Effect of van der Waals interactions in the DFT description of self-assembled monolayers of thiols on gold


The structure and energetic properties of self-assembled monolayers (SAMs) of alkanethiol derivatives (simple alkanethiols, mercaptoalkanoic acids and aminoalkanethiols with different chain length) adsorbed on the metallic Au(111) surface are investigated through periodic DFT calculations. To sort out the effect of van der Waals (vdW) interactions on the DFT calculations, the results of the standard GGA–PBE functional are compared with those obtained with approaches including the vdW interactions such as those incorporating the Grimme’s (GGA–PBE-D2) and the Tkatchenko–Scheffler’s (GGA–PBE-TS) schemes, as well as with the optB86b-vdW density functional. The most significant difference between the two sets of results appears for the adsorption energies per thiol molecules: The standard functional predicts energy values 30–40 % lower than those obtained when the van der Waals interactions are taken into account. This is certainly due to a better description of the lateral interactions between the chains of the thiols when including the van der Waals effects. Differences are also found between the adsorption energies predicted by density functionals taking into account the vdW corrections, with values increasing in the order GGA–PBE-D2 < GGA–PBE-TS < optB86b-vdW. Furthermore, the functionals considering dispersion interactions favor much more tilted orientations of the SAMs over the surface with respect to those found using the standard GGA functional (the SAMs’ tilt angles increase from 17°–24° to 37°–46°), being the former in closer agreement with available experimental data. In contrast, the SAMs’ precession angle and monolayer thickness are less affected by the type of DFT exchange–correlation functional employed. In the case of low surface coverage, the chains of the thiols adopt more tilted configurations and tend to lay side-down onto the surface.


Self-assembled monolayers (SAMs) of thiols on metallic surfaces have been and still are being extensively studied due to their practical applications and functionalities. This kind of SAMs has been used namely as modifiers of metal electrodes, with variation of the metal electrode functionality with the SAM used [14], or as modifiers, which confer magnetic properties to the metal surface [5]. In addition, they have been applied as agents for the growth of thin films [6], C60 islands [7] or neuronal cells [8], of the immobilization of nanoparticles [9] or β-cyclodextrins [10], and for the aggregation of nanoparticles [11]. Other important applications of these SAMs include their use as sensors and biosensors [12], or even as reactants that can act in reactions on surfaces [13]. Following these important applications, several research works have dealt with the study of the thiol SAMs’ structure [1425] or with the development of new techniques aimed at creating patterned surfaces [2628]. It has been found that desorption studies are very useful in the study of the SAMs’ structure [29, 30].

It is well documented that thiols adsorb dissociatively on gold surfaces through their sulfur atoms upon breakage of the S–H bond [3136] and form SAMs when the coverage is near to the monolayer. The formation of the SAMs is affected by the presence of surface defects [33, 37], by the thiol chain length which can distress the SAMs functionality [3841], by the thiol terminal groups [42] which can lead to lateral interactions, by the formation of surface oxides [4345] or by the thiol concentration [31, 46, 47]. Furthermore, the presence of adatoms on the surface has been claimed as an important factor toward the formation of thiol SAMs on gold surfaces [4851], and, in particular, it has been found that methanethiol leads to a strong surface reconstruction during its adsorption [52].

The thiols used in the preparation of SAMs are usually alkanethiols [21, 27, 47, 53] or alkanethiols with the other end of the alkyl chain terminated with an organic acid group [54] or with an amino group [8, 9]. SAMs formed by mixing different types of alkanethiols are also quite common [28, 55]. The terminal group of the thiols can be altered by X-ray irradiation [56] or by photooxidation [57]. Despite that alkanethiols, aminoalkanethiols and mercaptoalkanoic acids are by far the most employed and investigated, other types of thiols such as thiophenethiols [5863] have also been used for fabricating SAMs.

The important applications of thiol SAMs attracted also the attention of the theoreticians who focused their work in studies of their formation and resulting structures. Different theoretical methods have been employed in such studies, being widely spread in this field molecular dynamics (MD) simulations [42, 6471] and density functional theory (DFT) [34, 39, 50, 7279] calculations. The former methods are able to extract information on the dynamics of the formation of the SAMs at the atomic level, as well as their follow-on structural properties, whereas the latter ones are more useful for the study of bond formation or lateral interactions among the thiol chains in the SAMs. Monte Carlo simulations have also been used in the study of thiol SAMs [80].

These theoretical methods are then particularly helpful for verifying many aspects of the packing and phase behavior of SAMs and may provide a detailed description of the SAM structures. For example, both allow an easy estimation of parameters like the tilt and precession angles of the thiol chains into the SAMs or the monolayer thickness. The tilt angle corresponds to the angle between the thiol chain and the normal to the surface in the adsorption point, while the precession angle corresponds to the angle between the thiol chain projection into the xy plane (surface) and the x-axis (for additional information please refer to Fig. 2 of Ref. [81]). The tilted SAMs’ structures are adopted to maximize the interaction between chains, and normally thiol SAMs exhibit tilt angles between 20° and 35° depending on the type of chains [15, 33, 40, 47, 53, 64, 82, 83]. In addition, it has been suggested that the tilt angle of the thiol chains depends on parameters such as the temperature, the nanoparticle size, the chain length (only for short thiols, <20 CH2 groups) [69] and the deposition of metals on the surface [84]. Here, it should be mentioned that the reconstruction of the surface detected in MD simulations has been checked to be an artifact caused by the potential used in such simulations, by comparison with the reconstructed (postulated as unstable) and unreconstructed SAMs energies using DFT [65].

All the results obtained so far within DFT theoretical studies of SAMs resorted to standard DFT functionals, which do not account for van der Waals dispersion forces. In this work, we go one step ahead in the theoretical study of thiols SAMs onto a gold (111) surface by determining their binding energies and structures, through periodic DFT calculations with and without the consideration of van der Waals (vdW) forces. Three different types of thiol SAMs are compared namely: alkanethiols SAMs (hexane-1-thiol or undecane-1-thiol), SAMs formed by thiols terminated in an organic acid group (6-mercaptohexanoic acid and 11-mercaptoundecanoic acid) and SAMs formed by thiols terminated in an amino group (6-aminohexane-1-thiol and 11-aminoundecane-1-thiol). In fact, these thiols were chosen because they arise as the most frequently used in the preparation of SAMs on gold [9, 10, 28, 46, 55]. Additionally, with this selection of thiols, we also consider the most habitually chain lengths and terminal groups (methyl, carboxylic or amino) of thiol SAMs on gold.

This work is organized as follows. The computational methods are described in detail in Sect. 2, while the calculated results are reported and discussed in Sect. 3. Finally, the most important conclusions are summarized in Sect. 4.

Computational details

DFT approach

All the DFT calculations were carried out with the VASP 5.3.3 computer code [8587], together with the GGA–PBE density functional proposed by Perdew et al. [88] to obtain the electron density. Due to the predictable effect of the dispersion forces in the calculations, these were considered in this work by using the Grimme’s (GGA–PBE-D2) [89], the Tkatchenko–Scheffler’s (GGA–PBE-TS) [90] schemes and by the consideration of the optB86b-vdW density functional [91]. D2 corrections employed the common C6 Grimme’s parameters for the H, C, O, S and N atoms, while the C6 parameter for gold was taken from Ref. [92] (14.99 J nm6 mol−1) where it was optimized for the interaction of thiols with the Au(111) surface. The expression for the dispersion energy in the TS method is essentially the same that used in the D2 method; however, the dispersion coefficients and damping function are charge-density dependent. Therefore, this method is able to account for variations in vdW contributions of atoms due to their local chemical environment [90]. The optB86b-vdW is a density functional that approximately takes into account the dispersion forces, and is framed in the scheme of the non-local van der Waals density functional (vdW-DF) of Dion but where the exchange functional was optimized for the correlation part [91]. For additional details on these approaches and applications, please refer to the recent review by Prates Ramalho et al. [93].

The effect of core electrons on the valence shells was described using the projected augmented-wave (PAW) method due to Blöch [94] and further implemented by Kresse and Joubert [95], together with a plane-wave basis set used to span the valence electronic states. The cutoff energy for the plane waves was 415 eV, found to be sufficient for energy and geometry convergence in previous works concerning adsorptions and reactions on gold surfaces [96, 97]. In addition, the conjugate-gradient algorithm was used for the relaxation of the ions during the spin-polarized calculations, and a 3 × 3 × 1 Monkhorst–Pack k-points grid was used for the integrals in the Brillouin zone for a correct energy convergence.

Slab models

The infinite Au(111) gold surface was modeled using the three-dimensional (3D) periodic-slab approach, being the same approach used to model the interaction of this surface with the thiol SAMs considered in this work.

The initial positions of the gold atoms in the slab used for the generation of the Au(111) surface by its repetition in the three spatial dimensions were obtained using the lattice parameter for bulk gold taken from a previous work [98]. Following on, bulk gold was cut along the (111) plane for obtaining a slab with three layers of gold atoms and forming a (3 × 3) unit cell with respect to the minimal unit cell for the (111) Miller index surface. The unit cell represented by this slab is a hexagonal prism with the angle between the x- and y-axes being 120° and the two other involving the xz- and yz-axes of exactly 90°. The resulting Au(111) surface model contains 27 gold atoms and assures that the adsorption energy of the thiols is converged with respect to the slab thickness. The Au(111) surface is characterized by four different adsorption positions, i.e., top, bridge, fcc hollow (above a subsurface octahedral cavity) and hcp hollow (above a subsurface tetrahedral cavity) sites. A representation of these adsorption sites can be seen in Fig. 1.

Fig. 1

Top, hollow hcp and hollow fcc adsorption sites on the Au(111) surface. Bridge sites correspond to the lines connecting top sites

It was necessary to consider three thiol molecules in each gold slab to obtain the correct thiol SAMs’ configurations during the replication of the unit cell. Models with only one thiol chain on the slab and corresponding to the 1/3 ML coverage were also built in order to consider the coverage effects in the thiols adsorption. In both situations, the positions of the gold and thiol atoms were completely relaxed.

Results and discussion

Structure of thiol SAMs adsorbed onto the Au(111) surface

The most stable configurations for the thiol SAMs were determined, starting from several initial trial configurations and adsorption sites of the Au(111) surface (Fig. 1), by energy minimizations to sample minima corresponding to equilibrium structures. We considered the adsorption of the thiols in thiolated form since it is well established that the S–H bond breaks during the adsorption of thiols on gold surfaces [3136] leading to H2 formation [34].

The adsorption energies per thiol molecule (E ads) of the thiols forming the SAMs were computed by the following expression:

$$E_{\text{ads}} = (E_{{{\text{slab}} - ({\text{thiol}})_{n} }} - E_{\text{slab}} - n \times E_{\text{thiol}} )/n$$

where E slab refers to the electronic energy of the gold slab used, E thiol to the molecular electronic energy on the gas phase of the correspondent thiol molecule in thiolated form and \(E_{{{\text{slab}} - ( {\text{thiol)}}_{n} }}\) to the electronic energy of the correspondent slab-thiol supersystem; n is 3 or 1 for 1 ML or 1/3 ML surface coverages, respectively, and it refers to the number of thiol molecules per slab considered. Consequently, the adsorption energies E ads are given per thiol molecule and negative values mean energetically favored adsorptions. Additionally, in the case of the 1 ML surface coverage (i.e., n = 3), Eqs. 2, and 3,

$$E_{{\text{int} \_{\text{Au}} - {\text{S}}}} = (E_{{{\text{slab}} - ({\text{thiol}})_{n} }} - E_{\text{slab}} - E_{{({\text{thiol}})_{n} }} )/n$$
$$E_{{\text{int} \_{\text{thiol}} - {\text{thiol}}}} = (E_{{{\text{slab}} - ({\text{thiol}})_{n} }} - E_{\text{slab}} - n \times E_{{({\text{thiol}})}} )/n$$

were employed to calculate the Au–sulfur interaction energy per thiol molecule, E int_Au–S and the interchains interaction energy per thiol molecule, E int_thiol–thiol for thiols forming the SAMs. In these equations, \(E_{{{\text{slab}} - ({\text{thiol}})_{n} }}\), n and E slab are as in Eq. (1), while \(E_{{({\text{thiol}})_{n} }}\) corresponds to the total energy of the thiol molecules frozen in their optimized geometries onto the Au(111) surface but without the 27 Au atoms of the metal slab, and \(E_{{ ( {\text{thiol)}}}}\) corresponds to the total energy of a single thiol chain frozen in its optimized geometry on the slab (i.e., without two of the three thiol molecules and the gold surface). Note that the sum of the values determined using Eqs. (2) and (3) does not correspond exactly to the value obtained with Eq. (1) because the thiol molecule used as reference in the latter equation is fully optimized in vacuum, while in the former cases, frozen geometries of the thiols in their adsorbed states are employed.

We began our investigation by determining the most favorable configurations for the adsorption of two representative alkanethiols on the Au(111) surface, i.e., the hexane-1-thiol and the undecane-1-thiol. The results concerning to the alkanethiol adsorption energies, tilt and precession angles of the thiol chains and monolayer thickness for the most stable structures of these alkanethiol SAMs on Au(111) are given in Table 1. In Fig. 2, we present the most favorable configurations for these thiols, computed by using the GGA–PBE-D2 functional (these structures are similar to those obtained using GGA–PBE-TS and optB86b-vdW). As it can be seen, the packing of the alkanethiols forming a compact monolayer is characterized by the alkanethiols adsorbed through their sulfur atoms on bridge positions and adopting a tilted structure similar to that obtained experimentally for the hexane-1-thiol closely packed phase [46] or to that found through MD simulations [81]. These tilted structures allow for better interactions between the chains with concomitant stabilization of the system. In the case of the structures relaxed with functionals taking into account the dispersion forces, the tilt angles calculated with the GGA–PBE-D2, GGA–PBE-TS and optB86b-vdW are, respectively, 45.7°, 45.0° and 44.8° for hexane-1-thiol, and 40.8°, 41.4° and 41.5° for undecane-1-thiol SAMs. These values are higher than those attained without taking into account the vdW forces (GGA–PBE functional), i.e., 17.5° and 23.5°, respectively. The tilt angle (GGA–PBE) for the undecanethiol SAM on Au(111) is similar to the experimental values found for the hexadecane-1-thiol SAM (22°) [53] and for the decane-1-thiol SAM (20°) [76]. Nevertheless, for the hexane-1-thiol SAM, the tilt angle computed with GGA-PBE is slightly lower than that obtained through MD simulations (23°) [81]. Moreover, the precession angles obtained indicate that the hexane-1-thiols adopt a next–next-nearest-neighbor (NNNN) tilt direction [99], and, in the case of the undecane-1-thiol SAM, the chains are oriented as in nearest-neighbor (NN) and NNNN configurations. To sum up, it seems that the inclusion of van der Waals forces in the calculations leads to an excessive tilt of the SAM chains, but the precession angle and the monolayer thickness are less affected. Interestingly, the values obtained for angles and thickness with the GGA–PBE-D2, GGA–PBE-TS and optB86b-vdW functionals are very similar, indicating that these quantities do not depend on the strategy employed to introduce the effects of the dispersion interactions in the DFT calculations.

Table 1 Adsorption energies (E ads, given per thiol molecule in eV) and structural properties for the most stable configuration of the studied thiol SAMs on Au(111) calculated with the PBE, PBE-D2, TS and optB86b-vdW methods
Fig. 2

Top (left) and side (right) views of the most stable SAMs obtained with the PBE-D2 approach for hexane-1-thiol (a) and undecane-1-thiol (b) on Au(111). Green stands for gold, yellow for sulfur, blue for carbon and white for hydrogen

The adsorption energies per thiol molecule are 0.42 eV (GGA–PBE-D2), 0.72 eV (GGA–PBE-TS) and 0.69 eV (optB86b-vdW) more negative for the SAMs with undecane-1-thiol than for the SAMs with hexane-1-thiol, showing the importance of the lateral interactions between the thiols in the SAMs. Such increment in the adsorption energy on going from the hexane to the undecane chain is not found when the calculations are performed with the GGA-PBE approach (cf. Table 1). The adsorption energy difference between undecane-1-thiol and hexane-1-thiol increases in the order GGA–PBE ≪ GGA–PBE-D2 < GGA–PBE-TS ≈ optB86b-vdW. This ordering is similar to that found for adsorption energies of the thiols (i.e., GGA–PBE < GGA–PBE-D2 < GGA–PBE-TS < optB86b-vdW), which suggests that the contribution of the dispersion interactions arising from the optB86b-vdW method is larger than those arising from the consideration of the other computational approaches.

We also examined the effect of the inclusion of the van der Waals forces in the thiols interatomic distances. All the interatomic distances for the most stable configuration of each thiol (alkanethiols, aminoalkanethiol and mercaptoalkanoic acids) SAMs are presented in the schemes depicted in Fig. 3. Some interatomic distances between atoms in different thiol chains are also provided to show the hydrogen contacts (N–H or O–H distances) established between thiols terminal groups and to measure the distance between thiol chains (H–H or C–C distances). In general, for alkanethiol SAMs the inclusion of the van der Waals forces with any of the three approaches considered in this work has a weak influence in the thiols interatomic distances and their values are similar to those computed with the GGA-PBE approach. Still, the C–C and H–H distances computed with the GGA–PBE-D2 approach are ~0.2–0.7 Å shorter than those calculated with the GGA–PBE approach, while those calculated with the GGA–PBE-TS and optB86b-vdw functionals are slightly shorter in the case of the SAMs with hexane-1-thiol or slightly longer in the case of the SAMs with undecane-1-thiol when compared with those calculated with the standard GGA–PBE approach. However, striking differences are seen in the case of the distances between the sulfur and the gold surface, which become shorter after the consideration of the van der Waals interactions.

Fig. 3

Interatomic distances (Å) for the bonds in the thiols of SAMs on gold (labels CH, NH and OH) and shortest interatomic distances between atoms in neighboring thiols (labels H–H, C–C and O–H)

Following on, we studied the formation of SAMs on Au(111) of two thiols terminated with an amino group, i.e., the 6-aminohexane-1-thiol and the 11-aminoundecane-1-thiol. The most favorable configurations for the 6-aminohexane-1-thiol and 11-aminoundecane-1-thiol SAMs are shown in Fig. 4. The 6-aminohexane-1-thiol and 11-aminoundecane-1-thiol SAMs are characterized by thiols adsorbed on bridge positions through their S atoms and being the thiol chains tilted with respect to the surface normal. The tilt angles are similar to those obtained for the alkanethiol SAMs, i.e., 16.3°, 46.1°, 43.0° and 46.0°, with GGA–PBE, GGA–PBE-D2, GGA–PBE-TS and optB86b-vdW, respectively, in the case of the 6-aminohexane-1-thiol chains and 20.9°, 43.9°, 40.9° and 41.0° in the case of the 11-aminoundecane-1-thiol chains, being in both cases the GGA-PBE values closer to the experimental value (i.e., 26°) [82]. As in the case of simple alkanethiol SAMs, the inclusion of the van der Waals corrections seems to overestimate the tilt angles and it also leads to the differentiation between the adsorption energies for long and short aminoalkanethiol SAMs. This is in concordance with a better estimation of the interaction among the thiol chains when van der Waals forces are included in the calculations. In fact, the interatomic distance (C–C) between carbon atoms in different aminoalkanethiol chains for 11-aminoundecane-1-thiol is shorter by about 0.2 Å when van der Waals forces are considered in the calculations, while the distances in the thiol chains are almost the same (see schemes for aminoalkanethiols interatomic distances in Fig. 3). For SAMs with the 6-aminohexane-1-thiol, the GGA–PBE-D2 functional predicts shorter C–C distances than those calculated with the GGA–PBE functional but the values obtained with GGA–PBE-TS and optB86b-vdw functionals are similar to those obtained with the GGA–PBE approach. The effects in the precession angles and in monolayer thicknesses are more modest when van der Waals interactions are considered. Interestingly, the angles and thicknesses predicted by the calculations with GGA–PBE-D2, GGA–PBE-TS and optB86b-vdW functionals are similar, but the adsorption energies increase in the order GGA–PBE-D2 < GGA–PBE-TS < optB86b-vdW. The adsorption energy differences between 11-aminoundecane-1-thiol and 6-aminohexane-1-thiol become more negative in the same order, more precisely by 0.43 eV (GGA–PBE-D2), 0.66 eV (GGA–PBE-TS) and 0.70 eV (optB86b-vdW) showing again that the dispersion effects are more pronounced in the case of the calculations employing the optB86b-vdW functional. The precession angles obtained indicate that the SAMs of the aminothiols adopt NNNN configurations. In addition, as it can be seen in Fig. 4, the most favorable structures for the SAMs of the aminoalkanethiols are characterized by perpendicular orientation of the amino groups to the direction of the chain tilt in the case of 6-aminohexane-1-thiol and by the formation of hydrogen bonds between amino groups of neighboring aminoalkanethiols in the case of the 11-aminoundecane-1-thiol.

Fig. 4

Top (left) and side (right) views of the most stable SAMs obtained with the PBE-D2 approach for 6-aminohexane-1-thiol (a) and 11-aminoundecane-1-thiol (b) on Au(111). Green stands for gold, yellow for sulfur, light-blue for carbon, dark-blue for nitrogen and white for hydrogen

The orientations on the surface calculated for the SAMs of the 6-mercaptohexanoic and 11-mercaptoundecanoic acids are analogous to those described above for those obtained with the hexane-1-thiol and undecane-1-thiol compounds, respectively. According to previous MD simulations [64], there are several possible orientations of the carboxyl terminal groups of these SAMs. The configurations of the SAMs of 6-mercaptohexanoic and 11-mercaptoundecanoic acids (Fig. 5) obtained with DFT in this work resemble intermediate configurations between the two extreme cases reported in Ref. [64]. In these SAMs, the 6-mercaptohexanoic and the 11-mercaptoundecanoic acids are adsorbed on bridge positions through their sulfur atoms and adopting tilted structures. In the case of 6-mercaptohexanoic acid, the tilt angles are 23.1°, 41.1°, 40.3° and 40.5°, with GGA-PBE, GGA-PBE-D2, GGA-PBE-TS and optB86b-vdW, respectively, while in the case of the 11-mercaptoundecanoic acid, the tilt angles are 24.2°, 37.3°, 37.6° and 37.6°, with GGA–PBE, GGA–PBE-D2, GGA–PBE-TS and optB86b-vdW, respectively. The angles obtained with the standard GGA–PBE are closer to the classical MD values in Ref. [64] than when the comparison is made with the approaches incorporating the van der Waals interactions. Once again, the inclusion of the van der Waals forces corrections seems to overestimate the tilt angles of the thiol chains of the SAMs. The higher adsorption energies predicted by the DFT–PBE-D2, DFT–PBE-TS and optB86b-vdw functionals are in concordance with the interatomic distances presented in the schemes of Fig. 3 for the mercaptoalkanoic acids studied here. The O–H distance between different thiols is shorter, about 0.2–0.4 Å when van der Waals forces are considered in the calculations, i.e., the hydrogen bond between different thiol chains is stronger when van der Waals forces are considered in the calculations. Interestingly, C–C distances are not significantly affected by the inclusion of the van der Waals forces in the calculations in the case of the SAMs based on mercaptoalkanoic acids.

Fig. 5

Top (left) and side (right) views of the most stable SAMs obtained with the PBE-D2 approach form 6-mercaptohexanoic acid (a) and 11-mercaptoundecanoic acid (b) on Au(111). Green stands for gold, yellow for sulfur, light-blue for carbon, red for oxygen and white for hydrogen

The effect of the consideration in the calculations of the vdW forces on the values of the precession angles and monolayer thicknesses is more modest. The values obtained for the precession angles indicate that the 6-mercaptohexanoic acid adopts a configuration between NNNN and next-nearest-neighbor (NNN) into its SAM while the 11-mercaptoundecanoic acid adopts a configuration more close to NN [99]. In the case of the mercaptoalkanoic acids SAMs, the adsorption energy per thiol molecule is higher in the compounds with the longer alkyl chains even when van der Waals interactions are not considered (cf. Table 1). This must be related to the formation of more efficient hydrogen bonds between the carboxylic terminal in the SAMs obtained with the thiols with larger alkyl chains and also with the fact that these interactions, which are correctly described with the GGA-PBE approach, are much more favorable than the dispersive interactions between the chains.

The contributions of the lateral chain–chain and of the sulfur–metal interactions for SAMs obtained with the six different compounds considered in this work calculated with Eqs. (2) and (3) are reported in Table 2. As it can be seen, the Au–sulfur interaction clearly dominates over lateral interchains interaction for all the thiols. It is also found that the Au–sulfur interaction is not dependent on the type of thiol used to obtain the SAM as can be concluded by the similar values calculated for this interaction for all the thiols considered. Lateral interchain interactions depend on the chain length (−0.63 eV for hexane-1-thiol vs −1.07 eV for undecane-1-thiol; −0.97 eV for 6-mercaptohexanoic acid vs −1.46 eV for 11-mercaptoundecanoic acid; −0.71 eV for 6-aminohexane-1-thiol vs −1.25 eV for 11-aminoundecane-1-thiol) and on the thiol terminal group (−0.63 eV for hexane-1-thiol vs −0.71 eV for the 6-aminohexane-1-thiol vs −0.97 eV for the 6-mercaptohexanoic acid; −1.07 eV for undecane-1-thiol vs −1.25 eV for 11-aminoundecane-1-thiol vs −1.46 eV for the 11-mercaptoundecanoic acid). Lateral interactions in thiols with terminal carboxylic groups are stronger than lateral interactions between thiols with terminal amino groups, and the latter are stronger than lateral interactions in alkanethiols.

Table 2 Estimation of the contribution for the adsorption energy of the Au–sulfur (E int_Au–S, eV) and interchains (E int_thiol–thiol, eV) interactions obtained with the PBE-D2 approach

Finally, we also investigated with the GGA–PBE-D2 method the adsorption of the six thiols at 1/3 ML coverage where the formation of SAMs is not possible. The optimized configurations are represented in Fig. 6, and the adsorption energies are given in Table 3. As it can be seen in Fig. 6, the thiols with shorter chains adopt configurations with tilt angles much larger than those discussed above (values between 60° and 80°). These configurations allow a better interaction of the thiol with the gold surfaces being this result similar to that obtained in Ref. [100] for methanethiol adsorption at low coverage. The adsorption energies reported in Table 3 for the thiols with shorter chains are similar to those obtained for the same thiols at the 1 ML coverage which indicates that the magnitude of the interaction of the chains with the gold surface is similar to the chain–chain interactions in the SAMs. In the case of the thiols having larger chains, the lateral interaction of their chains with the surface and among them is not possible (tilt angles are of about 40°) and the adsorption energies for these thiols are lower than those for the same thiols in the SAMs.

Fig. 6

Views of optimized configurations for different thiols adsorption at 1/3 ML coverage: a hexane-1-thiol, b undecane-1-thiol, c 6-aminohexane-1-thiol, d 11-aminoundecane-1-thiol, e 6-mercaptohexanoic acid and f 11-mercaptoundecanoic acid. Green stands for gold, yellow for sulfur, light-blue for carbon, dark-blue for nitrogen, red for oxygen and white for hydrogen

Table 3 Adsorption energies (E ads, given per thiol molecule in eV) and structural properties for the most stable configuration of the different thiols on Au(111) at 1/3 ML coverage calculated with the PBE-D2 approach


In this work, DFT calculations were carried out to elucidate the structure of SAMs of thiols on the Au(111) surface. SAMs with different terminal groups and chain lengths are addressed, namely (1) terminated in a methyl group: hexane-1-thiol and undecane-1-thiol; (2) terminated in an amino group: 6-aminohexane-1-thiol and 11-aminoundecane-1-thiol; and (3) terminated in a carboxylic group: 6-mercaptohexanoic acid and 11-mercaptoundecanoic acid. In order to assess the effect of the van der Waals interactions upon the results of the DFT calculations, the results pertaining to a common GGA approach, i.e., using the PBE exchange–correlation functional, are compared to those obtained with approaches including dispersion interactions, namely the PBE-D2, the PBE-TS and the optB86b-vdw functionals. The thiol SAMs are characterized by the tilt of the thiols chains which favors the interaction among the thiol chains and terminal groups. The consideration of the van der Waals forces in the calculations leads to a higher tilt of the thiol chains with values about 40° and to larger adsorption energies when compared to the values obtained without the consideration of the van der Waals interactions. Tilt angles calculated with the former approach (PBE) are closer to experimental and theoretical MD results reported in the literature than those obtained with the latter methods (PBE-D2, PBE-TS, optB86b-vdw functionals). The structures obtained for the SAMs with the PBE-D2, PBE-TS and optB86b-vdW functionals are similar, but adsorption energies increase from the former to the latter. Thus, it can be concluded that the inclusion of the van der Waals interactions in the calculations overestimate the tilt angle. Finally, the inclusion of the van der Waals forces in the calculations leads to different adsorption energies for long and short thiols possessing the same terminal group, which is related to a better description of the interactions between the thiol chains and also among thiol terminal groups.


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Thanks are due to Fundação para a Ciência e Tecnologia (FCT), Lisbon, Portugal, and to FEDER for financial support to REQUIMTE (projects Pest-C/EQB/LA0006/2013 and NORTE-07-0124-FEDER-000067-NANOCHEMISTRY) and to CICECO (project Pest-C/CTM/LA0011/2013) and for Programa Investigador FCT. This work is supported also by FCT through project PTDC/QUI–QUI/117439/2010 (FCOMP-01-0124-FEDER-020977) co-financed by Programa COMPETE. JLCF acknowledges FCT for the grant SFRH/BPD/64566/2009 co-financed by the Programa Operacional Potencial Humano (POPH)/Fundo Social Europeu (FSE); Quadro de Referência Estratégico Nacional 20092013 do Governo da República Portuguesa.

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Correspondence to José L. C. Fajín or M. Natália D. S. Cordeiro.

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Published as part of the special collection of articles derived from the 9th Congress on Electronic Structure: Principles and Applications (ESPA 2014).

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Fajín, J.L.C., Teixeira, F., Gomes, J.R.B. et al. Effect of van der Waals interactions in the DFT description of self-assembled monolayers of thiols on gold. Theor Chem Acc 134, 67 (2015). https://doi.org/10.1007/s00214-015-1666-y

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  • Gold (111) surface
  • Thiols
  • Periodic density functional theory
  • van der Waals effects