Van der Waals Interaction Really Matters: Energetics of Benzoic Acid

Article pubs.acs.org/JPCC

Van der Waals Interaction Really Matters: Energetics of Benzoic Acid on TiO2 Rutile Surfaces Wolfgang Heckel, Tim Würger, Stefan Müller, and Gregor Feldbauer* Institute of Advanced Ceramics, Hamburg University of Technology, 21073 Hamburg, Germany S Supporting Information *

ABSTRACT: Density functional theory (DFT) has been applied to elucidate the adsorption structures and energetics of benzoic acid on TiO2 (110), (100), and (011) rutile surfaces. We demonstrate that ab initio calculations of interacting carboxylic acids require an exchangecorrelation functional with van der Waals (vdW) correction to yield reliable results, even for very small aliphatic species like acetic acid. On the (110) surface, benzoates dimerize due to intermolecular vdW interaction and form a 2 × 2 superstructure, which explains experimental findings already reported in the literature. The lateral vdW attraction between benzoates is even enhanced on (100) and (011) surfaces because of advantageous substrate periodicities, resulting essentially in only one geometrical adsorbate species.

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INTRODUCTION Functionalization of surfaces is currently a prominent research topic in materials development. Recently, specifically processed hybrid materials composed of inorganic nanoparticles and organic linkers showed extraordinary mechanical properties due to intermolecular interaction.1 Since the early 1990s, dyesensitized solar cells2 have attracted interest by promising to be a cheap and environmentally friendly alternative to conventional semiconducting photovoltaic devices. For these two fields as well as for photocatalysis, TiO2 rutile functionalized with carboxylic acids serves as a prototype system.3−6 Thanks to numerous studies, a consensus on the energetically favorable adsorption structure of small carboxylic acids adsorbed on the most stable TiO2 surface, the (110), has been reached. Typically, the adsorbate dissociates into a carboxylate species, binding toward two adjacent undercoordinated surface Ti atoms in a bidentate manner, and an H+ forming a hydroxyl group at an undercoordinated, protruding surface oxygen atom, a “bridging oxygen”. That holds for formic acid (HCOOH),8,9 acetic acid (CH3COOH),10 benzoic acid (C6H5COOH),11,12 various amino acids,13,14 and many others (e.g., see ref 5 and references therein). As an example of this structure, acetic acid on TiO2 (110) rutile is shown in Figure 1.

This paper has three objectives: 1. Significance of van der Waals (vdW) interaction between adsorbates: In organic matter, contributions of vdW interactions between molecules are decisive for the mechanical properties. We demonstrate that already very small aliphatic side chains (namely CH3) of carboxylic acids experience a significant attractive interaction due to vdW forces over distances which are typically occurring in adsorption processes. Consequently, to reflect adequately the adsorption energetics of inorganic− organic interfaces, DFT requires a vdW-including exchange-correlation functional. 2. Dimerization of benzoic acids on TiO2 (110): The lateral interaction of adsorbed molecules on TiO2 (especially on (110)) continues to be a subject of debate. In addition to the question of saturation coverage, the influence of different side chains attached to the carboxyl group on the stability of the interface has not been quantified yet. Using aromatic instead of aliphatic side chains, a significant gain of binding energy resulting from more attractive, lateral vdW interactions should occur. Although the adsorption structure of benzoic acids on TiO2 (110) has been investigated intensely,10−12,15−20 a common consensus could not be achieved. Particularly, ab initio energetics are lacking. Here, we investigate the adsorption of benzoic acid on TiO2 (110) surfaces, quantify the binding energies, allow for dimerization of adsorbates, and compare the phenomena with acetic acid. 3. Quantitative analysis of the benzoic acid adsorption on other TiO2 surfaces: In the technical usage of TiO2 nanoparticles, several surface orientations occur. Consequently, it is necessary to elucidate and quantify the

Figure 1. Bidentate adsorption structure of dissociated acetic acid on TiO2 (110) rutile. Color code: Ti = blue, substrate O = red, acid O = dark red, C = brown, H = whitish. All presented structures are visualized using VESTA.7 © XXXX American Chemical Society

Received: April 3, 2017 Revised: July 19, 2017

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DOI: 10.1021/acs.jpcc.7b03149 J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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COMPUTATIONAL DETAILS DFT Calculations. For the DFT calculations, we used the Vienna Ab initio Simulation Package (VASP)27−30 with its implemented projector augmented-wave (PAW) pseudopotentials.31,32 We set the energy cutoff of the plane wave basis to 520 eV. The k-point meshes employed in this study are described below following the introduction of the relevant model systems. For most of the calculations, we applied the exchange-correlation (XC) functional optB88-vdW,33 which performs excellently for noncovalently bound complexes.34 This functional belongs to the class of van der Waals density functionals (vdW-DF) which are based on an approach introduced by Dion et al.35 Such functionals consider vdW interactions to be pairwise additive, but they do not use external input parameters. Within this approach, the XC energy is defined as

adsorption phenomena at other low-indexed, energetically favorable surfaces like (100) and (011). The available literature21−26 does not treat these surfaces sufficiently. Therefore, we also identify structures and the energetics of laterally interacting benzoic acids on TiO2 (100) and (011). Adsorption of benzoic acid on TiO2 (110) at room temperature leads to a saturation coverage of θ ≈ 0.2 monolayers (ML).12,16 Here, 1 ML denotes one benzoic acid molecule per undercoordinated surface Ti atom. In the 0.2 ML regime, the tendency for a local ordering of three to four benzoates in a chain along the [11̅0] direction has been reported.16 This feature indicates analbeit weakattraction between adsorbates over a distance of ≈6.5 Å, which corresponds to the length of the surface unit cell in [11̅0]. Furthermore, by performing photoelectron diffraction (PhD) experiments, benzoates are found to adsorb essentially upright and aligned in [001] direction with no indication for more than one benzoate species.12 In this context, a species denotes adsorbates exhibiting the same adsorption geometry. A nearly fully covered rutile (110) surface (θ ≈ 0.5 ML) can be prepared by slight heating to ≈370 K and further exposure to adsorbates.12,16 The resulting structure gives rise to a 2 × 2 pattern in a recent low-energy electron diffraction (LEED) experiment.15 It is reported to diminish rapidly during electron bombardment and end up in a long-term stable 2 × 1 pattern, which is supposed to be identical to the previously reported ones.10,20 Structures that yield a 2 × 2 pattern are clearly seen in scanning tunneling microscope (STM) experiments.10,15,20 Those studies reveal pairwise (sometimes 3-fold) agglomerated benzoate rows, which run in [001] direction. The origin of these arrangements has been discussed controversially. The conception of two different coexisting benzoate species forming dimers via attractive vdW interaction of their phenyl rings is supported by an X-ray absorption spectroscopy (XAS) experiment.19 It reveals at least two benzoate species with a comparably high azimuthal difference of 60°−90°, frequently referred to as “T”-type shape. However, the STM study of Grinter et al.16 does not observe any multimerization. All attempts to verify, correct, or reject the structurally obvious “T”-type model suggested in ref 10 are not satisfying. Especially, none of the existing density functional theory (DFT) studies concerning benzoic acid adsorption on TiO211,12,17,18 can contribute sufficiently to this subject, because they all apply exchange-correlation functionals which are not able to account for the long-range vdW interactions. After presenting details of our ab initio calculations and the model systems, we initially demonstrate in the section Van der Waals Interaction between Carboxylic Acids that the application of vdW-including exchange-correlation functionals is crucial to describe the energetics of carboxylic acids subject to lateral interactions. Subsequently, we present our approach to test all possible orientations of dimer-forming benzoic acid molecules within a manageable computing time. In the section Results and Interpretation, we display the favored geometries and their binding energies on the three bulk-terminated (which means fully relaxed, but with a 1 × 1 superstructure) rutile surfaces (110), (100), and (011). Finally, the results of this study are summarized and linked to the literature.

vdW − DF E XC [ρ] = EGGA(X)[ρ] + E LDA(C)[ρ] + Enl(C)[ρ]

(1)

In this form a GGA exchange term EGGA(X) is employed and the correlation is divided into a local ELDA(C) as well as a nonlocal Enl(C) part. While the local contribution is obtained within the local density approximation (LDA), the nonlocal correlation is calculated from the electron densities interacting via a model response function. Specifically, the GGA exchange term of the optB88-vdW functional is based on the B88 functional.36 The “opt” functionals have been successfully applied to various systems.37−43 Particularly, optB88-vdW is considered to capture well the subtleties of weak interactions during the adsorption of organic molecules.44−46 Various alternative methods which intend to account for vdW interactions within DFT exist; for an overview, see ref 47. While many of the pairwise additive approaches rely on predetermined input parameters to obtain the dispersion interaction, the opt functionals of Klimeš et al., which we use here, calculate the dispersion interaction directly from the electron density. Thus, they are considered to be more general.47 Methods that go beyond the pairwise additivity are computationally very demanding and are not considered in this work. For example, the computational cost of the “random phase approximation” (RPA) method, 48,49 which gives generally very promising results, is about 3 to 4 orders of magnitude higher than for a GGA calculation even without any relaxations. This isat least for the rather large systems investigated herecurrently prohibitive. In comparison, calculations with the opt functionals are just about 50% more expensive than GGA ones. In order to demonstrate the necessity of a vdW-corrected functional for simulating carboxylic acids with DFT and to compare optB88-vdW results to previous studies, results obtained with the standard-GGA functional PBE50,51 are shown as well. If relaxations are allowed (see next paragraph), atomic positions were updated by a conjugate gradient algorithm until the forces were less than 5 meV/Å. Model Systems. For each surface orientation, periodic supercells consisting of ten O-Ti-O trilayers were set up. The atoms in the two innermost trilayers were held in their bulk-like positions, whereas all other atoms were allowed to relax. The resulting surface energies were calculated according to the equation B


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The Journal of Physical Chemistry C Esurf =

1 O − Ti − O O − Ti − O (Eslab − Nslab ·E bulk ) 2(

gain arising from lateral intermolecular vdW interaction. These cases are indicated clearly in the subsequent discussion. The distance between periodically repeated slabs amounts at least to 14 Å. The applied dipole correction52,53 accounts for the slab asymmetry. The k-space sampling was carried out by using the Monkhorst-Pack scheme54 with a 3 × 5 × 1 mesh for the (110) 2 × 2, the (100) 2 × 2, and the (011) 1 × 2. For other lateral cell sizes, the mesh was adapted appropriately. Van der Waals Interaction between Carboxylic Acids. Carboxylic acids have the potential to interact attractively via vdW forces between their side chains. Aiming at a correct quantitative description of the vdW interaction within the DFT-framework, it is crucial to apply an exchange-correlation functional which accounts also for the weak long-range forces. The widely used local or semilocal potentials are not capable to do so.58 To prove this aspect for the particular case of carboxylic acids, we carried out test calculations of interacting acetic acid molecules employing the functionals optB88-vdW and PBE. For this purpose, we set up test-supercells containing one acetic acid molecule only. The dimensions of these cells and the positioning of the molecule within these cells were identical to a rutile (110) 3 × x surface slab cell, allowing us to vary the intermolecular distance d = x·a√2 (a: lattice constant). Applying the functional optB88-vdW, we find a considerable potential depression leading to intermolecular attraction, while essentially no attraction occurs with PBE (see Figure 2). Furthermore, this test setup shows a remarkable amount of binding potential between carboxylic acids. With a CH3 side chain, acetic acid forms a very small aliphatic representative of the carboxylic acids. Nevertheless, neighboring molecules release up to ≈0.1 meV binding energy (see Figure 2) without allowing for any inclination or dimerization. Longer aliphatic or even aromatic side chains are supposed to cause an even higher energy gain. Repeating these test calculations with benzoic acid proves the expected trend. Despite having no further degree of freedom (no spatial or angular flexibility), benzoic acids show an attractive potential of up to ≈0.2 meV when applying optB88-vdW and no attraction when evaluated with PBE. Summing up these tests, in contrast to (semi)local exchangecorrelation functionals the functional optB88-vdW is able to describe vdW interactions qualitatively and quantitatively in a more realistic fashion. Therefore, it seems to be suitable to elucidate the formation of benzoic acid dimers on TiO2 surfaces and will be used for this study. Scanning the Configuration Space of Benzoic Acid Pairs with Adsorption-Like Boundary Conditions. When setting up a surface slab cell including two randomly oriented adsorbing molecules, the probability to match a start geometry which relaxes into to the energetic ground state is practically zero. Commonly implemented algorithms for ionic relaxation in DFT codes are designed neither to move atoms over a larger distance nor to overcome larger energy barriers. Hence, it cannot be expected that the benzoic acid molecules find their energetically most favorable dimer position just by the minimization of the occurring forces with the implemented relaxation routines. To boost the chances to find the best dimer configuration of benzoic acids on TiO2 surfaces and at the same time limit the computational cost, we propose the following route:

(2)

Here, Eslab is the energy of a surface slab consisting of NO‑Ti‑O slab O-Ti-O units with twice the surface area ( . EO‑Ti‑O is the bulk energy of a O-Ti-O unit in rutile bulk. Values for Esurf can be found in Table 1. The lateral size of the supercells as well as the Table 1. Lattice Parameters a, c and Surface Energies Esurf of TiO2 rutile PBE lattice constants [Å] surface energy [meV/Å2]

a

a c (110) (100) (011) (011) 2 × 1a

21

experiment (15 K)55

optB88-vdW

4.652 2.970 25 37 58 27

4.631 2.972 52 65 83 58

4.587 2.954

Reconstruction according to refs 56 and 57.

fixed atomic positions of the innermost TiO2 trilayers in each cell originate from DFT-optimized rutile bulk structures. The fully relaxed lattice parameters for both functionals, PBE and optB88-vdW, are also listed in Table 1. All values are in excellent agreement with previous publications.21 To reduce the computational effort in the subsequent adsorption study, we removed one-half of each symmetric surface slab, ending up with asymmetric five-layer slabs. The lowermost two trilayers were fixed in their current positions (atoms of layer five are still in their bulk-like positions), while the atoms of layer 1−3 were able to respond to forces occurring due to adsorption. A possible influence of the unnatural bottom side on the adsorption was ruled out by evaluating the binding energies 1 E B = (nEadsorbate,gas + Esubstrate − Eslab) (3) n (difference between total energies of educts, nEadsorbate,gas and Esubstrate, and total energy of the product, Eslab, divided by the number of adsorbed molecules per cell n) of acetic acid for both, the symmetric 10-layer slab and the asymmetric 5-layer slab (see Table 2). Since no significant differences could be found, the 5-layer slab is assumed to provide sufficient accuracy and was used throughout the adsorption study. Table 2. Binding Energies EB of Acetic Acid on TiO2 Rutile Surfaces in eV with Respect to Model System Size and Symmetry PBE (110) (100) (011)

21

optB88-vdW

10-layer slab

10-layer slab

5-layer slab

1.12 1.05 1.54

1.91 1.94 2.27

1.92 1.94 2.26

To allow for dimerization of two neighboring benzoic acids adsorbed on TiO2 rutile, we chose 2 × 2 supercells for the (110) and (100) surfaces and a 1 × 2 supercell for the (011) surface. By default, we adsorbed two molecules per supercell, which corresponds to a coverage of θ = 0.5 ML. In specific cases, either just one adsorbate was added to the supercells or the lateral cell size was varied in order to quantify the energy

1. We position two benzoic acid molecules only (i.e., without a substrate) in periodic supercells, which have C


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Figure 2. Interaction of (a) acetic and (b) benzoic acid molecules as a function of intermolecular distance with and without vdW-corrected exchange-correlation functional. (c) The interaction energy ΔE is defined as the difference between the total energies of a molecule in a rutile (110) 3 × x (see text) and a 4 × 2 surface slab cell. Color code: O = red, C = brown, H = whitish.

Figure 3. Scheme of two benzoic acid molecules in a periodic supercell. Both molecules are tilted and twisted independently. The order of inclination angles throughout the study is φ, ψ, ϑ and φ′, ψ′, ϑ′, respectively. In the (0°,0°,0°) position (light brown), the C−C bond between the carboxyl group and the phenyl ring lies parallel to the long axis of the supercells and the phenyl ring plane coincides with the carboxyl group plane. The φ/φ′ rotation axis is defined by the C−C bond; in a φ/φ′ rotation the phenyl ring atoms are twisted only. The ψ/ψ′ rotation axis is perpendicular to the carboxyl group plane and intersects the molecule in the carboxyl C atom; in a ψ/ψ′ rotation, the phenyl ring atoms are tilted only. The ϑ/ϑ′ rotation axis is defined by the line through the two O atoms; a ϑ/ϑ′ rotation twists all atoms of the corresponding molecule. The brown rotated molecule represents the (30°,15°,30°) position. The cell sizes correspond to the surface unit cells. Blue arrows mark positions of periodic images. For clarity, H atoms are hidden.

the dimensions of the TiO2 (110) 2 × 2, the (100) 2 × 2, and the (011) 1 × 2, respectively. The alignment of the two molecules mimic the bidentate adsorption manner; that is, the coordinates of all four carboxylate oxygen atoms correspond to positions of bidentate adsorbed carboxylic acids. Hence, the intermolecular distance of d = a√2 in the case of the (110) cell and a in cases of the (100) and the (011) cell is preserved. The carboxylic H atom, which dissociates during adsorption, is placed in the vicinity of one O atom to retain molecular saturation. 2. These two benzoic acid molecules are tilted and twisted independently according to their inclination angles φ, ψ, ϑ and φ′, ψ′, ϑ′ depicted in Figure 3. The range of the azimuthal angles φ and φ′ is not restricted at all, ϑ and ϑ′ are limited to the upper hemisphere, and ψ and ψ′ to ± 30°. The sampling interval is 15° for all angles. For each sample geometry, atomic positions are fixed, and the DFT energy is evaluated. Thus, an energy landscape on a 6D angle space (φ, ψ, ϑ, φ′, ψ′, ϑ′) is obtained. 3. On the basis of this data, we figure out all local energy minima and their corresponding molecular orientations. For all of them, we perform a DFT calculation including

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TiO2 surface slabs in the super cell and allow for relaxations as described in the section Computational Details. By doing so, the energetically most favorable arrangement of benzoic acid dimers on TiO2 can be worked out. The possibility of monomeric behavior is included as limiting cases.

RESULTS AND INTERPRETATION Images of the most favorable conformations of dimer forming benzoic acids on TiO2 rutile surfaces are presented in Figure 4. Corresponding binding energies, inclinations, and further data of the energetic analysis are collected in Table 3 and will be discussed in the following. Allowing for dimerization on the TiO2 (110) rutile surface, adsorbed benzoic acid molecules favor the arrangement depicted in Figure 4(a) and (b). Two neighboring acids form pairs along the [11̅0] direction: one stands nearly upright with its molecular plane approximately perpendicular to the surface plane (ψ = 7°, ϑ = 0°) and the other is clearly tilted (ψ′=−3°, ϑ′=−39°), reducing the lateral distance between the neighboring phenyl rings. Both phenyl rings are twisted significantly (φ = 22°, φ′=19°) to prevent repulsive interactions between their D


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Figure 4. Adsorption structures of two benzoic acids per surface unit cell allowing for dimerization. The corresponding data can be found in Table 3. Color code: Ti = blue, substrate O = red, acid O = dark red, C = brown, H = whitish.

Table 3. Binding Energies EB and Inclinations of Benzoic Acid Molecules on TiO2 Rutile Surfaces surface

unit

coverage

EB

EAB

φ

ψ

ϑ

φ′

ψ′

ϑ′

graphics

orientation

cell

[ML]

[eV]

[meV/Å2]

[°]

[°]

[°]

[°]

[°]

[°]

see Figure 4

0.5 0.5 0.25 0.25 0.5 0.5 0.5 0.5

2.17 2.12 2.12 2.28 2.31 2.30 2.72 2.70

56 54 27 29 84 84 107 106

22

7

0

19 22

−3 −4

−39 −33

4a,b

23 12 20 24 28 28

2 4 4 5 1 1

−3 1 36 31 31 32

6 21

−2 3

−37 36

4c,d

29

−3

31

4e,f

(110) (110) (110) (110) (100) (100) (011) (011)

2 2 2 4 2 2 1 1

× × × × × × × ×

2 1 2 2 2 1 2 1

We explicitly considered the prototype “T” model of ref 10 as a starting geometry, too. This model consists of two upright benzoates with azimuthal angles φ = 0° and φ′ = 90°. In this case, we face the computational flaw that the relaxation algorithm is not able to rotate the molecules enough to reach their subtle energy minima. While the structure does not change much during relaxation, the corresponding energy is 0.16 eV less favorable than the value of the ground-state structure shown in Figure 4a. For a further analysis of lateral vdW interaction between the adsorbates, we took into account structures with half of the adsorbate density (i.e., 0.25 ML). For this purpose, we removed one benzoic acid in the 2 × 2 dimer adsorption cell to double the intermolecular distance in [110̅ ] direction to ≈13.1 Å,

periodic images in [001] direction (further discussed below). In this configuration, a coverage of 0.5 ML is achieved and an average binding energy of 2.17 eV per molecule is observed. If all adsorbing molecules are forced to take the very same configurationi. e. adsorbing one acid in a 2 × 1 surface cell the energetically most favorable arrangement fairly resembles the molecular inclination of one of the dimer building acids mentioned above (φ′=22°, ψ=−4°, ϑ=−33°). This additional constraint results in a binding energy that is 0.05 eV lower than with dimerization. That means, a dense layer of benzoic acids on TiO2 (110) (θ = 0.5 ML) forming a 2 × 2 superstructure by pairwise assembled adsorbates is energetically slightly more favorable than a 2 × 1 pattern. E


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expected LEED pattern for benzoic acid adsorption on TiO2 (100) is a simple 2 × 1 as it is supposed to be for even smaller carboxylic acids like formic or acetic acid. A clear prediction for the LEED pattern for (011) cannot be given. On closer examination of the absolute binding energies, the high value of 2.72 eV for (011) attracts attention. In this work, we consider the adsorption at the bulk-terminated surface only. Among clean (011) surface terminations, the 2 × 1 reconstructed one is the most stable,56,57 exceeding the bulkterminated one in stability by far.21 Thus, we deal with a fairly unsaturated surface, which explains the high binding energy. At this point it cannot be unambiguously determined whether the clean 2 × 1 superstructure turns into to the bulk-terminated surface due to and during benzoic acid adsorption. However, the discussion in ref 21 about formation enthalpy in case of carboxylic acid adsorption clearly points toward that conclusion. Comparing the binding energies of benzoic acid and acetic acid (cf. Tables 2 and 3), one notices generally higher values for the former. While at (110) the ratio EB(benzoic acid)/EB(acetic acid) amounts only to a factor of 1.13, the TiO2 (100) and (011) substrates allow for considerably more effective intermolecular vdW interaction with ratios of 1.19 and 1.20, respectively. Hence, the exchange of the rest groups permits to tune the binding energies and thus the mechanical properties of the interface.

assuming that the vdW interaction does not contribute significantly in this case. The result is a binding energy of 2.12 eV per molecule, as high as in the monomeric case. Thus, the potential energy gain due to attractive vdW forces is evened out by the additional constraints in the latter case. Furthermore, we enlarged the dimer adsorption cell to a 4 × 2 unit cell to double the space between the dimerized benzoates and their periodic images in [001] direction. This leads to an augmented binding energy of 2.28 eV per adsorbate and to a less pronounced twisting of both dimer-forming molecules (φ = 12°, φ′=19°). Hence, benzoic acids, which are adsorbed densely in [001] direction, obviously disturb each other sterically via the edges of their phenyl rings. To compensate for this effect, the rest groups twist, which costs 0.11 eV per molecule. This finding agrees with the DFT result of Busayaporn et al.,12 who stated that the alignment of the molecular plane is parallel to [001], if benzoates are not adsorbed densely in this direction. The maximum value in binding energy per molecule (2.28 eV) confirms the experimental studies using STM16 and PhD:12 The adsorption energy is minimized by an attractive lateral interaction of directly neighbored benzoates in [11̅0] direction and by a nonrestricted rotational adjustment of the molecular planes along [001], enabled by a nondense adsorption of benzoates in this direction. If the sample is not exceptionally treated with heat or other energy sources, this might result in a saturation coverage clearly less than 0.5 ML. However, according to experiments,12,16 the energy barrier that has to be overcome to increase the saturation coverage to 0.5 ML lies at moderate ≈370 K. Once this threshold is exceeded, a higher binding energy gain per area E BA =

EB A

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CONCLUSION Van der Waals forces play a decisive role in the interaction of carboxylic acids adsorbed on TiO2 surfaces. While, as expected, the resulting amount of additional binding energy per molecule is larger for acids with an aromatic side chain, the effect cannot be neglected for those with aliphatic side chains. The necessity of choosing an exchange-correlation functional for DFT calculation which accounts for vdW interaction has been demonstrated twice in this study. Acetic acid molecules attract each other when applying a vdW-corrected functional, while without vdW correction they appear to nearly ignore each other until repulsion sets in. Furthermore, the energetically favorable, dimer forming 2 × 2 superstructure of benzoic acids adsorbed on TiO2 (110) rutile could only be identified due to the use of a vdW functional (cf. ref 12). At the (110) surface, two neighboring benzoates gain additional binding energy by edgeto-face interaction of their phenyl rings, and thus form a suitable candidate to explain the 2 × 2 superstructure reported in the experimental literature.10,15,20 However, the small energetic difference (0.05 eV) to the nondimer-forming 2 × 1 superstructure does not allow a definite prediction of the existing structure in UHV experiments. At the (100) surface, the given adsorbate distance fits so well that no dimerization at all is needed to maximize the binding energy. The neighboring phenyl rings interact via their plane-parallel πsystems. This is also the case at (011), where a slight energy gain could be identified due to a beneficial distribution of the dissociated H atoms and, subsequently, enhanced surface buckling. The achievable range of binding energies by varying the substrate’s surface orientation and the adsorbate’s side chain opens manifold possibilities in tailoring custom-made interfaces. Beyond that, we presented a way to master a rather complex configuration space of organic adsorbates on periodic substrates with manageable computational effort. With this study, we put ab initio DFT simulations of hybrid interfaces with increasing organic content on a stable footing.

(4)

(A = area per adsorbed molecule) can be achieved by increasing the adsorbate density. Up to θ = 0.5 ML, EAB nearly scales with the coverage. Finally, from the energetic point of view the adsorbate superstructure is expected to be a close-packed, dimerized 2 × 2 pattern in agreement with, for example, ref 15. However, the energetic difference to the 2 × 1 superstructure is so small that this less favorable structure might still emerge in experiments, depending on the preparation procedure. Interestingly, no significant energy gain due to dimerization can be found at the TiO2 (100) and (011) rutile surfaces. Both surfaces provide adsorption sites such that the distance of the anchoring carboxylic groups of adsorbed benzoates is a = 4.63 Å and thus 1.92 Å shorter than for the (110) surface. Apparently, the consequently achievable distance between neighbored, plane-parallel phenyl rings results in an attractive lateral interaction which energetically cannot be outmatched by any edge-to-face phenyl ring (C−H/π-system) configuration. While on the (100) surface all benzoates relax into the very same species (φ = φ′, ψ = ψ′, ϑ = ϑ′) and thus form no dimers at all, a slight difference is found for the ψ angles of benzoates on (011) (ψ−ψ′ = 4°). The minor energetic difference of 0.02 eV between the monomeric and the dimeric calculation at (011) can hardly be attributed to an increased vdW attraction but rather to the higher degree of freedom, which enables e. g. surface buckling, and an advantageous distribution of the dissociated H atoms: rows of uncovered bridging Os along [01̅1] alternate with fully hydroxylated bridging O rows (see Figure 4e). On the other surfaces, this special H distribution does not appear to be beneficial. Based on these results, the F


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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b03149. Geometrical data of benzoic acid dimers on TiO2 (110) (CIF) Geometrical data of benzoic acid dimers on TiO2 (100) (CIF) Geometrical data of benzoic acid dimers on TiO2 (011) (CIF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 (0)40 428783644. Fax: +49 (0)40 428782647. ORCID

Gregor Feldbauer: 0000-0002-9327-0450 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank W. Mayr-Schmölzer for fruitful discussions. We gratefully acknowledge financial support from the German Research Foundation (DFG) via SFB 986 “M3”, project A4.

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REFERENCES

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