A comparative DFT study of the adsorption of H2O molecules at Bi, Hg, and Ga surfaces

Surface Science 609 (2013) 91–99

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A comparative DFT study of the adsorption of H2O molecules at Bi, Hg, and Ga surfaces Vladislav Ivaništšev a, Renat R. Nazmutdinov b,⁎, Enn Lust a a b

University of Tartu, Institute of Chemistry, Ravila Str. 14A, 50411 Tartu, Estonia Kazan National Research Technological University, K. Marx Str. 68, 420015 Kazan, Republic of Tatarstan, Russian Federation

a r t i c l e

i n f o

Article history: Received 10 July 2012 Accepted 21 November 2012 Available online 28 November 2012 Keywords: Water adsorption Density functional theory Cluster model Electric double layer Hydrophilicity Bismuth Mercury Gallium

a b s t r a c t Adsorption of a H2O molecule on Bi, Ga and Hg electrode surfaces is studied in the framework of cluster model at the density functional theory (DFT) level. At bismuth(111) single crystal plane the hollow site is energetically more preferable for the H2O adsorption (− 31.1 kJ mol −1), while the adsorption at top site of Hg and Ga metal surfaces is confirmed to be energetically the most preferable (−35.6 and − 24.7 kJ mol −1, respectively). The calculations for Bi(111), Hg, and Ga are further extended to include the effect of external electrical field, and data analysis is completed with the help of the mean field approximation in order to model adsorbed water behaviour in the H2O molecules' bilayer. An associate of 13 H2O molecules is modelled in order to address the influence of lateral interactions in a water bilayer. The Ga surface is argued to be more hydrophilic than the Bi(111) and Hg surfaces. Despite the weaker adsorption energy of a single H2O molecule at the Ga surface, water molecules at the Ga/water interface are additionally stabilized by stronger hydrogen bonds. We stress the important role of the H2O bilayer at a metal electrode surface, which depends on the atomic corrugation of a metal surface. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Interactions at the electrode–electrolyte interface, foremost interactions of H2O molecules with the metal surface as the most common interaction belong undoubtedly to one of the fundamental topics of electrochemistry. By drawing a realistic microscopic picture of the adsorption of H2O molecules at a metal surface, one may significantly elucidate pivotal problems of the electrical double layer (EDL) structure, and gain a deeper insight into the mechanism of reactions occurring at a metal–solution interface [1]. One of the problems is disentangling the interplay between different contributions to potential drop across the EDL, and is directly related to the hydrophilic properties of metal electrodes [2]. Hydrophilicity of metal single crystal surfaces (in other words, wetting) originates from a delicate balance between direct H2O–metal interaction and H2O–H2O hydrogen bonding [3,4]. Altogether they determine the interfacial structure of a metal and water in several layers of depth from the interfacial border [5], as well as govern the potential drop across the interface. Local interfacial interactions had been extensively investigated using periodic DFT calculations at (111) [6,7] and (110) [8] surfaces of d-metals. It was usually argued that the difference in wetting ability between hydrophilic (Rh, Pd, Pt) and hydrophobic (Cu, Ag, Au) metal surfaces is due to the ability of the adsorbed H2O molecule both to bond to a metal surface, and to form hydrogen-bonds. Recent ⁎ Corresponding author. Tel.: +7 843 231 89 83; fax: +7 843 2365768. E-mail address: [email protected] (R.R. Nazmutdinov). 0039-6028/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.susc.2012.11.009

calculations also make a link between the most favourable interfacial structure and potential drop across a metal/solution interface [9,10] for a large number of d-metals. Experimentally measured potential drop in the EDL is used as a common characteristic of hydrophilicity. To the best of our knowledge hydrophilicity was not estimated for sp-metals using theoretical DFT calculations, except for earlier attempts [11–14]. A thoroughgoing interest to the hydrophilicity problem is known to result from the interpretation of anomalously high capacitance of EDL at gallium in aqueous solutions [15,16]. At the potential of zero charge (PZC) in surface-inactive electrolyte solution the differential capacitance of the dense part of EDL is different for the following metals: Hg, Ga, In, Bi, and Cd [15–17]. Going from negative to positive potentials the capacitance value rises more rapidly for gallium, than for the abovementioned metals, especially for Bi and Hg [2]. Traditionally such a peculiar feature is attributed to the chemisorption of H2O molecules at the gallium electrode [18]. However, in this study we aim to show that the direct interaction of a H2O molecule with gallium surface may not determine solely the metal hydrophilicity, as indicated in explanations of experimental results [15] (see also references therein). The adsorption of a single H2O molecule has been investigated earlier at Ga7–20 clusters (LanL2DZ and 6-311G(d,p) basis sets) [13], at Bi24–46 clusters (LanL2MB and 6-31G** basis sets) [14], at Hg6–7 clusters1 (LanL2DZ and 6-31G** basis sets) [11,19]. Ab initio SCF [11,13], MP2 [13,19], MP4 [11,13], and B3LYP [11,13,14] methods were employed. In

1

A larger Hg cluster was used by Sellers and Sudhakar [19].

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this work we continue our research at the unified computational level using clusters of similar sizes. The main goal is to elucidate the hydrophilic properties of metals in terms of the nature of H2O–metal bonding and lateral interactions in a H2O bilayer at the metal surface. In this work we modelled electrode surfaces as clusters. Another frequently used way is performing periodic DFT calculations. Both methods have evident advantages and limitations. For example, in the cluster approach the delocalized nature of the metallic orbitals could not truly be reproduced; some problems with describing the extended layers of water molecules at metal surfaces should be mentioned as well. All these problems can be readily addressed in a periodic DFT model. One of the advantages of finite cluster models is that they can easily be charged, whereas in periodic DFT calculations the unit cells have to be neutral. On the other hand, work function changes can easily be derived in periodic calculations, whereas potential drops can only be indirectly estimated in cluster calculations. Nevertheless, our model calculations performed for different Gan and Hgn clusters (n=7–73) predict the work function (i.e., εHOMO) values in very reasonable intervals: 4.57–4.95 eV (Ga) and 4.09–4.55 eV (Hg), that reproduce good experimental values, 4.35 eV (Ga) and 4.5 eV (Hg). Using the cluster model we can employ an impressive arsenal of quantum chemical methods of different levels developed for a long time to describe the electronic properties of molecular systems; this makes cluster calculations rather flexible. Although the periodic DFT codes are efficient enough to allow ab initio molecular dynamics, there are still clear limitations both in the system size, and in simulation times (see, for example, Ref. [9]). 2. Computational details The quantum chemical calculations were performed at the DFT level with the hybrid functional B3LYP as implemented in the Gaussian 09 program code [20]. The standard 6-31G** basis set was employed to describe the O and H atoms. The valence orbitals of the bismuth (6s 26p3), mercury (6s25d10), and gallium (4s24p1) atoms were described by double-ξ basis set (LanL2DZ), except some calculations for bismuth using Gaussian minimal basis set (LanL2MB). The effect of inner layer electrons was addressed by the Hay–Wadt effective core potential (ECP). Additional polarization functions were used for Bi, Ga and Hg [21,22]. The gallium surface was modelled by clusters with face-centred cubic packing for which each surface atom has 10 nearest neighbours. In the model the nearest gallium atom–atom distance (0.29 nm) refers to the main peak of radial distribution function for liquid gallium [23]. The same distance parameter for liquid Hg was taken to be 0.30 nm [24]. The bismuth(111) surface (in rhombohedral notation) was modelled by clusters for which the distance between neighbouring metal atoms within the same layer is equal to the Bi bulk value (0.454 nm); distances of 0.159 nm between sublayers (within a bilayer) and 0.235 nm between the bilayers were used [25]. Geometry of the metal clusters was fixed and surface relaxation processes were not allowed.

90°); perpendicular towards the surface, pointing H-atoms towards the surface (H-down, θ = 180°), and perpendicular outwards the surface, pointing O-atom towards the surface (H-up, θ = 0°). The values of ΔEad were compared to those estimated from the potential energy–distance curves (PECs): plateau

ΔEad ðzÞ ¼ EMe−H2 O ðzÞ−EMe−H ;

ð2Þ

plateau

where EMe − H is the energy of the system at 1 nm distance. Plotting PECs, only partial optimizations were performed with the oxygen atom restricted to move along the surface normal, passing through the adsorption site under study. In rare cases of disagreement, we preferred PEC Eq. (2) to Eq. (1), and revised our calculations until full agreement of results. Calculations with the full optimization of H2O molecule geometry were done after such preliminary studies. 2.2. Choice of cluster size Among symmetrical clusters consisting of 7, 10, 16, 22, 31, 34, 64 and 71 metal atoms, respectively, two clusters Me31 and Me34 were selected for further investigation (in the case of Ga and Hg). The metal–oxygen distance (z0) and internal H2O geometry were optimized, while the position of the oxygen atom and tilt angle (θ=0°) were restricted. As indicated in Figs. 2 and 3 and Table 3, the average ΔEad(H-up) and z0 values for Ga are equal to −23 kJ mol−1 and 0.259 nm, respectively. Average ΔEad(H-up) and z0 values for Hg are equal to −34 kJ mol−1 and 0.296 nm. The very low adsorption energy for the Ga31–H2O system (Fig. 2) is explained by the electronic effects of open shell due to the even number of electrons in the system. To avoid such effects we used a three layered cluster with 34 atoms primarily for gallium and also for mercury. We considered additional atoms in a cluster as an environment for local adsorption sites at a modelled metal surface. From this point of view, the choice of medium size clusters is most balanced between lower CPU-time consumption and reliable results. 2.3. Choice of basis set The choice of basis sets rested on the results of test calculations for the systems BiH, Bi–H2O, Bin with the LanL2DZ, LanL2MB, CEP-31g basis sets for Bi atom and the LanL2DZ, 6-31G** and 6-311G** (with and without diffuse functions) cc-pVDZ basis sets for H and O [14]. For Ga and Hg (Me2, Me16–H2O) the basis sets Lanl2DZ, Lanl2MB, ECP60MWB, aug-cc-pVDZ, 6-31G**, and 6-311G** were tested. For gallium dimer test calculations with Lanl2DZ with polarization functions and ECP yield the results (dGa–Ga = 0.281 nm and Ebind = − 117 kJ mol − 1) which are the closest to the experimental data (dGa–Ga = 0.275 nm and Ebind = −114 kJ mol−1) [26]. Reasonable results (dGa–Ga =0.250 nm and Ebind = −114 kJ mol−1) for Ga show augmented basis functions, such as aug-cc-pVDZ, which might describe

2.1. Adsorption energy The metal–H2O interaction energy, i.e. adsorption energy (ΔEad) as a function of the distance and orientation was calculated as follows: ΔEad ¼ EMe−H2 O −EMe −EH2 O ;

ð1Þ

where E denotes the total energy. A certain orientation was described by z0 and θ, where z0 is the optimized metal–oxygen atom distance, which was calculated from the position of the nearest layer of metal atoms; tilt angle (θ) describes the H2O molecule orientation relative to the surface normal (Fig. 1a). We examined mainly three orientations of H2O molecule with some restrictions for the internal geometry: parallel to the surface (H-par, θ =

Fig. 1. (a) A single H2O molecule adsorbed on-top at Ga7 cluster; tilt angle (θ) is 60°; (b) a fragment of the associate 13 H2O molecules representing two types of the molecules adsorbed.

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[21,22]. Triple-ζ basis sets for metals and lighter atoms might give better results as well, but calculations with such basis sets are CPU time consuming and probably results obtained cannot be compared to our previous studies, contrary to our intentions. 2.4. Effect of exchange-correlation functionals and the BSSE

Fig. 2. Adsorption energy of a single H2O molecule vs cluster size calculated for Ga (●) and for Hg (■).

weak interactions better [27]. However, calculations with such basis sets are highly CPU time demanding. On the other hand, combination of Lanl2DZ with addition of polarization functions for metal and 6-31G** for H and O gives comparatively good and reliable results (Table 1) in a much shorter time. Calculations with Lanl2MB converge even faster, and for Bi Lanl2MB and Lanl2DZ lead to comparable results (see Table 1). However, calculations using Lanl2MB overestimate and underestimate the interaction energies for gallium dimer (Ebind =−54 kJ mol−1) and for H-down orientation in Ga16–H2O system (Ead =−2.4 kJ mol−1), respectively. Therefore, most balanced approximation was found to be a combination of two double-ζ basis sets LanL2DZ and 6-31G, which we augmented by polarization functions

There are three important issues to be considered. Firstly, the B3LYP functional is not in general well-suited to describe metals [28]. It is not surprising for hybrid functionals, because the ab initio Hartree–Fock method fails to reproduce properly the band structure of metals. On the other hand, the popular Perdew–Burke–Ernzerhof (PBE) functional that reliably reproduces most properties of metals does not properly describe bulk water [29,30] and the wetting behaviour of water on metal surfaces [31,32]. Secondly, a new class of exchange-correlation functionals was developed recently which makes it possible to address better van der Waals (vdW) interactions. The importance of VdW interactions to describe the water adsorption at metal surfaces was stressed in works [31–33]. Thirdly, the basis set superposition error (BSSE) is crucial to describe both metal clusters [34] and the metal–water interaction [35]. We performed a set of test calculations using the PBE and two vdW corrected functionals (CAM-B3LYP and M06-2x), in order to clarify the points mentioned above; the BSSE was calculated as well. The results are compiled in Table 2. It can be seen that the PBE, CAM-B3LYP and M06-2x functionals predict larger values for the metal–water interaction as compared with the B3LYP, although qualitatively the results remain the same. The BSSE was found to be very large for the B3LYP, PBE and CAM-B3LYP functionals and the corrected ΔEad values are too small and unrealistic. However, the adsorption energy values obtained by using the M06-2x and corrected to the BSSE look quite reasonable and even comparable with the uncorrected B3LYP predictions (Table 2). Taking into account this fact, as well as the observation that qualitatively our results are not sensitive to the choice of functional, in further calculations we restricted ourselves to the B3LYP level without correcting the BSSE. 2.5. Comparison with previous studies The first results of DFT calculations on the adsorption of H2O at Ga and In surfaces have been reported in Refs. [12,13]. Using the LanL2DZ basis set for Ga atoms and the 6-311G** basis set for O and H atoms we practically reproduced a value of − 21.9 kJ mol − 1 [13] for the adsorption energy (on-top site of Ga16 and H-up position). Our value (− 22.7 kJ mol − 1) is slightly different, as it refers to the fully optimized geometry of the H2O molecule, while in Ref. [13] its internal geometry was fixed. The water adsorption at the Hg surface was previously investigated using ab initio SCF calculations corrected to the many-body perturbation theory (MP4 level) [11]. The adsorption energy was estimated to be −38.5 kJ mol−1. The B3LYP level of theory used by us in this work gives the lowest value of −37.9 kJ mol−1 for Hg31 cluster. One should not be mistaken, however, by the proximity of the energy values, as they depend on the basis sets, cluster size, and a fortiori on computational methods (Table 1, Figs. 2, 3, Refs. [11,13]). Again, it has to be Table 1 Adsorption energy of a single water molecule (ΔEad) adsorbed at the most preferable site, equilibrium metal–O atom distance (dMe–O) and reorientation energy (δΔEad) calculated for different Men clusters and basis sets.

Fig. 3. Metal surface–oxygen distance calculated for a water molecule adsorbed at Ga (●) and Hg (■) surfaces as a function of the cluster size.

Basis set for the metal atom −ΔEad(H-up)/kJ mol−1 δΔEad/kJ mol−1a dMe–O(H-up)/nm a

Bi24

Bi24

Ga16

Ga16

Hg16

Hg16

MB 28 14 0.218

DZ 31 12 0.225

MB 31 28 0.235

DZ 25 16 0.272

MB 24 20 0.290

DZ 34 24 0.299

δΔEad = ΔEad(H-down) − ΔEad(H-up).

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Table 2 Adsorption energy (ΔEad/kJ mol−1) and the basis set superposition error (BSSE/kJ mol−1) calculated for a water molecule at the Bi(111), Ga and Hg clusters. The 6-31G** basis-set was used for the H and O atoms; for the metal atoms the LanL2DZ basis set and effective core potential was employed.a H-upb orientation

B3LYP −ΔEad

BSSE

−ΔEad

BSSE

−ΔEad

BSSE

−ΔEad

BSSE

c −ΔEad

Bi24–H2O Ga34–H2O Hg34–H2O

28.0 24.8 34.3

26 24 27

37.6 36.3 40.5

24 27 29

33.4 30.8 39.5

25 25 27

41.3 36.8 44.8

20 20 21

20.9 17.0 24.0

a b

PBE

CAM-B3LYP

M06-2x

c The BSSE corrected adsorption energy (ΔEad /kJ mol−1) calculated using the M06-2x functional is given in the last column. The optimized geometry obtained at the B3LYP level for the most preferable adsorption site and orientation was used in all calculations.

emphasized that in the present work we investigate the hydrophilic properties of sp-metals (examined first theoretically in Refs. [11–14]) in the framework of a unified computational level. We believe that this enables the avoidance of computational artefacts and the clearer judgement of important qualitative trends. It should be noted that the same level of theory and cluster approach was used in a number of similar studies of the H2O molecule adsorption at Cu, Ag, Au and Pt surfaces [36–39]. As this work is aimed mainly at a comparative study (the comparison of hydrophilic properties of three different metals), we recalculated our data for Bi(111)–H2O interaction obtained previously in Ref. [14] using the LanL2DZ level to describe the Bi atoms.

with a relatively low energy cost. For example, the reorientation energy decreases in the order: Hg > Bi ≈ Ga (Tables 1, 3), and the interaction energy differences between top, bridge and hollow sites are almost zero (Table 3). Thus, the gallium–H2O interface may relax easier under a disturbance made by an applied electric field. 3.2. Effect of applied electric field In our calculations the surface charge density (σ) was modelled by an external homogeneous electric field as implemented in the

3. Results and discussion 3.1. Preferable orientation of H2O at metal surfaces For Ga and Hg surfaces on-top site was confirmed to be energetically the most preferable: ΔEad(H-up) and z0 values amount to − 24.7 kJ mol − 1, 0.267 nm, and − 35.6 kJ mol − 1, 0.296 nm for Ga34 and Hg34, respectively. In contrast, a water molecule adsorbed prefers the hollow site at Bi24 (ΔEad(H-up) = − 31.1 kJ mol − 1 and z0 = 0.225 nm, see also Ref. [14] for other details). Thus, due to specific atomic corrugation, distance between favourable sites grows in a sequence: Bi surface (0.26 nm) b Ga surface (0.29 nm) b Hg surface (0.30 nm). However, in contrast to the H2O molecule adsorption on mercury and bismuth, at gallium surface the bridge, hollow and on-top sites are almost closely preferable (Table 3). The reorientation energy of H2O molecule at Hg34 is noticeably higher (19.8 kJ mol−1), as compared with that for the favourable positions at the Ga34 (7.9 kJ mol −1) and Bi24 (11.9 kJ mol−1) clusters. For all three surfaces the adsorption entails a minor change in the H2O internal geometry: the H\O\H valence angle is slightly increased in the following sequence: H2O in gas phaseb adsorbed at Bi≈ adsorbed at Hgb adsorbed at Ga. The bond length r(O\H) practically does not change. The dependence of the metal surface–H2O interaction energy on the tilt angle θ at Hg and Bi surfaces (Fig. 4) indicates that the H2O molecule is bound preferentially through the O atom in orientation perpendicular to the surface plane (H-up). However, the energy difference for tilting by 60° is small and comparable with thermal fluctuation energy at room temperature (kBT = 2.4 kJ mol −1). Although for gallium a tilted orientation (60°, see Fig. 1a) is the most preferable, the energy difference for tilting from the most stable orientation (in a range of ±60°) is comparable to kBT. The difference between E(H-up) and E(H-par) adsorption energies reported in Refs. [12,13] is also below 2kBT. According to the analysis performed in Ref. [40] the preference for a perpendicular (H-up) orientation of a water molecule when adsorbed on Hg and Bi(111) might be an indication of a strong metal image dipole interaction, whereas a tilted orientation on Ga might indicate a certain contribution of covalent bonding. It was indicated in the previous studies that the energy barrier for rotation over the Bi(111) surface normal is less than kBT [14], as well as for some other metal surfaces [29]. We may conclude, therefore, that water molecules are the most mobile at the gallium surface, since they may change their orientation and adsorption position

Table 3 Averaged adsorption energies of a water molecule in H-up orientation (ΔEad), equilibrium metal surface–oxygen atom distance (z0) calculated for different Ga and Hg clusters and three different adsorption sites. The mean values were estimated by averaging over the results obtained for several clusters. A root-mean-square error (RMSE) for a set of the results is given in parentheses. Cluster

Site

−ΔEad(H-up)/kJ mol−1

z0/nm

Ga7–71 Ga31–34 Ga31–34 Hg7–71 Hg31–34 Hg31–34

Top Bridge Hollow Top Bridge Hollow

23(1); 10(4)a 22(3) 22(4) 34(2); 17(2)a 27(7) 27(5)

0.259(8) 0.281(12) 0.299(10) 0.296(4) 0.300(7) 0.307(10)

a

The reorientation energy (δΔEad/kJ mol−1).

Fig. 4. Adsorption energy of a single H2O molecule (ΔEad) calculated for Bi (▼), Ga (●) and Hg (■) as a function of the tilt angle θ (see Fig. 1a).

V. Ivaništšev et al. / Surface Science 609 (2013) 91–99 →

Gaussian 09 program suite [20]. Electric field ( F ) is given by the equation: →

F¼

σ : ε0

ð3Þ

11 Taking into account that one atomic unit→ equals to 5.14· h i 10 V/m,
 4 −2 the relation between σ μC cm 10 a:u: is given as and F → σ ¼ −9:10⋅10−2 F . The H2O adsorption energy dependence on the surface charge density was calculated for three different orientations: H-par, H-up, and H-down (Fig. 5). The orientation H-down becomes more favourable as compared with H-up when going from negative to positive surface charges. The reorientation of a water molecule takes place via the H-par orientation. Since for the gallium cluster the tilted orientation of H2Oads is more preferable in the vicinity of zero charge potential, the reorientation energy barrier was found to be relatively low. On the contrary, a high value for the reorientation barrier is predicted for mercury (Fig. 5). For a certain adsorption site at the Bi(111) surface, we might even expect the absence of the reorientation energy barrier at some charge density values, while for the other sites the corresponding values are noticeable. The dependence of the lateral interaction energy on the surface charge density was calculated using the mean field theory [11,14,41]. Further the notation ΔEdip is used for the adsorption energy of a water molecule ad corrected to the lateral interactions in terms of the mean filed theory. The ΔEdip term results from the electrostatic dipole–dipole interactions ad of H2O molecules in an assumed surface layer modelled by a lattice of dipoles. The data shown in Fig. 5 were fitted by a linear equation. As can be seen from Fig. 6, ΔEdip has the lowest value for Hg34–H2O. The evaluated ad ΔEdip value for Ga (−24 kJ mol−1 at σ=0) is close to the deepest adad sorption energy of a single H2O molecule (ΔEad = − 28 kJ mol − 1, Fig. 4), while for the Hg and Bi surfaces this quantity is almost 10 kJ mol − 1 lower than the uncorrected adsorption energy. As a

Fig. 5. Adsorption energy of a single H2O molecule (ΔEad) as a function of surface charge density (σ) calculated for the most preferable surface sites of Bi24 (▼), Ga34 (●) and Hg34 (■) clusters. The deepest ΔEad values corresponding to a certain orientation of H2O molecule (H-up, H-par, H-down) are displayed. Empty marks refer to the adsorption energy for H-par orientation at Bi and Hg, respectively. Filled ♦ and ◄ marks refer to the adsorption energy for H-down orientation at Bi hollow II and bridge sites.

95

result, in this approximation the strength of the metal surface– H2O interaction becomes comparable for the three metals. The H2O binding energy was found to be insensitive to disorder parameter ξ, which was introduced into the mean field theory to correct the energy of electrostatic interaction of a given H2O molecule with the dipole lattice environment (see details in Ref. [14]). Using this parameter we can address defects in the dipole lattice. For ξ = 1, all favoured sites are assumed to be occupied, thus the structure is ordered. The ξ value of 0.6 corresponds to a disordered structure similar to an ice-like network, in which two thirds of favourable sites are occupied. At ξ = 0, there are no H2O molecules adsorbed. It appeared that ξ has a negligible effect on ΔEdip in a reasonable range of ξ from 1 to 0.3. ad Only a weak influence of ξ on the capacitance and potential drop values was observed. 3.3. Dependence of potential drop on surface charge density The hydrophilicity of a metal surface is characterized by the potential drop in EDL across the metal surface/aqueous electrolyte solution interface: ΔMe χ ¼ δχ sMe þ δχ s , where δχ sMe is the potential drop in the metal surface layer in contact with the solvent molecules and δχ s is the potential drop in the solvent surface layer. It is convenient to consider the potential drop at the PZC, and to use mercury as a reference electrode [2,15]: Hg

Hg

s

Hg

ΔMe χ ¼ ΔMe χ−ΔHg χ ¼ ΔMe δχ Me þ ΔMe δχ s :

ð4Þ

The absolute potential drop δχsMe at the PZC was estimated as follows:   s Me Me=s δχ Me ¼ εHOMO −εHOMO =F;

ð5Þ

Me=s

where εMe HOMO and εHOMO are energies of the highest occupied molecular orbital (HOMO) for the metal cluster and adsorption complex, respectively, and F is the Faraday constant. The results of DFT calculations with external electric field for a single H2O molecule and an associate of 13 H2O molecules are shown in Fig. 7. The similar model was also

Fig. 6. The adsorption energy corrected to dipole–dipole interaction in a monolayer of H2O molecules in terms of the mean field approximation (Edip ) as a function of surface ad charge density (σ) calculated for Bi (▼), Ga (●) and Hg (■).

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employed in our previous work [14] for a narrow interval of external electric field. The results obtained for the H2O associate overestimate the potential drop in the metal surface layer in contact with the solvent molecules (δχ sMe ). A similar conclusion was made in Ref. [10] on the basis of periodical DFT calculations — there is an over- or underestimation in adsorption energy in the case of H-up/down water bilayer at a metal surface. As follows from periodical DFT calculations [9,10], the potential drop strongly depends on the orientation of H2O molecules at the interface. An enlargement of the adsorption complex in the cluster approach should in principle lead to similar results as give the periodical DFT calculations, but at higher cost in terms of CPU-time. More promising and less resource-consuming would be a combination of slightly enlarged adsorption complex (of 4 molecules accounting different configurations)with the dipole lattice model of the adsorbed H2O monolayer. Namely, the statistically averaged results for a single H2O molecule seem to be more reliable, than the results for the associate of 13 H2O molecules. For averaging we multiplied the HOMO energy difference for the adsorption complexes in H-up, H-par or H-down orientations by the corresponding fractional population, calculated using the s mean field theory [14]. The obtained value for ΔHg Me δχ Me amounts to − 0.05 V for bismuth and gallium (Fig. 7). As can be justified from   Me=s s Me Fig. 7, the capacitance C ¼ F∂σ=∂ εHOMO −εHOMO (inverse slope of s

the δχ Me ,σ-dependence) has very high negative value for mercury and bismuth, thus it does not contribute to the total capacitance of the metal layer, and equals −15 μF cm−2 for gallium. The total capacitance of
 Me=s metal layer can be defined as C sMe ¼ 1=C s þ 1=C Me −1 ¼ F∂σ=∂εHOMO [15,17], where C Me ¼ F∂σ=∂εMe HOMO . The calculated CMe value for bismuth (− 22 μF cm − 2) is in agreement with those reported in Ref. [17]: − 21 μF cm − 2 (Rice model), − 28 μF cm − 2 (Leiva–Schmickler– Henderson model). The same value for the metal capacitance was estimated for mercury. A considerably lower value of CMe (−8 μF cm−2) was found for Ga. Therefore, the total capacitance of the metal layer s (CMe ) at Bi and Hg surfaces in contact with H2O is determined mainly by metal layer capacitance CMe [11,12]. In contrast, the total capacitance is strongly influenced (through Cs) by the adsorption of H2O molecules at the gallium/water interface, similarly to platinum [42].

Fig. 7. Change of the HOMO energy of the metal clusters (ΔEHOMO) induced by a water molecule adsorbed (filled marks) and by the associate of 13 H2O molecules (empty marks) calculated for Bi (▼) Ga (●) and Hg (■) as a function of surface charge density (σ).

Potential drop δχ s in the surface layer of water molecules was defined as follows: δχ s ¼ ρs hμ ⊥ i ¼ −

ρs hsiμ ε0

ð6Þ

where ρs is the surface density of the H2O molecules, μ is the dipole moment of H2O molecule, hμ ⊥ i is the averaged normal projection of dipole moment in the H2O monolayer, and dimensionless parameter 〈s〉 is numerically calculated for σ values from −0.0455 to 0.0455 C/m 2, and has the meaning of a difference between the fractional population in H-up and H-down orientations. The δχ s dependence on surface charge densiHg ty is shown in Fig. 8. The differences of δχs for two metals are: ΔBi δχ s ¼ 0:25 V and ΔHg δχ ¼ 0:5 V. It has the same meaning as defined in Refs. s Ga [15,17] only at PZC (σ = 0), at which the capacitance values (the inverse slope of dependence in Fig. 8) amount to −3.8, −3.4, and −3.1 μF/cm2 (ξ = 1) for Bi, Ga, and Hg, respectively. Although the computed capacitances have meaningful values, the potential drop in the surface solvent layer is clearly overestimated in the case of bismuth and, especially, for mercury electrodes [17]. Emets   Hg s and Damaskin evaluated the potential drop ΔHg Me δχ Me þ ΔMe δχ s q¼0

from experimental data to be approximately 0 V for bismuth and 0.26 V for gallium [15]. Lust et al. [17] estimated the value of 0.1 V for bismuth (Table 2 in Ref. [17]). Our estimations give 0.25 V and 0.5 V for Bi and Ga relatively to Hg, respectively. There is a simple reason, why our DFT computational results combined with mean field approximation overestimate the potential drop. The main deviation is due to δχ s , which is a function of 〈s〉 according to Eq. (5). The 〈s〉 values show whether the H-up, or H-down orientation is predominant, and the δχ s values at fixed σ are more positive for gallium (see Fig. 8). Data shown in Figs. 4 and 5 explain this trend: part of the H2O molecules easily change their orientation under an applied electric field, however, most of the H2O molecules lie in parallel orientation even at a charged gallium surface. As the parallel orientation in our model does not contribute to the potential drop, the δχ s values have higher absolute values

Fig. 8. Solvent potential drop (χs ) calculated for different types of a monolayer of H2O molecules at Bi (▼) Ga (●) and Hg (■) as a function of surface charge density (σ). Empty marks refer to a close-packed structure (ξ = 1), which is more probable for Hg/water and Ga/water interfaces due to larger lattice parameters for these metals. Filled marks correspond to a less dense lattice (ξ = 0.6, ice-like bilayer) which is more probable for Bi/water interface [14].

V. Ivaništšev et al. / Surface Science 609 (2013) 91–99

for Bi and Hg as compared with that for Ga. For Bi and Hg the model, however, underestimates the number of H2O molecules lying parallel at the metal interface, as it does not take into account local short-range interactions (H-bonds). To elucidate the importance of neighbouring H2O molecules, we first addressed solvent effect in terms of the polarizable continuum model (PCM), and then investigated the lateral interactions considering a model associate of 13 H2O molecules adsorbed on a metal surface.

Table 4 Adsorption energy of a single water molecule (ΔEad in kJ mol−1) calculated on the basis of the PCM at certain values of the medium dielectric constant (ε) for the Bi, Ga and Hg clusters.

Bi24–H2O Ga34–H2O Hg34–H2O a

3.4. Solvent effect in the framework of the PCM

b

For Bi24, Ga34 and Hg34 clusters we calculated energies of hydration using the PCM for two different values of dielectric constant (ε= 5 and 80, see Table 4). The higher value corresponds to solution bulk, while the lower one describes the lowering of the dielectric constant of the polar medium at a metal/solution interface. The adsorption energy of the H2O molecule at the gallium surface decreases noticeably with the rise of the dielectric constant of modelled medium, while at the bismuth surface it slightly decreases, and for the Hg34–H2O system the adsorption energy remains constant. This is due to the calculated hydration energy, which is negative for the Ga34–H2O complex (–11 kJ mol−1), and close to zero for Bi24–H2O and Hg34–H2O. A difference in the adsorption energies for a water molecule induced by two different ε values is very close for the Ga34–H2O and Hg34–H2O complexes but slightly lower for the Bi24–H2O adsorption complex (Table 4, last column). 3.5. Effect of lateral interactions in a monolayer of adsorbed water molecules To test the influence of H-bonds on the H2O adsorption energy, we have performed DFT calculations of a 13 H2O associate (which models some fragment of an assumed ice-like structure) on the Bi24, Hg34, and Ga34 clusters (Fig. 1b). In this absorption complex seven H2O molecules are situated closer to the surface at the hollow sites of the Bi24 cluster, and the other six molecules are positioned at hollow II sites [14]. For the Hg34 and Ga34 clusters, all molecules occupy on-top sites only (Fig. 1b). The projections of all oxygen atoms to the metal surface were fixed and eight parameters describing orientation were optimized. 2 The central H2O molecule in the water cluster and its surrounding area were the focus of attention. The calculated bonding energies are collected in Table 5. We are aware of the fact that our model of an adsorbed water associate is highly approximative. Recent experimental studies [4,43,44] point to a more complicated disordered structure of water layers at metal surfaces; cooperative effects (enhancement of H-bonds due to the presence of metal) pffiffiffi might pffiffiffi take place. A bilayer structure of adsorbed H2O molecules, ( 3 × 3) R30°, was found to be stable only at certain metal surfaces like SnPt(111) alloy [45]. The most rigorous way to model charged electrochemical interfaces is ab initio molecular dynamics which remains so far rather CPU time consuming. That is why we employed a crude model with pruned configuration space on the first step. The interaction energy of the central molecule with the metal surface was estimated according to Eq. (1). The geometry of the central molecule was described by four fixed parameters taken from the associate geometry optimized at the previous step. The hydrogen-bonding energy of the central molecule (ΔEsHbond ) was estimated as follows:

s

ΔEHbond ¼

 1  ΔE13H2 O −ΔE7H2 O −E6H2 O ; 15

ð7Þ

2 The optimized parameters are r(O\H), HOH angle, metal surface–H2O plane angle and distance r(metal–H2O) for each type of adsorbed H2O molecules (Figs. 1b, 9).

97

−ΔEada (H-up, ε = 1)

−ΔEad (H-up, ε = 5)

−ΔEad (H-up, ε = 80)

−ΔEadb (ε = 80 →ε = 5)

31 25 36

34 35 36

35 36 35

30 34 35

Adsorption from gas phase is assumed. ΔEad ¼ EMe−H2 O ðε ¼ 5Þ−EMe ðε ¼ 5Þ−EH2 O ðε ¼ 80Þ.

Table 5 Adsorption bond energy (ΔEad/kJ mol−1), H-bond energy (EsHbond ) and the energy of bs adsorption of a water molecule from solution bulk to the water bilayer (EHbond ) at Bi(111) and Ga surfaces calculated for the central water molecule in the model 13 H2O associate for three different surface densities (σ); tilt angle (see Fig. 1a) values are listed as well.

−ΔEad/kJ mol

−1

−EsHbond /kJ mol−1

bs −Ead /kJ mol−1

θ/°

σ, μC cm−2

Bi

Ga

Hg

+1 0 −1 +1 0 −1 +1 0 −1 0

26 26 25 27 27 27 13.5 12.6 11.6 59

25 21 21 29 30 31 15.0 12.7 12.5 109

26 21 21 28 29 29 14.5 10.4 11.1 110

where “13H2O”, “7H2O” and “6H2O” refer to model water clusters composed from thirteen, seven and six H2O molecules, respectively.3 The geometry of such fragments was described by eight fixed parameters taken from the optimized geometry of the initial 13 H2O associate. The adsorption energy of a single H2O molecule from solution bulk into the water bilayer can be recast as a sum of three different terns: bs

s

b

ΔEad ¼ ΔEad þ ns ΔEHbond −nb ΔEHbond ;

ð8Þ

where ns and nb are the average numbers of hydrogen bonds at a surface and in bulk. The H-bond energy for bulk H2O calculated at the same theory level is ca − 27 kJ mol −1 [46]; we assumed that ns ≈ 1.5 and nb ≈ 2. It is evident that ns is less than 2 due to a part of the intramolecular OH bonds, that does not contribute to the H-bonds [47,48]. The results of molecular dynamics simulations reported in Refs. [37,38] also predict a small decrease in the number of H-bonds (from 2 to 1.6) going from the water bulk to the Hg [49] and Pt [50] surfaces. The ΔEad and ΔEsHbond terms are presented in Table 5. The metal surface–H2O binding interaction was found to be weaker than or comparable to H-bonding interactions (Table 5). The binding energy values for bismuth and gallium agree in general with those shown in Fig. 4 (at tilt angles (θ) of 60° and 110°, respectively). The θ values correspond to the geometry of central H2O molecule in the 13 H2O associate at Bi(111) and Ga (see Fig. 9). The hydrogen bonding network is more stretched at mercury as compared with bismuth and gallium, therefore, the water molecules in the bilayer are pushed away from the Hg surface. On the other hand, hydrogen-bonding is the strongest at Ga and the energy of adsorption bond is higher for gallium even at a negative surface charge (Table 5). In order to elucidate the effect of H-bonds, we have performed additional calculations of an associate consisting of 13 H2O molecules, similar to that we considered at the metal surfaces (Fig. 9). The 3 The number 15 in the denominator of Eq. (6) results from 15 intramolecular OH bonds in the 13 H2O associate contributing to H-bonds (Fig. 9).

98

V. Ivaništšev et al. / Surface Science 609 (2013) 91–99

associate was relaxed with a restriction to the O\O distance and the hydrogen-bonding energy was calculated as a function of O\O distance, shown in Fig. 10. Minimum hydrogen-bonding energy was found for the distance close to the Ga–Ga interatomic distance of 0.29 nm. A bit shorter distance of 0.28 nm is characteristic for d-metals, such as Pt, Pd and Rh. The role of d-metal surface as a template for H2O bilayer was investigated in a number of works [6,7]. It was found that for d-metal the lattice constant, i.e. atom–atom interatomic distance has a minor influence on the bilayer stability. This originates from the fact that the metal surface–H2O bond at Pt, Pd or Rh is stronger as compared with the H-bond (or much weaker as for Ag and Au surfaces). Again, the interaction energy of a single water molecule with the Hg, Ga and Bi(111) surfaces differs significantly. However, if the H-bonding effect is addressed, the hydrophilic properties of these three metal surfaces become very close. The gallium surface is even slightly more hydrophilic than Bi(111) and Hg. It should be stressed that our conclusions are based on calculations of the adsorption enthalpies. On the other hand, differences in the adsorption energy for on-top, hollow and bridge sites, as well as the reorientation energy were found to be the smallest for the gallium surface. The Ga/H2O interface, therefore, should be more disordered at room temperature as compared with bismuth and mercury and the adsorption entropy of water molecules should be less negative for gallium. This entails more negative values for the adsorption free energy and favours finally the gallium hydrophilicity. 4. Conclusions The behaviour of a single H2O molecule at Bi, Ga and Hg electrode surfaces was studied in the framework of a cluster model at DFT level. The mean field approximation was employed in order to model the electrostatic interactions between the H2O molecules in the adsorption layer and to compare the hydrophilic properties of three metal surfaces; the effect of external electric field was examined as well. So far gallium is commonly treated among electrochemists as the most hydrophilic metal among sp-metals; this conclusion is based on the EDL capacitance measurements. The calculated potential drop across the metal/H2O layer interface is in contradiction with this conclusion, which might be regarded as a drawback of the model insufficiently describing local intermolecular interactions. An associate of water molecules at the metal surfaces was considered to address the effect of local H-bonds on the water adsorption energy. We found that the H2O adsorption at gallium surface is stronger basically due to a slightly stronger H-bonding in the adsorption layer at the Ga/water interface.

Fig. 10. Energy of hydrogen bond (ΔEHB) in the optimized associate of 13 H2O molecules as a function of interatomic O\O distance (l). Filled marks refer to H-bond energy calculated using the data for 13 H2O molecules associate at the Bi (▼) Ga (●) and Hg (■) clusters. Empty marks correspond to H-bond energy calculated for the associate in the absence of metal cluster assuming its optimized geometry at the metal surface.

The strength of H-bonds in the H2O associate was shown to depend on the O\O distance, i.e. on specific atomic corrugation of a metal surface. It might be concluded on the basis of this finding that the gallium surface is slightly more hydrophilic than the Bi(111) and Hg surfaces. As for some problems ahead, a microscopic interpretation of the experimental EDL capacitance curves for Ga/aqueous solutions still remains a tour de force. Quantitative estimations of the water adsorption free energy can be considered as another challenging problem. A comparative ab initio or Car–Parinello molecular dynamics study of the water layers on the Bi, Ga and Hg surface would be very useful to get a molecular level insight into hydrophilicity problems. It would be also tempting to investigate comprehensively the adsorption behaviour of different small H2O associates of 4–7 molecules, which is less resource demanding. Acknowledgments The authors thank Prof. K. Lust and Ph.D. J. Jeromenok for the care with which they reviewed the original manuscript. We acknowledge the opportunity to perform calculations at a cluster in the Institute of Physics (University of Tartu). This work was partly supported by the Russian Foundation for Basic Research (project no. 11-03-01186-a) and the Estonian Science Foundation (project no. 8357) and Basic Financial Project (1.2.0401.09-0079). This research was also supported by European Social Fund's Doctoral Studies, Internationalisation Programme DoRa, and Estonian Centre of Excellence in Research project TK117T “High-technology Materials for Sustainable Development”. References

Fig. 9. Optimized geometry of 13 H2O associates adsorbed at the Bi (a) and Ga (b) clusters; H-bonds are shown with dotted lines.

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