BOijπ − Deπ BOijππ

(3)

These lead to good agreement between DFT and the new ReaxFF PES for angles between 170 to 190° in Figure 1. The original and new values of the ReaxFF parameters are presented in Table 1. Table 1. Original and New ReaxFF Parameters Au−S (roσ) Au−Au (pbe2) S−Au−S (Θo,o) S−Au−S (pval4)

Figure 1. Potential energy surface for S−Au−S bending in CH3−S− Au−S−CH3 using PBE, original ReaxFF, and new ReaxFF parameters.

original ReaxFF

new ReaxFF

2.1505 0.3319 20.0000 1.7970

2.0600 0.3325 5.0000 2.7871

To verify that other small thiolate gold clusters are reasonably represented by these new parameters, we calculate bond lengths and angles using PBE and ReaxFF calculations. Figure 2 shows the comparison of bond lengths and angles in HSCH3, AuSCH3, and Au(SCH3)2. In HSCH3, the bond lengths of S−C and S−H using ReaxFF are only 0.01 and 0.02 Å longer, respectively, than the PBE values. The S−C bond in AuSCH3 is 0.04 Å shorter than the PBE calculation. Because of this close agreement, no changes to S−C or C−H bond

examined the PES with single point calculations using both original ReaxFF and PBE for S−Au−S angles ranging from 130° to 220°. It is clear that the potential energy surfaces calculated by DFT and original ReaxFF are not in good agreement. The energy should reach a minimum at 180° as observed in the DFT calculations. Therefore, reparameterization of the ReaxFF parameters is necessary. Numerous parameters have been considered in this work, but only a few that make a significant difference in geometries and B



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Figure 2. Bond lengths and angles of HSCH3, AuSCH3, and Au(SCH3)2 clusters with PBE, original ReaxFF, and new ReaxFF calculations. Gold/ sulfur/carbon/hydrogen are colored black/yellow/gray/white.

Figure 3. S−Au−S angles of Au(SCH3)3 cluster with PBE, original ReaxFF, and new ReaxFF. Gold/sulfur/carbon/hydrogen are colored black/ yellow/gray/white.

small thiolate gold clusters. In addition, the S−H bond distance is in fairly good agreement between new ReaxFF and PBE calculations in Figure 2. Overall, new ReaxFF does a reasonable job for prediction of the Au−S, S−C, and S−H bond lengths and the Au−S−C angles. One of the aims of developing ReaxFF parameters for Au− S−C−H systems is to enable the study of reactive processes such as ligand exchange. In a recent investigation of ligand exchange on Au102(SR)44, a transition state was found in which three sulfur atoms bound to gold.59 The PBE optimized structure of Au(SCH3)3 is shown in Figure 3b. The structure shows the three sulfur atoms attached on the gold atom in which the three S−Au−S angles are 79.0°, 133.7°, and 147.4°. The original ReaxFF parameters predict a S−S bond (Figure

parameters are indicated. However, in AuSCH3 and Au(SCH3)2 clusters, the original ReaxFF Au−S bond lengths are 2.40 and 2.49 Å, respectively, while the bond lengths are 2.26 and 2.28 Å with the PBE calculation. In addition, the Au−S−C angles are not in good agreement with the PBE calculations. The new ReaxFF parameters yield improvements for Au−S distances and Au−S−C angles. In addition, new ReaxFF is better than original ReaxFF for the calculation of Au−S−C angles. The Au−S−C angle is calculated to be 104.16° with PBE, 97.94° with original ReaxFF, and 99.20° with new ReaxFF for the AuSCH3 molecule. The Au−S−C angles with new ReaxFF (100.50°) are also closer to the PBE calculation (105.49°) in Au(SCH3)2. Even though the S−C bond lengths with original ReaxFF and new ReaxFF are shorter than ones of the PBE calculation, these values are close to the PBE calculation in C



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3a), which varies dramatically from the PBE calculations in which no disulfide bond is present. Thus, a change of parameters is needed for a reasonable prediction of the geometry of the Au(SCH3)3 cluster. We found pval4 value (1.7970 → 2.7871) of S−Au−S angle parameters makes significant geometrical changes in eqs 2a−2c. The structure calculated with new ReaxFF yields no S−S bond as in the PBE calculation. Even though the three S−Au−S angles using new ReaxFF are not in exact agreement with PBE calculation in Figure 3b, these angle values are much better than those of the original ReaxFF. To make sure that these new parameters will work for gold− t h i o l a t e n a n o c l u st e r s s uc h a s A u 2 5 ( S C H 3 ) 1 8 − , 6 0 Au38(SCH3)24,38 and Au144(SCH3)60,46 we compare bond lengths and angles. The larger gold thiolate clusters were optimized with the PBE/TZP level of theory. We choose one of the staples of the clusters and show atom numbers in Figure 4. We compare distances and angles of Au−Au, C−S, Au−S, S− Au−S, C−S−Au, and Au−S−Au using the PBE calculation, original ReaxFF and new ReaxFF calculations and experimental data in Tables 2−4. In Au25(SCH3)18, the C−S−Au angles using the original ReaxFF are close to the PBE calculations while the Au−Au, C− S, and Au−S bond lengths and S−Au−S and Au−S−Au angles are not in good agreement with the PBE calculations. The average Au distances are 3.21 Å (PBE), 3.10 Å (original ReaxFF), and 3.08 Å (new ReaxFF). The S−Au−S angles differ greatly (about 20°) between original ReaxFF and the PBE calculation in Table 2. The S−Au−S angles using the new ReaxFF (average 161.5°) are much closer to the PBE calculation (average 173.8°). For Au−S−Au angles, Au(atom number 5)−S(atom number 31)−Au(atom number 8) angles are 90.6° (PBE), 79.7° (original ReaxFF), and 82.5° (new ReaxFF); Au(8)−S(30)−Au(23) angles are 100.2° (PBE), 79.2° (original ReaxFF), and 85.0° (new ReaxFF); and Au(23)−S(42)−Au(15) angles are 89.4° (PBE), 80.7° (original ReaxFF), and 82.2° (new ReaxFF). The new ReaxFF calculation is better for predicting the Au−S−Au angles in agreement with PBE than original ReaxFF. As a consequence, we have improved prediction of S−Au−S and Au−S−Au angles. The average Au−Au bond distances using new ReaxFF have shorter distances than those of the original ReaxFF. The C−S distances using both original ReaxFF (about 1.74 Å) and new ReaxFF (1.76 Å) are shorter than ones of the PBE calculation (1.85 Å); the distances using new ReaxFF are slightly closer to the PBE calculation. It should be noted that we have not modified any C−S bond parameters; these slight improvements in C−S bond distances come entirely from geometrical changes in other parts of the nanocluster. For the Au−S distances, original ReaxFF has longer distances than those of the PBE calculations; new ReaxFF calculations for Au−S distances are in better agreement with the PBE calculation. The C−S−Au angles of both original ReaxFF and new ReaxFF are in good agreement with the PBE calculations. C−S−Au parameters have not been adjusted, so it is important to note that the geometrical changes in the rest of the nanocluster have not decreased the accuracy of these values (and, in fact, have resulted in a very slight improvement). In Au38(SCH3)24, the average Au−Au distances are 3.05 Å (PBE), 2.98 Å (original ReaxFF), and 2.98 Å (new ReaxFF) in Table 3. The original ReaxFF calculates the Au−S bond lengths to be longer than those of the PBE calculations while the new ReaxFF calculates the Au−S bond lengths to be in good

Figure 4. Structures of Au 25 (SCH 3 ) 18 − , Au 38 (SCH3 ) 24 , and Au144(SCH3)60 nanoparticles. Gold/sulfur/carbon/hydrogen are colored black/yellow/gray/white.

agreement with the PBE calculations. In addition, the C−S bond lengths using original ReaxFF and new ReaxFF are a little shorter than those of the PBE calculations. The S−Au−S angles using new ReaxFF are in better agreement with the PBE calculations than those predicted with original ReaxFF. The S(58)−Au(70)−S(76) angles are D



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Table 2. Bond Lengths and Angles of Au25(SCH3)18− Using PBE, Original ReaxFF, and New ReaxFF

average Au−Au C(49)−S(31) C(48)−S(30) C(60)−S(42) Au(5)−S(31) Au(8)−S(31) Au(8)−S(30) Au(23)−S(30) Au(23)−S(42) Au(15)−S(42) S(31)−Au(8)−S(30) S(30)−Au(23)−S(42) C(49)−S(31)−Au(8) C(48)−S(30)−Au(8) C(60)−S(42)−Au(23) Au(5)−S(31)−Au(8) Au(8)−S(30)−Au(23) Au(23)−S(42)−Au(15)

PBE

original ReaxFF

new ReaxFF

expt.16

3.21 Å 1.85 Å 1.85 Å 1.85 Å 2.45 Å 2.35 Å 2.35 Å 2.36 Å 2.35 Å 2.45 Å 173.6° 173.9° 103.8° 105.8° 102.6° 90.6° 100.2° 89.4°

3.10 Å 1.74 Å 1.75 Å 1.74 Å 2.58 Å 2.50 Å 2.50 Å 2.49 Å 2.45 Å 2.6 Å 152.3° 153.8° 102.8° 102.6° 102.8° 79.7° 79.2° 80.7°

3.08 Å 1.76 Å 1.76 Å 1.76 Å 2.50 Å 2.45 Å 2.44 Å 2.44 Å 2.45 Å 2.49 Å 160.9° 162.0° 102.0° 103.0° 103.5° 82.5° 85.0° 82.2°

3.09 Å 1.93 Å 1.67 Å 1.74 Å 2.37 Å 2.32 Å 2.30 Å 2.30 Å 2.33 Å 2.39 Å 173.1° 173.3° 104.8° 97.7° 105.5° 85.9° 101.9° 85.7°

distances using both original ReaxFF and new ReaxFF are calculated to be shorter than those of the PBE calculations in Table 4. The Au−S and C−S distances using new ReaxFF are Table 4. Bond Lengths and Angles of Au144(SCH3)60 Using PBE, Original ReaxFF, and New ReaxFF average Au−Au Au(60)−S(159) Au(68)−S(159) Au(68)−S(160) Au(61)−S(160) C(219)−S(159) C(220)−S(160) S(159)−Au(68)−S(160) Au(60)−S(159)−C(219) Au(68)−S(160)−C(220) Au(60)−S(159)−Au(68) Au(68)−S(160)−Au(61)

average Au−Au Au(7)−S(58) Au(70)−S(58) Au(70)−S(76) Au(82)−S(76) Au(82)−S(64) Au(18)−S(64) C(112)−S(58) C(136)−S(76) C(88)−S(64) S(58)−Au(70)−S(76) S(76)−Au(82)−S(64) C(112)−S(58)− Au(70) C(136)−S(76)− Au(70) C(88)−S(64)−Au(82) Au(7)−S(58)−Au(70) Au(70)−S(76)−Au(82) Au(82)−S(64)−Au(18)

original ReaxFF

new ReaxFF

expt.33

3.05 Å 2.44 Å 2.35 Å 2.35 Å 2.35 Å 2.35 Å 2.43 Å 1.84 Å 1.84 Å 1.85 Å 170.9° 170.1° 107.1°

2.98 Å 2.53 Å 2.51 Å 2.50 Å 2.49 Å 2.46 Å 2.58 Å 1.75 Å 1.75 Å 1.74 Å 153.1° 154.7° 102.6°

2.98 Å 2.46 Å 2.48 Å 2.44 Å 2.43 Å 2.43 Å 2.48 Å 1.76 Å 1.76 Å 1.76 Å 158.9° 162.2° 102.8°

3.00 Å 2.40 Å 2.30 Å 2.30 Å 2.30 Å 2.29 Å 2.37 Å 1.85 Å 1.83 Å 1.84 Å 171.4° 172.6° 104.2°

106.9°

102.7°

103.6°

105.6°

101.7° 88.2° 99.1° 95.0°

103.0° 77.1° 79.7° 81.7°

102.8° 79.6° 85.9° 84.7°

104.2° 84.7° 103.2° 87.1°

original ReaxFF

new ReaxFF

3.07 Å 2.46 Å 2.35 Å 2.34 Å 2.46 Å 1.83 Å 1.83 Å 179.6° 107.2° 106.2° 87.2° 88.4°

3.01 Å 2.70 Å 2.52 Å 2.52 Å 2.71 Å 1.73 Å 1.73 Å 161.2° 102.8° 102.3° 71.4° 71.0°

3.00 Å 2.58 Å 2.49 Å 2.48 Å 2.60 Å 1.75 Å 1.75 Å 169.5° 104.7° 102.8° 74.9° 75.2°

in good agreement with the PBE calculation. Average Au−Au distances using new ReaxFF are close to the original ReaxFF. The S−Au−S angle using the new ReaxFF (169.5°) is also close to the PBE calculation (179.6°). Furthermore, the Au− S−Au angles using new ReaxFF are better than those of original ReaxFF in Au144(SCH3)60 as shown in Table 4. Consequently, we find that bond lengths and angles in large gold thiolate nanoparticles calculated with our new ReaxFF parameters are in good agreement with the PBE calculations and are much better than those computed with the original ReaxFF. Since isomer energies should also be reproduced well with ReaxFF, we have studied the energies of several Au38(SCH3)24 isomers that have previously been investigated. We optimized four different structures denoted C3h,38 D3,38 Is1,41 and n440 using the PBE/TZP level of theory. In Table 5, the D3 structure

Table 3. Bond Lengths and Angles of Au38(SCH3)24 Using PBE, Original ReaxFF, and New ReaxFF PBE

PBE46

Table 5. Energy Comparison of Au38(SCH3)24 Clusters between the PBE Calculation and New ReaxFF clusters

PBE (eV)

new ReaxFF (eV)

C3h D3 Is1 n4

−691.54 −692.05 −691.63 −688.97

−612.60 −612.84 −612.51 −602.62

and the n4 structure are the most and the least stable, respectively, using the PBE calculation. The single point calculations of Au38(SCH3)24 isomers using new ReaxFF are performed. The energy comparisons are similar to the PBE calculations: D3 is the most stable structure and n4 is the least stable structure using the new ReaxFF parameters. However, C3h is the most stable structure and n4 is the least stable structure using the original ReaxFF parameters. Thus, we find that the new ReaxFF calculations reproduce the isomer ordering of this system. Relative energies of Au40(SCH3)24 clusters are shown in Table 6. Several isomers of Au40(SCH3)24 clusters have recently been optimized using DFT by Malola et al., and these are denoted A1, A2, B1, and B2.61 These clusters consist of a Au26 core, six (RS−Au−SR) units, and four (RS−Au−SR−Au−SR) units. Jiang reported a very stable isomer of Au40(SCH3)24 in

170.9° (PBE) and 158.9° (new ReaxFF); the S(76)−Au(82)− S(64) angles are 170.1° (PBE) and 162.2° (new ReaxFF). Like Au25(SCH3)18, the S−Au−S angles using original ReaxFF are not in good agreement with the PBE calculation: the difference in the angles is about 17°. Both original ReaxFF and the new ReaxFF are close to the C−S−Au angles with the PBE calculation. The Au(7)−S(58)−Au(70), Au(70)−S(76)− Au(82), and Au(70)−S(76)−Au(82) angles using the new ReaxFF (79.6°, 85.9°, and 84.7°) are in reasonable agreement with the PBE calculations (88.2°, 99.1°, and 95.0°) and represent improvement over original ReaxFF (77.1°, 79.7°, and 81.7°) for the Au−S−Au angle calculations. In the largest gold thiolate cluster, Au144(SCH3)60, the Au−S distances using new ReaxFF are again calculated to be shorter than those of original ReaxFF and the Au−Au and C−S E



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Table 7. Adsorption Energetics of Methythiolate on Golda

Table 6. Relative Energies of Au40(SCH3)24 Isomers with New ReaxFF and PBE

energies

energy (eV) clusters

new ReaxFF

PBE61

A1 A2 B1 B2 Jiang Corner Oblate Tetra Tetra2

0.0 0.39 −1.13 −1.60 −3.28 −0.53 0.35 −4.47 0.04

0.0 0.32 0.42 1.05 −0.0962

structures 1; simple adsorption 2; Au−SR unit 3; −(Au−SR)−polymer 5; simple + surface vacancies 6; simple + RS−Au−SR unit + surface vacancy 8; RS−Au−SR unit 9; RS−Au−SR unit a

2013.62 The isomer consists of a Au25 core, three (RS−Au−SR) units, and six (RS−Au−SR−Au−SR) units. Even though the ordering of the relative energies using new ReaxFF is in not good agreement with DFT calculations, the most stable structure is the one from Jiang using both new ReaxFF and DFT calculations. (Relative energies in Table 6 are based on the numbers reported in refs 61 and 62). In Table 6, we also present the relative energies of four additional structures: two corner-fused icosahedra (Corner), triangular oblate derived from a polyicosahedral structure (Oblate), and two different tetrahedral structures (Tetra, Tetra2) that were also examined by Malola et al. The Tetra structure is found to be the lowest structure. Various adsorption models of methylthiolate on gold surfaces (Figure 5) have been calculated at 300 K using the structures supported in ref 53. The simulations produce reasonable structures using new ReaxFF. Even though the simulations using original ReaxFF also reproduced structures well, the relative adsorption energies have some discrepancies with DFT calculations.53 Using new ReaxFF, the relative adsorption energies are very close to DFT calculations in Table 7. The lowest energy structure is predicted to be structure 9, which has individual staple units on the Au surface, rather than structure 3 containing −(Au−SR)− polymers that was predicted with the original set of parameters. ReaxFF also appears applicable to the calculation of cis−trans isomerization energies on surfaces.

original

new

DFT

ReaxFF

ReaxFF

ref 36

h1 h2 h3 h5 h6

0.0 2.06 −1.37 0.32 −0.19

0.0 1.03 −0.16 0.27 −0.26

0.0 1.28 −0.19 −0.53 −0.48

h8 h9

−0.35 −0.33

−0.38 −0.47

−0.78 −0.84

The structure numbering refers to the structures in ref 36.

Previous work has shown that the trans form of CH3S−Au− SCH3 on Au(111) is 0.04 ± 0.10 eV more stable than the cis form.63 In our work, the trans form of a single CH3S−Au− SCH3 unit on surface 9 is predicted to be 0.03 eV more stable than the cis form. Therefore, the new ReaxFF parameters are applicable to simulations of thiolate SAMs on gold surfaces. As with all parametrized methods, sometimes compromises must be made in order to make the parameters applicable to the widest variety of systems. In this case, we have developed a set of ReaxFF parameters that is applicable to both gold− thiolate nanoparticles and gold−thiolate SAMs. However, the gold−gold distances in the nanoparticles and the isomer ordering of Au40(SCH3)24 do not match PBE. In order to improve the agreement between ReaxFF and PBE further for gold nanoparticles, we have also developed an additional set of new parameters that work well specifically for gold thiolate nanoparticles (denoted “NP-specific ReaxFF”). This set of parameters is presented in the Supporting Information (SI, Table 1S). Although these parameters improve the accuracy significantly for nanoparticles, they do not work well for surface calculations. The NP-specific parameters are in good agreement with PBE for the PES of S−Au−S angle bending between 170 and 190° as shown in Figure 1S in the SI. The NP-specific ReaxFF calculations are significantly better than new ReaxFF for Au−S bond lengths and Au−S−C angles (SI, Figure 2S). These parameters also produce no erroneous S−S bond in

Figure 5. Thiol adsorption structures as listed in Table 7. Gold/sulfur/carbon/hydrogen are colored black/yellow/gray/white. F



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Notes

Au(SCH3)3 unlike original ReaxFF (SI, Figure 3S). The Au− Au, Au−S, and C−S bond lengths and Au−S−Au angles in large gold thiolate nanoparticles using the NP-specific ReaxFF are better than those of new ReaxFF. In addition, S−Au−S and C−S−Au angles using NP-specific ReaxFF are similar to new ReaxFF (SI, Tables 2S-4S). Therefore, these NP-specific parameters may be useful for optimizing geometries of similar systems. Energy comparisons using the NP-specific ReaxFF calculations are similar to the PBE calculations on Au38(SCH3)24 (SI, Table 5S) and improve the relative energies of Au40(SCH3)24 structures (SI, Table 6S) relative to new ReaxFF.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G.-T.B. and C.M.A. are grateful to the National Science Foundation for support under Grant No. CHE-1213771. The authors thank Dr. Tommi Järvi for providing input files, helpful discussions, and comments on this manuscript. The authors thank the groups of Prof. Hannu Häkkinen and Dr. De-en Jiang for sending coordinates for Au40(SCH3)24. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. OCI-1053575.

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CONCLUSION In this study, reparameterization of the ReaxFF force field for Au−S−C−H systems has been investigated. We examine the bond lengths and angles for small gold thiolate clusters such as HSCH3, AuSCH3, Au(SCH3)2, and Au(SCH3)3 as well as larger systems. Our ReaxFF parameters have been improved to yield significant changes of geometries and energies for small and large thiolate gold clusters. We have developed one set of parameters that provides improvements for gold−thiolate nanoparticles and SAMs in addition to a nanoparticle-specific version. The S−H, C−S, and Au−S bond distances using new ReaxFF are in good agreement with the PBE calculation and the Au−S−C angles using new ReaxFF are also very close to the PBE calculations for small thiolate gold clusters. The S− Au−S angles are not exactly the same between new ReaxFF and the PBE calculations, but new ReaxFF calculation for the angles is much better than original ReaxFF. In large gold thiolate clusters including Au25(SCH3)18−, Au38(SCH3)24, and Au144(SCH3)60, the Au−Au and C−S distances using new ReaxFF are calculated to be longer than ones of original ReaxFF; the Au−S distances using new ReaxFF are calculated to be shorter than ones of original ReaxFF. Overall, the Au−S and C−S bond lengths using new ReaxFF are in good agreement with the PBE calculations. The average Au−Au bond distances using new ReaxFF are close to the original ReaxFF. The S−Au−S angles are calculated to be very close between new ReaxFF and the PBE calculation and both new ReaxFF and original ReaxFF calculations are very close to the PBE calculation for C−S−Au angles. Even though the Au− S−Au angles using new ReaxFF are not in perfect agreement with the PBE calculation in Au25(SCH3)18− and Au38(SCH3)24 clusters, these values are much better than those of original ReaxFF. The Au−S−Au angles in Au144(SCH3)60 cluster are in good agreement between new ReaxFF and the PBE calculation. In addition, the relative isomer energies for Au38(SCH3)24 are reproduced correctly. We report the relative energies of Au40(SCH3)24 using new ReaxFF. These parameters are also applicable for surface simulations of gold−thiolate SAMs.

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ASSOCIATED CONTENT

* Supporting Information S

Additional data as discussed in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

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