Influence of Force-Field Parameters on the Atomistic Simulations of

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The Influence of Force Field Parameters on the Atomistic Simulations of Metallic Surfaces and Nanoparticles Takieddine Djebaili, Stéphane Abel, Massimo Marchi, and Johannes Richardi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09857 • Publication Date (Web): 16 Oct 2017 Downloaded from http://pubs.acs.org on October 16, 2017

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The Journal of Physical Chemistry

The Influence of Force Field Parameters on the Atomistic Simulations of Metallic Surfaces and Nanoparticles Takieddine Djebaili1,2, Stéphane Abel3,4, Massimo Marchi3,4, and Johannes Richardi1,2,* 1

Sorbonne Universités, UPMC Univ Paris 06, UMR 8233, MONARIS, F-75005, Paris,

France 2 CNRS, UMR, MONARIS, F-75005, Paris, France

3 Commissariat à l’Énergie Atomique, DRF/Joliot/SB2SM/LBMS & CNRS UMR 9198, Gif sur Yvette 91191 Cedex 4 Institut de Biologie Intégrative de la Cellule (I2BC), Institut Frédéric Joliot, CEA, CNRS, Univ Paris-Sud, Université Paris-Saclay, F-91198, Gif-Sur-Yvette cedex, France Abstract The influence of the interaction model on the adsorption of butanethiolate on gold surfaces and nanocrystals has been studied with molecular dynamics simulations. The results obtained for three different head group sizes are compared to experiments. The use of the largest head group induces new organizations of the ligands in the case of nanocrystals and Au(100) surfaces, while no such difference is observed for Au(111). As a consequence, this model does not reproduce the higher surface coverage experimentally observed for nanocrystals. This shows that the evaluation of the quality of force fields cannot be restricted to the study of specific surfaces. Some properties such as the occupation frequencies of adsorption sites markedly depend on the nanocrystal size.

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1. Introduction For reliable molecular modeling and simulation of materials the quality of the force field and in particular of the non bonded parameters is a key parameter. This has led to a large number of force fields such as Amber, CHARMM, etc.1-3 which have continuously been developed to improve the agreement with quantum chemical and experimental results. The reliability of force fields used for biomolecular systems has reached today a good level. To our best knowledge for nanoparticles, a systematic study of the reliability of force fields has not yet been carried out so far. Thus, several force fields were proposed for the system gold-alkanethiolates4-21, but the results have never been compared. Our investigation has been primarily concerned with the issue of extending a force field designed for molecular adsorption on continuous planar surfaces of specific geometry to nanocrystals of different sizes and structure. In this context, we have compared the simulation results obtained for different values of the thiolates head group size on a series of Au nanocrystals and on Au planar surfaces. The dimensions of the head group were changed by varying the thiolate Lennard-Jones parameter, sSS, which in literature takes values ranging from 3.554 to 4.97 Å5. In particular, we compare the results for sSS = 4.25 Å4, 4.45 Å 12 and 4.97 Å5, which are the three values most widely used in the literature. We have focused on the sSS parameter, since it corresponds to the size of the head group and largely influences the molecular organization of the thiolates21. The molecular organization of thiolates on Au(100) and Au(111) and on octahedral, icosahedral and cubic nanocrystals are investigated by molecular dynamics. Due to the use of massively parallel computations we were able to carry out MD simulations of nanocrystals up to the size of 10 nm which are systems where only little information by simulations was available until now. As we will see, all three values for sSS lead to very similar results for the organization of the alkane thiolates on a Au(111) surface. In contrast on a Au(100) surface, the largest sSS values yields an organization completely different from the other two ones. More surprisingly even for nanocrystals made of Au(111) surfaces, the organization observed for the largest sSS values is markedly different compared to the other ones. In particular, our simulations show that accurate interaction parameters cannot be determined using only a single surface such as Au(111) as this has been often done in the literature. The

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results here reported can be used for future development of force fields for nanomaterials. Recently many efforts have been done to improve the gold-thiolate force fields 18-20,23. The aim is to explain the formation of the c(4x2) superstructure often observed on Au(111) surface in coexistence with the hexagonal structure. This superstructure is presumably related to the formation of vacancies and adatoms stabilized by the formation of S-Au-S staples19,20. Since in the present work the mobility of Au atoms is restricted, we do not take into account the surface defects and therefore our study is limited to the simple hexagonal assembly. To our best knowledge all published models are also not able to predict the c(4x2) superstructure as observed in DFT calculations and experiments19,20. Actually, the initially formed vacancies and ad-atoms will come together to form large holes and clusters during a longer simulation run. We focus here on the simple hexagonal structures formed on flat Au(111) facets. These force fields were chosen to enable us a systematic study of large nanocrystals up to 10 nm, since the constraint of gold atom motion considerably decreases the computation time. Moreover, this approach allows an interpretation of the results which would be probably more difficult when several organizations co-exist. The paper is organized as follows. In a first section, the different force fields for the system gold – alkane thiolate proposed in the literature are reviewed and our choice of force fields used here is explained. In a second section, the simulation method is discussed. Then, the molecular organization of butane thiolates on Au(111) and Au(100) surfaces are compared for the three interaction models. We will only study butane thiolates, since recent simulations show a small influence of the alkane chain length on the molecular organizations. Finally, we present the results for octahedral, icosahedral and cubic gold nanocrystals made of Au(111) and Au(100) facets, respectively. The simulation results are compared with a large amount of experimental data for the surface coverage, molecular assemblies and occupation of adsorption sites obtained by TEM, thermogravimetry, SAXS, mass spectrometry and elementar analysis. This work leads to new physical insight as it shows that ligands may behave similarly on a facet while they behave very differently on other facets and nanocrystals.

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2. Methods 2.1. The interaction models for gold-alkanethiolate systems We identified all force fields used in the literature for the gold-alkanethiolate system to the best of our knowledge. There are important differences in the description of the interaction between the different alkanethiolate head groups and the attraction between the head group and the gold atoms. Here we focus on the head group interaction of the thiolates. Regarding intramolecular interactions, there are only slight differences between the interaction models. Table 1. The various parameters for Lennard-Jones interactions of alkane thiolates used for gold-alkane thiolates simulations. CH3

CH2

S e/kB[K] s[Å] e/kB[K] s[Å] e/kB[K] s[Å]

Pool et al. 12 Also used by Djebaili et al. 21,22 Hautman et al. 4 Also used by - model S: Mahaffy et al. 7, Fartaria et al.10 - model SI: Ghorai et al.13, Jiménez et al.15, Olmos-Asar et al.18, Ahn et al.16 - model SII (modified) : Alexiadis et al.17 - model S (with sSS=4.45 Ak ): Luedtke et al.6,8 - model S (with different LenardJones values for carbones): Pohjolainen et al.23 Siepmann et al. 5

Also used by Longo et al. 19 Lal et al.9 Lubna et al. 11

108

3.76

56

3.96

126

S : 126 S : 200 3.905 I SII: 126

4.45

S : 3.55 SI: 4.25 SII: 4.10

88.1

3.905

59.4

88.1

3.905

59.4

3.905

200

4.97

98 98

3.75 3.75

46 46

3.95 3.95

126 232

4.45 3.62

Table 1 summarizes the parameters of intermolecular interactions between the alkanethiolate sites and the articles where these models have been used. This table shows that there are mainly three models of interaction used in the literature. Besides the model of Pool et al., the ones proposed by Hautman et al. and by Siepmann and al. have been the

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most widely used. In the following, to distinguish these models, only the name of the first author is often employed. The most important difference among the three models of interaction is the sSS interaction parameter. It plays a crucial role in organizing the thiolate molecules and has a value of about 4.45 Å for the Pool model, a higher one of 4.97 Å for the Siepmann model, and a lower value of 4.25 Å for the Hautman model (SI). The value of 3.55 Å of the S model seemed to us unrealistically small and was excluded. Thus, we chose these three values of sSS: 4.25, 4.45 and 4.97 Å to carry out simulations of the adsorption of butanethiolate on flat gold surfaces with (111) and (100) planes and for octahedral, icosahedral and cubic nanocrystals. Our recent simulations have shown that the influence of the alkane chain length is small21,22. Therefore, we restrict our simulation to butanethiolate only. Please note that we have decided to use the same values for all other interaction parameters, which correspond to the model by Pool and only the sSS is changed. Therefore, the results presented for the sSS of Siepman or Hautman do not precisely correspond to their models. We have chosen to do so, to enable an easier interpretation of our results and to avoid the mixing of the influence of several interaction parameters, which may also lead to compensatory effects. In the future, it would be interesting to study the impact of the force field differences other than sSS on the simulation results for these three interaction models. Of course, our paper does not aim to criticize the models proposed by Siepman, Hautman and others, because we do not exactly use these models. 2.2. Simulation Method The adsorption of butanethiolates on the gold surfaces or nanocrystals is studied by molecular dynamics (MD) simulations using the GROMACS 4.5.5 MD package27 which allows for highly parallel calculations. Up to 120 processors were employed to study NC diameters until 10 nm. The build-up of the NC-butanethiolate system, short test simulations and the analysis of the trajectories were carried out with a home-written simulation code NATOMOS. At the beginning of the simulations, the bare Au NC or surface is surrounded by an excess of thiolates corresponding to a surface density of around 16 Å2 and 20 Å2 per molecule typically observed for Au NCs and surfaces. We noticed that the results are independent of the excess thiolate concentrations within the statistical accuracy of the method. A time step of 1 fs was used and the temperature was kept constant at 300 K with the Nose-Hoover thermostat (time constant:

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0.4 ps). The atomic configurations were saved every 100 steps for the analysis. The parameters of the simulations are given in the Supporting Information (Tables S1 to S3). 3. Results and Discussion 3.1. The molecular organization of thiolates on (111) and (100) gold surfaces We first calculated the average area occupied by adsorbed thiolate which corresponds to the total area of the planes (111) or (100) divided by the total number of thiolate molecules adsorbed on these planes. The results are given in Table 2. An error of around 3% was estimated by comparing the simulation results obtained from different initial configurations. Table 2. Average area occupied by thiolate adsorbed on planar gold surfaces, for three different values of sSS and compared with experimental results. In addition, the occupation frequencies of the adsorption sites, the Rst values and the average distances of neighboring head groups are given. Rst is the ratio between the numbers of hollow adsorption sites and adsorbed thiolates. Errors for the area per thiolate were computed from 3 different runs performed with different starting conditions.

area / thiol in Au(111) Å2 Au(100)

sSS = 4.25 Å

sSS = 4.45 Å sSS = 4.97 Å Experiment

20.7 ± 0.6

21.2 ± 0.6

22.3 ± 0.7

21.4 28,29

19.9 ± 0.6

21.0 ± 0.6

25.1 ± 0.8

20.6 28,29

Au(111)

5.77

5.90

6.20

Au(100)

2.28

2.42

2.88

Occupation

Au(111)

79 %

84 %

90 %

hollow sites

Au(100)

90 %

88 %

48 %

Occupation

Au(111)

18 %

11 %

7 %

bridge sites

Au(100)

7 %

9 %

48 %

S-S distance

Au(111)

4.87

4.93

5.01

in Å

Au(100)

4.13

4.15

4.42

Rst

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Table 2 shows that the coverage of planar (100) planes is more sensitive to the interaction model than that of the Au(111) surfaces. Indeed, the average area occupied by adsorbed thiolate varies with the interaction model from 19.9 to 25.1 Å for the (100) surface, while it changes only from 20.7 to 22.3 Å for the (111) plane. Remarkably for the (111) plane all three models yield an average area per thiolate in agreement with the experiment within statistical errors, whereas the model with the highest sSS of 4.97 Å completely fails to reproduce the surface coverage of the Au(100) planes. In order to better understand these results, we look at the molecular organization of the thiolate head groups at both surfaces (Figure 1). All three interaction models reproduce the hexagonal self-assembled monolayers (SAMs) experimentally observed on Au(111) surfaces (see Figure 1a). In contrast, the organization on Au(100) can vary a lot depending on the sSS value (see Figure 1b). For sSS values of 4.25 and 4.45 Å, the thiolate head groups form stripes with two or three lines. Within the stripes a simple square organization is observed, where the head groups occupy the hollow sites of the Au(100) plane. These stripes are separated by two lines of the grid of gold atoms. In our previous paper this SAM structure was compared to experiments. We observed a general agreement with the experiments30,31, while some structural details were different. For example, it seems that the distance between the lines in simulations (see Figure 1a) is slightly contracted with a preference of the hollow sites with respect to experiments. In contrast, the use of a sSS values of 4.97 Å yields a completely different organization, which is a distorted hexagonal assembly. The origin of these differences and the preferred adsorption sites for the thiolates is discussed in the next paragraph. We will now discuss the preferred adsorption sites for the thiolate head groups. A look at the snapshots in figure 1 shows that preferred adsorption sites are 3-fold hollow and 4-fold hollow sites for the Au(111) and Au(100) planes, respectively. To quantify these observations, we have calculated the occupation frequencies of the adsorption sites. We distiguished four adsorption sites: on-top, bridge, 3f-hollow (for Au(111)) or 4fhollow Au(100)), where the S groups are in contact with one, two, three or four gold atoms, respectively. To calculate the occupation frequency of the adsorption sites, the same distance criteria as in our previous papers have been used21,22. The results are given in the table 2. The occupation of on-top has not been given since it is less than 5 % and can be easily deduced from the rest of the frequencies of hollow and bridge sites. We begin

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with the results for Au(111). For a sSS values of 4.45 Å, the occupation frequency of hollow sites is 84 % with an important occupation of 11 % for bridge sites. A closer look at the snapshots in Figure 1 shows that for the last ones the adsorption geometry often corresponds to a shifted bridge, where the head group is actually between three gold atoms with a closer contact to two of the three. It is interesting to note that DFT calculations and STM experiments32,33 have shown that the geometry of adsorption is actually well described by such a shifted bridge position. For a sSS value of 4.25 Å the occupation of hollow sites slightly decreases with respect to the bridge sites. In contrast, the use of 4.97 Å for sSS gives an occupation of more than 90 % for the hollow sites. In the case of the Au(100) plane, the use of 4.25 and 4.45 Å for sSS gives that 95% of the thiolates occupy the hollow sites while only 4 % are in bridge position. The use of 4.97 Å for sSS leads to a similar occupation of hollow and bridge sites, which is accompanied by the formation of a new organization for the thiolates.

a

sSS = 4.25 Å

sSS = 4.45 Å

sSS = 4.97 Å

Au(111)

b Au(100)

Figure 1. a and b: Snapshots of the positions of S groups (small circles) on the planar Figure 1 Au(111) and (100) surfaces, respectively, for the three models of interaction. The different colors mark the S groups participating in different molecular organizations.

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These organizations and occupations of adsorption sites can be explained by the distance of head groups and their size. Table 2 gives the average distance between two neighboring S atoms for the Au(111) and Au(100) plane. For the Au(111) surface, the distance of neighboring hollow sites occupied in the hexagonal order is 5 Å. This distance is larger than the head group size for all models and therefore a change of this interaction parameter does not largely influence the molecular organization of the thiolates. Table 2 shows that the average S-S distance decreases with smaller sSS to values much lower than 5 Å. This explains the possibility of the occupation of a larger fraction of bridge sites. On the Au(100) surface the distance of 4f hollow sites occupied for the square assembly observed using the smaller sSS values is only 4.07 Å. The average S-S distance obtained for these two models is in perfect agreement with this value. However, this distance seems to be too small when a sSS value of 4.97 Å is used, which explains the formation of a different organization with a larger S-S distance of about 4.4 Å in this case. We conclude that the Pool force field gives the best agreement with the experimental results for both (111) and (100) planes. 3.2. The molecular organization of thiolates on octahedral and cubic nanocrystals A crucial question arises here: When an interaction model does correctly describe a type of crystalline surface, can we trust it to simulate nanocrystals made of these facets? This is a very fundamental question, since the predictions observed on surfaces by molecular dynamics but also DFT calculations are often simply applied to nanocrystals. Here, we did not observe large differences in the case of the Au(111) plane. When the question posed above can be answered by yes, the results for octahedral nanocrystals made of (111) facets should not largely evolve with the different values for the head group size. Let us first examine the influence of the interaction model on the surface coverage of the NC surface using the three different sSS values. We studied gold NCs of a size between 1 and 10 nm, covered by butane thiolates for the three following types of NC: icosahedral, octahedral and cubic. The tables S4 to S6 in the Supporting Information give the detailed results of these simulations. The detailed results for sSS = 4.45 Å are given in the Supporting Information of our previous papers21,22.

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Figure 2 shows the evolution of the average area occupied by adsorbed thiolate as a function of the NC size for octahedral and cubic particles. The results for the icosahedral nanocrystals are shown in Figure S1 of the Supporting Information. Consistent with the results on the surfaces, the smaller values for sSS yield a similar average area per thiolate for the nanocrystals of all shapes. In contrast, when a sSS value of 4.97 Å is used, the average area per thiolate is significantly higher for NC of all shapes. More specifically, the smaller values for sSS correctly reproduces a decrease of the average area per thiolate of about 10 % for the nanocrystal compared to the surface which has been observed in many experiments34-36 (see discussion in our previous papers21,22). In contrast, using a large sSS of 4.97 Å leads to nearly the same average area per thiolate on planar Au(111) surfaces and icosahedral or octahedral nanocrystals (Figures 2a and S1). It is interesting to note that the same model yields an increase in the average area per thiolate for the corresponding cubic nanocrystals with respect to the experimental value for the Au(100) surface. The area per thiolate only slightly evolves with the NC size which has been explained in our previous papers.

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2

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a sSS = 4.45 Å sSS = 4.25 Å

sSS = 4.97 Å

b

sSS = 4.45 Å

sSS = 4.97 Å

sSS = 4.25 Å

Figure 2. Average surface area per adsorbed thiolate as a function of the NC diameter for octahedral (a) and cubic (b) NCs. The results using three different values for sSS are shown. The details of the determination of the NC surface are explained in our previous papers21,22. The results for the planar surface are those obtained by experiments. The values obtained by simulations for the planar surfaces using the different values for sSS are given in table 2.

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How can we understand these differences in the behavior of the nanoscale systems? We first tried to detect the formation of regular assemblies such as the hexagonal SAM which have been observed on the Au(111) surface in Figure 1. In the case of the (100) facets for cubic NCs, we searched for stripes, where the head groups occupy hollow sites forming a square SAM. As in our previous papers21,22, we use a percolation method to identify SAMs with the distance criteria published before. Figures 3a and b shows the percentage of thiolates participating in a hexagonal or square SAM for octahedral and cubic NCs, respectively. Figure S2 plots the results for icosahedral particles, which is very similar to those for octahedral particles. The results are given for the thiolates on the center and edges of the facets. A thiolate is counted for the edge when its head group is the closest to a hollow site on the edge. Let us first discuss the results for octahedral nanoparticles. When an intermediate sSS values of 4.45 Å is used, more than 90% of the adsorbed thiolates in the facet center take part in a SAM, while this percentage decreases to 70% on the edges. In our previous paper21,22, this low value was attributed to the formation of a new zigzag organization on the edges. This is proven by Figure S3 in the SI where the percentage of thiolates participating in a zig-zag assembly on the facet edges of octahedral icosahedral NCs is shown. The use of a smaller sSS value slightly decreases the percentage of thiolates participating in SAMs. In contrast, using a sSS values of 4.97 Å markedly increases the percentage of thiolates involved in SAMs which reaches 100%. In particular, on the edges around 97 % of the thiolate participate in a hexagonal SAM. This correlates to a total disappearance of the zig zag organization on the edges (see Figure S3). It is interesting to note that the frequency of adsorbed thiolates in the center increases with the NC size for the smaller sSS values. This is in contrast with the results for the highest sSS values which leads to a perfect hexagonal assembly even for octahedral NC of 2 nm. The formation of zigzag assembly is very important as discussed in our previous paper21,22, since it explains the decrease of the average area per thiolate for NCs compared to surfaces observed in experiment. Thus, the disappearance of the zig-zag organization for the largest sSS leads to the failure of reproduction of the decrease in the average area per thiolate in this case.

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a

sSS: 4.97 Å 4.45 Å, 4.25 Å

Hexagonal SAM

sSS = 4.45 Å sSS = 4.25 Å sSS = 4.97 Å

zigzag SAM

b Square SAM sSS = 4.45 Å sSS = 4.25 Å sSS = 4.97 Å

Figure 3. Frequencies of S atoms participating in the formation of a SAM of at least 3 members for octahedral (a) and cubic (b) nanocrystals using three different values for sSS. Sketches of the hexagonal, zigzag and square SAMs are shown for a better understanding. The arrows close to the y axis mark the SAM frequencies observed for the surface where the

sSS values used are indicated beside the arrows.

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The observed disappearance of zigzag SAMs is in agreement with the ratio between the numbers of hollow adsorption sites and adsorbed thiolates given in the tables 4 to 6 of the SI. For the small sSS values of 4.25 and 4.45 Å, a value close to 3 is obtained on the edges. This is explained by the zig-zag assembly where between two neighboring head groups one finds two unoccupied hollow adsorption sites. In contrast, for the highest sSS a larger ratio of about 4 is found. This is consistent with a hexagonal SAM, where one goes from one head group to its neighbor passing always three unoccupied hollow sites (see the sketch of both assemblies in Figure 3a). In the case of cubic NCs, for the smaller sSS values of 4.25 and 4.45 Å figure 3b shows that all thiolates participate in the square organization already observed on Au(100) planes. Even on the edges this frequency is around 90 %. In contrast, the use of the highest sSS value prevents the formation of square SAMs, both in the center and on the edges of the facets as already observed for the planar surface (see Figure 1). This phenomenon is probably at the origin of the larger average area per thiolate obtained for this model. Please note that the results for cubic nanocrystals only slightly depend on the NC size. For the Au(111) and Au(100) planes, we observed that the occupation frequencies of adsorption sites markedly depend on the head group size. In order to study this property in the case of nanocrystals, the occupation frequencies for nanocrystals were computed and the results are depicted in Figure 4. In addition to the on-top, bridge and hollow sites, we also calculated the occupation of the so-called edge sites for cubic NCs, which denote the sites on the edges characterized by the possibility of three Au-S contacts (see sketch in Figure 4). For large nanocrystals we find the same values of occupation frequencies given in table 2 for the planes except for the 4f hollow sites of the cubic NCs. This is due to the occupation of the edge sites which correspond to a large fraction of adsorption sites with respect to the facet centers even for large NCs. In the case of octahedral (Figure 4a) and icosahedral NCs (Figure S4) the occupation frequencies do not markedly depend on the NC size for the smaller sSS values studied, with a preference of the hollow site of about 60 %. The use of the largest sSS values leads to a much higher occupation frequency of hollow sites which decreases for smaller NCs. Thus, for NCs smaller than 4 nm a large fraction of occupied bridge sites (> 20 %) is observed. It is interesting to note that for a NC size of 2 nm, the use of 4.45 Å gives a peak in the occupation frequency of hollow sites of about 80 %. This effect is much less pronounced for a smaller sSS value. In the case of

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cubic NCs, the occupation frequency of 4f hollow sites markedly decreases with smaller NC size due to the occupation of the edge sites mentioned above (see discussion in our previous paper). For the two smaller sSS values the 4f hollow sites is largely preferred while for the largest sSS 4f hollow and bridge sites are occupied in similar proportions. As explained above this is due to the formation of a new molecular organization for the largest head group size.

a

on-top sSS = 4.45 Å sSS = 4.25 Å

b

on-top bridge

3f- hollow

bridge sSS = 4.97 Å

4f- hollow

edge

sSS = 4.45 Å sSS = 4.25 Å sSS = 4.97 Å

edge site

Figure 4. Occupation frequencies of the different adsorption sites for octahedral (a) and cubic (b) NCs for different interaction models. The results are shown for three different sSS values.

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sSS: 4.97 Å 4.45 Å 4.25 Å

(Å)

a

facet center facet edges

b (Å)

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sSS = 4.45 Å sSS = 4.25 Å sSS = 4.97 Å

sSS = 4.45 Å sSS = 4.25 Å sSS = 4.97 Å facet center facet edges

sSS: 4.97 Å

4.45 Å 4.25 Å

Figure 5. Average distances between neighboring S groups on the edge and in the center of the NC facets. Panels (a) and (b) show the results for octahedral and cubic NCs, respectively, for the interaction models. The arrows close to the y axis mark the average S-S distances observed for the surface taken from table 2.

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We finally turn to the average distance of neighboring head groups observed on the NCs. We found for the Au(111) and Au(100) planes that this property helps a lot to understand our results since it is directly related to the head group size varied here. Figure 5 shows the average S-S distances on the edges and in the center of the NC facets. In order to compare these average S-S distances with those observed for the surface, the values of table 2 are marked with arrows close to the y axis of the plots in figure 5. In the center of the nanocrystals the S-S distance is close to the surface value except for the octahedra and icosahedra for the two lowest sSS values of 4.25 and 4.45 Å. This shows that even the organization in the center of the nanocrystal facets is markedly different compared to the surface. For all three forms of NCs, the S-S distance increases with the sSS values in particular for the highest sSS. For the cubic NCs, using a sSS value of 4.97 Å gives a head group which is too large to fit in the square assembly. This leads to a new molecular organization even for the cubic NCs. For the octahedral and icosahedral NCs the use of the largest sSS value largely reduces the differences in the S-S distances between the thiolates adsorbed on the edges and in the center of the facets, typically observed for the other two models. This is due to the absence of the zigzag organization for this model. Indeed, the head group size in this case seems to be too large to enable the formation of a zigzag assembly. 4. Conclusion The adsorption of butane thiolate molecules on gold surfaces and nanocrystals have been studied by molecular dynamics for different head group sizes. First, the adsorption on Au(111) and Au(100) plane has been investigated. For the Au(111) plan, the average area per thiolate and molecular organization do not change with the head group size and are in good agreement with experiments. In contrast, these properties markedly depend on the head group size for Au(100). For the smaller head groups, the molecular assemblies in stripes known from experiments are observed, with some differences related to the stripe distance and directions as already discussed in our previous article. Also, the surfaces per thiolate obtained for these two models are in agreement with experiment. In contrast, for the largest head group size a new assembly appears with an average area per thiolate about 20 % large than the experimental value.

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For the Au(111) plan, besides the typical hollow site also a shifted bridge site is occupied which was also observed in DFT calculations and STM experiments32,33. In the second part of the paper, we studied the adsorption of thiolates on octahedral, icosahedral and cubic nanocrystals made of (111) and (100) planes, respectively. For the average surface per thiolate the two smaller head group size give a decrease of about 10 % for the nanocrystals with respect to the value of the Au(111) plane in agreement with the experiments as discussed in our previous articles. In contrast, for the largest head group size such a decrease is not observed. In the case of the octahedral and icosahedral nanocrystals this is explained by the lack of the zigzag assembly observed at the edges for the largest head group. This is consistent with the fact that for the smaller head group size a shorter average distance between the sulfur groups are observed which is not the case for the largest head group size. For the octahedral and icosahedral nanocrystals a large fraction of adsorbed bridge sites is observed with respect to the plane, which is consistent with a shorter average distance between the sulfur atoms in these cases even on the facet centers. In good agreement with experiments, the average surface of thiolate only slowly evolves with nanocrystal size which has been explained in our previous paper. In contrast, the frequency of SAMs and the occupation of sites markedly depends on the nanocrystal size. We have shown that the differences can be explained by the distance of adsorption sites usually occupied in the SAMs. They are significantly smaller for the SAM on Au(100) planes and for the zig-zag assembly on octahedral and icosahedral nanocrystals. Therefore, a change in head group size has more influence in these cases. To sum up, these investigations show that a change in ligand may have large influence on the molecular organization of the adsorbed molecules which is difficult to predict by the study of only one specific surface plane. In our case, we observe a good agreement with the experiment with only small differences for the two smaller sSS values in contrast to the larger head group. However, investigating the adsorption of thiol molecules on planar surfaces can help understanding the structural constraints related to a given choice of head group size. Indeed, for the sSS value of 4.97 Å the size of the head group is more than 20 % larger than the typical distance between neighboring S on a Au(100) facet. Notwithstanding, the smallest distance possible between head groups in nanocrystals

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depends to a large extent on the size of the facets and on the geometrical arrangement of the edges. But it also depends on many other factors: first, the attraction between the Au and S atoms may compensate the repulsion of the head groups. Second, the polarization of the surface may influence the compressibility of the head groups. This means that force fields have to be tested on various facets and nanocrystal shapes to verify their reliability to predict the molecular organization of ligands on metallic surfaces and nanocrystals. We would finally like to discuss the general limitations of the used force fields. The chemisorption of thiolates on gold leads to bonds between the gold atoms and the sulfur atoms. Since the S-Au bond strength is similar to that between Au atoms, this may lead to the breaking of Au-Au bonds and the formation of Au-S-Au units. As mentioned in the introduction, the classical force fields used here are not able to describe this process. Therefore, the adsorption geometry on bridge sites observed by DFT32,33 is not correctly described with this model. In addition, the formation of new assemblies with Au-S-Au units cannot be observed. Therefore, the improvement of force fields for the atomistic simulations of gold-thiolate systems is a very important issue in future. In particular, ReaxFF recently proposed20 should be able to better describe these phenomena.

ASSOCIATED CONTENT Supporting Information  The Supporting Information is available free of charge on the ACS Publications website at DOI: …. Tables S1−S6: the parameters and results for the simulations carried out for this study; Figures S1−S5: additional results discussed in the paper.

AUTHOR INFORMATION Corresponding Author *E-mail [email protected] (J.R.). Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was performed using HPC resources from GENCI- CINES/IDRIS (Grant

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2013-x2013086946, 2014-x2014086946) and the CCRE-DSI of Université P. M. Curie.

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TOC Graphic

sSS = 4.45 Å

sSS = 4.97 Å

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Influence of Force-Field Parameters on the Atomistic Simulations of

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