# First Principles Modelling of Dye Anchoring on (001) g-Monoclinic WO 3 Surfaces: The Role of Oxygen Vacancies

Azza Ben Jannet, Moncef Said, Michael Badawi, Mariachiara Pastore

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Azza Ben Jannet, Moncef Said, Michael Badawi, Mariachiara Pastore. First Principles Modelling of Dye Anchoring on (001) g-Monoclinic WO 3 Surfaces: The Role of Oxygen Vacancies. Journal of Physical Chemistry C, 2022, 126 (12), pp.5424-5434. 10.1021/acs.jpcc.1c10397. [hal-03871114](https://hal.science/hal-03871114)

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# First Principles Modelling of Dye Anchoring on
(001) γ-Monoclinic WO₃ Surfaces: The Role of
Oxygen Vacancies

Azza Ben Jannet,<sup>a,b</sup> Moncef Said,<sup>a</sup> Michael Badawi,<sup>b</sup> Mariachiara Pastore<sup>b,*</sup>

<sup>a</sup> Université de Monastir, Faculté des Sciences de Monastir, Laboratoire de la Matière Condensée et des Nanosciences (LMCN), LR11ES40, Avenue de l'Environnement, 5000, Monastir, Tunisie.

<sup>b</sup> Laboratoire de Physique et Chimie Théoriques (LPCT), Université de Lorraine & CNRS, UMR7019, 54500 Vandoeuvre-Les-Nancy, France.

*corresponding author: mariachiara.pastore@univ-lorraine.fr

Keywords: γ-Monoclinic WO₃; oxygen vacancies; dye adsorption; photocatalysis; DFT
**Abstract**

Here we focus on the dye's anchoring mechanism onto the (001) monoclinic $WO_3$ surface. We present first-principles simulations, based on density functional theory (DFT), to get atomistic insights of the adsorption of three different anchoring groups (Benzoic acid (BA), Catechol (Cat), Phenylphosphonic acid (PA)) onto the clean and oxygen-defective (001) $WO_3$ surfaces, considering implicit solvation effects and dispersion corrections. The results show that both BA and PA preferably adsorb in a molecular monodentate binding mode on clean surface, while the presence of oxygen vacancies on the surface makes the dissociative bidentate bridging the preferred binding mode. In the case of Cat molecule, two configurations were found to be close in energy in solution on clean surfaces, whereas the mono-deprotonated monodentate mode is the most stable one on defective surfaces. The presence of oxygen vacancies on the surface increases, in absolute value, the adsorption energies of the anchoring groups, without affecting their relative stability. The present results, providing for the first time atomic-scale details on the dye anchoring mechanism on monoclinic $WO_3$ substates and indicating un unfavorable W-W distance pattern on the surface (001) surface for anchoring traditional carboxylic, phosphonic and catechol anchoring groups, may suggest novel design rules for the optimization and the selection of alternative anchoring functionalities for $WO_3$-based DSSCs and hybrid photocatalysts.
Introduction

Among renewable energies the sun is by far the most abundant source, with irradiation of the
earth's surface at a rate of 1.2 × 10⁵ TW, largely exceeding the current worldwide power demand.
By the way, to be exploitable, solar energy has to be converted in heat, electricity or "stored" in
chemical bonds (fuels). ¹⁻⁵ Among the different pathways available to produce solar fuels⁵,
artificial photosynthesis, mimicking natural photosynthesis, uses sun light to split water into H₂
and O₂.⁶ In this context, photoelectro catalytic cell (PECs) require assembly of three key units to
collect solar light and perform the water splitting reaction: a light absorber, a water reduction and
a water oxidation catalysts.⁷⁻⁹ Hybrid photoanodes and photocathodes, obtained by functionalizing
n- and p-type semiconductor nanoparticles with molecular dye sensitizers and catalysts are, indeed,
an appealing approach to photoelectrochemical water splitting,⁹⁻¹¹ which allows to separate and
optimize the three main steps required to convert sunlight into chemical bond energies, namely, i)
light absorption (dye), ii) charge carriers separation/transportation (semiconductors) and iii)
chemical reactions (molecular catalysts). Moreover, an alternative approach, which has the
advantage of reducing the complexity of the molecules/oxide interface and minimizing the
shortcomings related to the optimization of dye/catalyst ratio on the surface and to the poor
stability of the molecular components, is to use the semiconductor for light harvesting and the
molecular component as a catalyst for water splitting.¹²⁻¹⁵ On the semiconductor side, different
materials have been reported¹⁶,¹⁷ for both water reduction¹⁸⁻²² and oxydation.²³⁻³⁰ Among the
different semiconductors, tungsten trioxide, WO₃ has received particular attention in
photocatalytic applications³¹⁻³⁶ ²⁵,²⁶,³⁷⁻⁴⁵ because of its good charge carrier transport properties,⁴⁶⁻
⁴⁹ high stability against photo-corrosion under acidic condition,⁵⁰,⁵¹ and fast water oxidation
kinetics.⁵²
The interface (linking) between the molecular components and the semiconductor is of pivotal
importance in determining the charge transfer and separation properties as well as the device
stability.⁵³⁻⁵⁶ Dyes and catalysts can interact with the metal oxide surface through different
mechanisms, including covalent attachment, electrostatic interaction, hydrogen bonding,
hydrophobic interaction, van der Waals forces, or physical entrapment.⁵⁷ Covalent adsorption by
chemical bonding is by far the most employed functionalization strategy, allowing for a better
control of the molecules packing and enhanced electronic coupling and charge transfer rates.
Therefore, chemical grafting represents one of the most important points to address for efficient
assembling of hybrid PECs and dye-sensitized solar cells. Historically, carboxylic and
cyanoacrylic acids are the most employed anchoring groups for both *n*- and *p*-type
photoelectrodes,⁵⁸⁻⁶³ although they show poor stability in water environments. On the other hand,
phosphonic acid provides excellent anchoring stability, with an adsorption strength estimated to
be approximately 80 times higher than that of the carboxylic acid, and negligible desorption in the
presence of water.⁶³,⁶⁴ Many alternative anchoring groups have been proposed and been tested,⁵⁷
such as hydroxyl groups⁶⁰. Contrarily to the deep knowledge and characterization that has been
achieved on the grafting mechanism of dye and catalysts on TiO₂ nanoparticles, only a few
experimental studies, addressing adsorption on WO₃ substrates, are available in the literature.⁶⁵⁻⁷⁰
Bishop et al.⁶⁹ studied the binding of citric acid to different metal oxide nanoparticles (ZnO, TiO₂,
Fe₂O₃, and WO₃), finding a weak adsorption onto the WO₃ surface, that was attributed to its
extremely low isoelectric point. WO₃ functionalization with polydopamine (PDA) has been also
reported in the context photocatalysis and immunosensor devices,⁶⁵,⁷⁰ indicating the formation of
a stable interface between PDA and WO₃ via catechol functionalities. Also, the binding constants
of the [Ru(bpy)₃]²⁺ dye anchored by either a phosphonate or an hydroxamate group to TiO₂ and
WO₃ surfaces was reported in Ref.⁶⁸, revealing, again, a stronger dye binding and a higher surface coverage on TiO₂ than on WO₃. The lower isoelectric point of WO₃ and the differences in the acidity of Lewis sites between the two metal ions (Ti⁴⁺ serves as stronger Lewis's acid site compared to that of W⁶⁺) were individuated as the main reasons of the different binding constants. Then, concerning defective WO₃ surfaces, the adsorption mode of aliphatic alcohols on oxidized and reduced WO₃ (001) surfaces was experimentally reported in Refs.⁷¹,⁷² Based on UPS measurements, methanol was found to molecularly adsorb on the oxidized surface and dissociatively adsorb on the reduced surface, and the difference was attributed to the heterogeneity of the oxidized WO₃ (001) surface, showing unfavorable distances between the acid/base pairs sites required to realize a dissociative grafting. Recently, Zhao et al.⁷³ reported the impact of the physical and chemical defects in γ-WO₃ (001) surface on the photocatalytic water splitting activity, showing that an appropriate amount of oxygen vacancies⁷³,⁷⁴ results in an increased adsorption of OH groups on the metal oxide surface and in a boosted catalytic activity.

This brief overview, clearly, reveals a lack of fundamental understanding in the interaction mechanism of traditional anchoring groups with clean and defective WO₃ substrates, that would definitely require a more systematic investigation. To this respect, quantum mechanical calculations have been widely applied to study the interface phenomena in molecule-functionalized semiconductors,⁶⁰⁻⁶²,⁷⁵⁻⁷⁷ and are a valuable tool for provide atomistic insights of dyes' anchoring group interactions with metal oxide surface. But, again, while a large number of theoretical studies on the dye adsorption modes on the TiO₂ surface have been reported (see for instance Refs⁵⁷,⁷⁸, and references therein), to the best of our knowledge, the theoretical characterization of the adsorption mechanism of common anchoring groups on WO₃ surfaces has not be afforded yet.
To address this specific issue related to the dye/WO₃ interface, here, we consider three commonly employed anchoring groups, namely Benzoic acid (BA), Catechol (Cat) and Phenylphosphonic acid (PA) (Figure 1) and we model their adsorption onto the clean and oxygen-defective (001) surfaces of monoclinic WO₃, taking into account implicit solvation effects and dispersion corrections. Although here we are using simplified models (basically restricted to the anchoring functionality) to get information on the adsorption mechanism of realistic dye sensitizers bearing these anchoring groups, it is worthwhile to stress that this is a common practice when investigating the dye/semiconductor interactions and that the conclusions drawn on small anchoring prototypes, on overall, still hold for the larger dye molecules, being the adsorption mainly driven by local interaction between the surface atoms and the anchoring unit.⁵⁶,⁷⁹ Several experimental and theoretical works have, indeed, shown similar adsorption behavior for different dyes/organic molecules, bearing similar functional groups, depending on the metal oxide surface.⁸⁰⁻⁸⁸ Evanko et al.⁸⁰ showed that the adsorption of organic acids, comprising double ring compounds, resembled the adsorption of smaller molecular weight organic acids with similar functionalities. Organic dyes often contain only one anchoring group, and their grafting properties are generally the same of those of their anchoring groups: for example, adsorption of perylene-carboxylic and perylene-phosphonic acids⁸⁷,⁸⁹ is similar to that of formic⁷⁵,⁹⁰ and phosphonic⁷⁶,⁸⁷ acids, respectively. Similarly, O'Rourke et al.⁸⁸ found a very little difference in the adsorption geometries between a simple model of the anchoring groups and the complete dye, with the largest change amounting to 2%. Thus, we can safely affirm that the present results obtained by using prototype molecules are still representative of the adsorption mechanism of realistic dye-sensitizers or molecular catalysts.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Molecular structure of a) Benzoic acid (BA) b) Catechol (Cat) and c) Phenylphosphonic acid (PA). The green, dark red, light blue and white spheres represent the C, O, P and H atoms of X molecule (X=BA, Cat or PA), respectively.</figcaption></figure>

The work is organized as follows: the computational procedure and structural models are presented in Section 2; the results obtained for the adsorption modes BA, Cat and PA onto both clean and defective (001) WO₃ surfaces in gas phase and implicit water are given in Section 3 and finally some conclusive remarks are reported in Section 4.

## 2. Computational Details

### 2.1 Calculations Settings

All the calculations were performed using the Vienna ab initio simulation package (VASP)⁹¹ with the projector augmented wave (PAW) approach.⁹²,⁹³ The semilocal Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional⁹⁴, along with the D3_BJ correction method of Grimme and co-workers⁹⁵ was employed. In order to benchmark PBE results we also performed calculations with rev-vdW-DF2 DFT functional⁹⁶ for selected configurations (see Table S1 in Supporting Information). In our calculations, the 5d and 6s (for W) and 2s and 2p electrons (for O) are treated as valence electrons. The Kohn-Sham equations were solved self-consistently with a threshold on
the energy change of 10⁻⁷ eV. A Gaussian smearing of 0.05 eV was used to help the total energy convergence. All the calculations were performed at Γ-point because of the large size of the employed cell (vide infra) with a plane-wave basis set energy cutoff of 500 eV. The structural relaxations, at both level of theory employed (PBE-D3_BJ and rev-vdW-DF2), have been carried out until all the forces were smaller than 0.02 eV/Å.

## 2.2 Structural Model

Primitive 32-atom unit cell of the room temperature (RT) monoclinic phase of WO₃ (space group P2₁/n) has been used to model the semiconductor substrate.⁹⁷ The unit cell was fully relaxed at PBE level with the D3_BJ Grimme's correction⁹⁵ to obtain lattice parameters a=7.44 Å, b=7.58 Å, c=7.76 Å, and β=90.72°, in agreement with the experimental values of a=7.31 Å, b=7.54 Å, c=7.69 Å, and β=90.9°.⁹⁸

The stable WO₃ (001) surface with the (√2 × √2)-R45° reconstruction⁹⁹ was obtained by cleaving the crystal perpendicularly to the c crystallographic axis (Figure 2a). This reconstructed surface presents half a monolayer of the top oxygen atoms missing alternately along a and b directions, to avoid surface dipoles,⁹⁹ leading to 6 and 5-coordinated W atoms. Previous theoretical studies have shown that four layers for WO₃ represent a good compromise between the size of the slab (i.e. the cost of the calculation) and the accuracy of the results.¹⁰⁰⁻¹⁰² Hence, a WₓO₃ₓ slab with x= 64 W atoms, corresponding to 4 layers (thickness of about 16 Å), has been adopted without freezing any layer in the structures optimizations. A vacuum space of 15 Å was used in order to avoid interactions between the replicated slabs along the c direction. For the calculations of isolated molecules, a cubic 30 Å-length box was used.
WO₃ is a reducible oxide and its surface can present high concentrations of oxygen vacancies, V₀, which can significantly improve the photoelectric behaviors.⁴⁹ More importantly here, V₀ gives rise to local coordinative unsaturated metal atoms, possibly affecting the adsorption energy and mode on the metal oxide surface.¹⁰³ Following the procedure reported in previous works,¹⁰⁴⁻¹⁰⁶ to model oxygen-deficient WO₃ surfaces, we have removed 1/8 of the oxygen atoms from the topmost atomic layer along the c axis (Figure 2b). Here we limit ourselves to investigate oxygen defects on the first surface layer, as they may more largely impact the coordination modes and their relative stability. Spin polarized calculations were performed to study oxygen defective surfaces. The ground state present a triplet spin configuration, in agreement with previous results,¹⁰⁴,¹⁰⁶ with the singlet being calculated about 0.2 eV higher in energy.
<figure><img src="image_3.png" /></figure>

**Figure 2.** Representative structure of (a) clean and (b) oxygen-defective (001) $WO_3$ surfaces and their corresponding structural features along a (c) and (d) and b axes (e) and (f), respectively. The light grey, dark grey and light red spheres represent the W, reduced $W_{6c}$ and O atoms of (001) $WO_3$ surface, respectively. Distances are in Å, angles in degrees.

## 2.3 Adsorption modes and adsorption energy calculations

We have considered monodentate (M) and bridging bidentate (BB) binding modes on undercoordinated tungsten surface atoms ($W_{5c}$), in both molecular and dissociative (D) forms; in the latter. The oxydrilic H atoms were transferred to one, or more, surface O-atoms ($O_t$), following the results of Ref. 104 To indicate coordination to the reduced $W_{6c}$ atoms on the defective surfaces we use M' and BB' labels, for the monodentate and bidentate bridging, respectively. It is important to note that, the crystal structure of monoclinic $WO_3$ is characterized by a structural anisotropy
along the three cell axes, leading to an alternating long-short W-O bond length¹⁰⁴. Therefore, we have considered the molecule grafted to the surface along both a and b directions.

The adsorption energy, corrected by a dispersive contribution ($\Delta E_{ads} = \Delta E_{DFT} + \Delta E_{disp}$), is calculated as:

$$ \Delta E_{ads} = E_{WO_3-x} - E_{WO_3} - E_x \quad (1) $$

Where, $E_{WO_3-x}$ is the total energy of the slab with adsorbed molecule and $E_{WO_3}$ and $E_x$ is the total energy of the isolated slab and molecule, respectively. Thus, by definition, a negative value of $\Delta E_{ads}$ corresponds to an exothermic adsorption.

As a matter of fact, solvation effects are essential for accurate modeling of dye/semiconductor interface in realistic environment. While continuum solvation models cannot accurately describe specific interactions between the adsorbate and the surrounding solvent molecules, they are computationally fast and reasonably accurate for computing free energies in solution.¹⁰⁷ Here we use implicit solvation calculations to refine our estimation of the adsorption energies, by making use of the Poisson-Boltzmann model to include the dielectric screening effect of the medium as implemented in VASPsol code.¹⁰⁸,¹⁰⁹ Using the relaxed geometries from gas-phase calculations, we have computed the adsorption energies in aqueous medium by performing single-point energy calculations on the gas-phase-optimized structures, with relative dielectric constant $\epsilon = 80$¹⁰⁸,¹¹⁰ and a Debye length of 3 Å.

# 3. Results and discussion

## 3.1 Benzoic acid
A preliminary screening of several adsorption configurations for BA on clean and defective (001) WO₃ surfaces has been performed, and here only the stable anchoring modes are reported and discussed. Table 1 lists the computed adsorption energies in vacuo and implicit water for the structures displayed in Figure 3. Some relevant optimized structural parameters for the isolated BA and the considered WO₃-anchored structures are reported in Table S2 in Supporting Information, while the changes in surface parameters upon BA adsorption on clean and defective (001) WO₃ surfaces are listed in Tables S3 and S4, respectively.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Optimized structure of benzoic acid on a) clean and b) defective (001) WO₃ surface. The light grey, black, and light red spheres represent the W, reduced W<sub>6c</sub> and O atoms of WO₃ surface, respectively. The dark red, green and white spheres represent the O<sub>BA</sub>, C and H atoms of BA molecule, respectively. Dashed lines indicate H bonding between the OH group and surface O atom.</figcaption></figure>
On the clean surface, as shown in Figure 3a, no stable BB configurations were found: this is the consequence of an unfavorable W<sub>5c</sub> – W<sub>5c</sub> distance, amounting to ~ 5.5 Å and being too large to coordinate the carboxylate group. Notice that on the TiO<sub>2</sub> (101) anatase surface, where the BB mode is generally the most stable one,⁷⁹ the distance between two undercoordinated Ti atoms is about 3.6 Å. Two molecular monodentate configurations, along *a* (*M*<sup>*a*</sup>) and *b* (*M*<sup>*b*</sup>) directions respectively, were found to be stable, with the latter being ca. 0.4/0.5 eV lower in energy in gas phase/solution than the former. Indeed, the new bonds formation between the molecule and surface W atoms leads to a structural rearrangement of the metal oxide surface close to the adsorption site.

To take into consideration this effect, the adsorption energy can be decomposed into two opposite contributions (ΔE<sub>ads</sub> = ΔE<sub>int</sub> + ΔE<sub>def</sub>(WO<sub>3</sub>) + ΔE<sub>def</sub>(X)): interaction (exothermic contribution) and deformation energies (endothermic contribution).¹¹¹,¹¹² The computed surface deformation energies ΔE<sub>def</sub>(WO<sub>3</sub>) of the all considered configurations and their corresponding structural parameters upon BA adsorption on clean surface are reported in Tables S3 in Supporting Information. The larger structural deformation energy calculated for *M*<sup>*a*</sup>(0.46 eV) with respect to *M*<sup>*b*</sup>(0.05 eV) explains the lower stability of the former both in vacuo/implicit solvent (-1.31/-0.74 eV vs. -1.72/-1.22 eV). Finally, a dissociative M adsorption, *M*<sub>D</sub><sup>*b*</sup> in Figure 3a, has been identified, being, however, poorly stable (ΔE<sub>ads</sub> = -0.22 eV in solution). Adsorption of H<sup>+</sup> on O<sub>t</sub> surface atom induces an additional deformation on the surface (ΔE<sub>def</sub>(WO<sub>3</sub>) = 1.47 eV), where the underneath O<sub>t</sub> – W<sub>6c,1</sub> – O<sub>2p</sub> – W<sub>6c,2</sub> bond lengths along *c* axis change from 1.710, 2.373 and 1.759 Å to 1.881, 2.125 and 1.801 Å, respectively (see Table S3 in Supporting Information). The adsorption energies calculated for the *M*<sup>*b*</sup> and *M*<sub>D</sub><sup>*b*</sup> configurations with the rev-vdW-DF2 functional (see Table S1 in Supporting Information) are consistent and in quantitative agreement with the ones obtained with PBE+D3_BJ approach, where the dissociative *M*<sub>D</sub><sup>*b*</sup> configuration is
less stable. Consequently, BA preferably adsorbs, on clean (001) WO₃ surface, in a molecular **M**<sup>b</sup>
binding mode forming H-bond with the O<sub>t</sub> surface atom, with the O<sub>BA,1</sub> – W<sub>5c</sub> and H<sub>BA</sub> – O<sub>t</sub> bond
lengths of 2.224 and 1.587 Å, respectively.

In the case of sub-stoichiometric WO₃ surface new configurations were considered (Figure 3b),
since the molecule can coordinate either to W₅c or to reduced W₆c surface atoms. For the
**M**<sup>b</sup> configuration, due to the impossibility of forming H-bond with neighbors O<sub>t</sub> atoms, the
calculated adsorption energy is lower than the one obtained on the pristine surface (-0.78 vs -1.22
eV). On the other hand, when BA adsorbs on the reduced W₆c atom, in both *b* and *a* direction,
(**M**'<sup>b</sup> and **M**'<sup>a</sup>), the interaction becomes stronger, with a rather short W–O distance, 2.150 and
2.127 Å, respectively (Table S2 in Supporting Information). Turning to the dissociated form, the
benzoate adsorbs in a stable BB binding configuration, with the two W–O bond lengths of 2.019
and 2.241 Å, for reduced W₆c and W₅c, respectively, with a strong structural rearrangement of the
surface (ΔE<sub>def</sub>(WO₃) = 2.43 eV, Table S4). In fact, after the formation of the covalent O<sub>BA</sub> – W₅c
bonds, the underneath W₅c – O<sub>2p</sub> and W'<sub>5c</sub> – O<sub>2p</sub> bond lengths, along *c* axis, increase from 1.745
and 1.782 Å to 1.759 and 1.945 Å, respectively, while in the second layer, the O<sub>2p</sub> – W₆c,₂ bond
lengths decrease from 2.268 and 2.002 Å to 2.244 and 1.856 Å, respectively. Significant
rearrangements also involve the bond angles, with the O<sub>1p</sub> – W₅c – O<sub>2p</sub> and O<sub>1p</sub> – W'<sub>5c</sub> – O<sub>2p</sub>
angles decreasing by about 4° and 21°, respectively, becoming close to 81.2° of O<sub>1p</sub> – W₆c – O<sub>2p</sub>
angle. For this bidentate structure, the calculated adsorption energy in water is -1.16/1.23 eV at
PBE+D3_BJ/ rev-vdW-DF2 level of theory, representing by far the most stable anchoring mode
among the ones considered here.
<table><caption>**Table 1.** Calculated adsorption energies upon anchoring benzoic acid on the clean and defective (001) WO₃ in vacuum and implicit solvent.</caption><thead><tr><th rowspan="2">Anchoring modes</th><th colspan="2">In vacuum</th><th>In implicit solvent</th></tr><tr><th>ΔE<sub>disp</sub> (eV)</th><th>ΔE<sub>ads</sub> (eV)</th><th>ΔE<sub>ads</sub> (eV)</th></tr></thead><tbody><tr><td colspan="4" style="text-align: center; font-weight: bold;">Clean surface</td></tr><tr><td>M<sup>a</sup></td><td>-0.46</td><td>-1.31</td><td>-0.74</td></tr><tr><td>M<sup>b</sup></td><td><strong>-0.62</strong></td><td><strong>-1.72</strong></td><td><strong>-1.22</strong></td></tr><tr><td>M<sup>b</sup><sub>D</sub></td><td>-0.57</td><td>-0.42</td><td>-0.22</td></tr><tr><td colspan="4" style="text-align: center; font-weight: bold;">Defective surface</td></tr><tr><td>M<sup>b</sup></td><td>-0.52</td><td>-1.28</td><td>-0.78</td></tr><tr><td>M'<sup>b</sup></td><td>-0.43</td><td>-1.43</td><td>-0.95</td></tr><tr><td>M'<sup>a</sup></td><td>-0.44</td><td>-1.43</td><td>-0.93</td></tr><tr><td>BB'<sup>a</sup><sub>D</sub></td><td><strong>-0.56</strong></td><td><strong>-1.65</strong></td><td><strong>-1.16</strong></td></tr></tbody></table>

## 3.2 Catechol

The catechol molecule (Cat), in its molecular, mono- and bi-deprotonated forms, can be adsorbed both “perpendicularly” and “parallel” to the (001) WO₃ surface, in line with what has been observed on silica supports.¹¹³ The calculated adsorption energies, in vacuum and water, for all the considered anchored structures shown in Figure 4, are gathered in Table 2. Table S5 in Supporting Information collects the main structural parameters obtained for the isolated Cat and anchored configurations on clean and defective (001) WO₃ surface, while Tables S6 and S7 report the
surface deformation energies and the changes in surface structural parameters upon Cat adsorption

on clean and defective (001) WO₃ surfaces, respectively.

<figure><img src="image_5.png" /></figure>

**Figure 4.** Optimized structure of catechol on a) clean and b) defective (001) WO₃ surface. The light grey, black, and light red spheres represent the W, reduced W₆c and O atoms of WO₃ surface, respectively. The dark red, green and white spheres represent the O_Cat, C and H atoms of Cat molecule, respectively. Dashed lines indicate H bonding between the OH group and surface O atom.
In the case of stoichiometric WO₃ surface (Figure 4a), four stable adsorption modes were identified after full structural relaxation. When Cat is in its molecular form, it can interact with the metal oxide surface in a bidentate-like mode, **BH-flat** in Figure 4a, by establishing two rather short H-bonds (ca. 1.6 – 1.7 Å) with the O_t atoms on the surfaces, inducing a slight surface structural change (ΔE<sub>def</sub>(WO₃) = -0.01 eV). When one of the two hydroxyl groups is dissociated, by proton transfer to the surface, the preferred monodentate binding is again a “flat” configuration (**M<sub>1D</sub>-flat** in Figure 4a) allowing for the formation of an H-bond with the surface, which stabilizes the covalent O–W bond. These two configurations are the most stable structures calculated in solution with an adsorption energy of about 0.9 eV, whereas, in vacuo, the bidentate structure **BH-flat** is significantly more stable than the monodentate one **M<sub>1D</sub>-flat** (1.60 vs. 1.38 eV). Similarly, the calculated adsorption energies of both configurations at rev-vdW-DF2 level of theory are close, with the **M<sub>1D</sub>-flat** one slightly favored in solution by about 0.32 eV (0.07 eV in vacuo). The electrostatic screening of the implicit medium, indeed, more largely affects the two H-bonds with respect to the covalent O-W one, thus destabilizing the **BH-flat** structure with respect to the monodentate one. Then for the monodeprotonated Cat another, less stable (by about 0.2 eV) monodentate structure can be identified, **M<sub>1D</sub>-ortho**, where the molecule lies « orthogonal » to the surface plane. Finally, deprotonation of both hydroxyl groups results in a poorly stable monodentate mode, for which the calculated adsorption energy is ca. 0.50 eV; again, an unfavorable distance between the two adjacent undercoordinated W<sub>5c</sub> atoms does not allow for a **BB** grafting.

As discussed above for BA, on the defective WO₃ surface, the presence of O vacancies leads to new possible configurations (see Figure 4b). For the undissociated Cat, the **BH-flat** adsorption mode, with two H-Bonds and not involving coordination to reduced W<sub>6c</sub> atom, is about 0.1 eV less
stable with respect to when adsorbed on the clean surface. Then, deprotonation of one of the
hydroxyl groups results in a monodentate structure, **M'<sub>1D</sub> - flat**, where the molecule strongly
binds by his O<sub>Cat,1</sub> on the reduced W<sub>6c</sub> atom (O - W distance of 1.883 Å) forming H-bond on the
surface through the undissociated OH group. By far this is the most stable structure among the
ones examined here, with a computed adsorption energy of -1.11 eV; rev-vdW-DF2 results in
Table S1 in Supporting Information confirm this picture, with a calculated adsorption energy in
water of -1.22 eV. Also, in this case, when the molecule is fully dissociated, only a poorly stable
monodentate configuration without possibility of H-bond was found, **M'<sub>2D</sub> - flat**, with a
calculated adsorption energy of -0.47 eV. As discussed above for BA, the presence of O vacancies
makes it possible to anchor the molecule in a bidentate fashion, by coordination to W<sub>5c</sub> and reduced
W<sub>6c</sub> atoms. The resulting optimized structure is indicated as **BB'<sub>2D</sub> - ortho** in Figure 4b and the
computed adsorption energy is -0.88 eV, being about 0.2 eV smaller than the one calculated for
the **M'<sub>1D</sub> - flat** adsorption, which is thus the preferred coordination mode of Cat on sub-
stochiometric WO<sub>3</sub> surface.
<table><caption>**Table 2.** Calculated adsorption energies upon anchoring catechol on the clean and defective (001) WO₃ in vacuum and implicit solvent.</caption><thead><tr><th rowspan="2">Anchoring modes</th><th colspan="2">In vacuum</th><th>In implicit solvent</th></tr><tr><th>ΔE<sub>disp</sub> (eV)</th><th>ΔE<sub>ads</sub> (eV)</th><th>ΔE<sub>ads</sub> (eV)</th></tr></thead><tbody><tr><td colspan="4"><strong>Clean surface</strong></td></tr><tr><td>M<sub>1D</sub> – ortho</td><td>-0.56</td><td>-1.16</td><td>-0.77</td></tr><tr><td>M<sub>1D</sub> – flat</td><td><strong>-0.55</strong></td><td><strong>-1.38</strong></td><td><strong>-0.96</strong></td></tr><tr><td>M<sub>2D</sub> – ortho</td><td>-0.50</td><td>-0.78</td><td>-0.51</td></tr><tr><td>BH – flat</td><td><strong>-0.57</strong></td><td><strong>-1.60</strong></td><td><strong>-0.97</strong></td></tr><tr><td colspan="4"><strong>Defective surface</strong></td></tr><tr><td>BH – flat</td><td>-0.49</td><td>-1.28</td><td>-0.86</td></tr><tr><td>M'<sub>1D</sub> – flat</td><td><strong>-0.81</strong></td><td><strong>-1.60</strong></td><td><strong>-1.11</strong></td></tr><tr><td>M'<sub>2D</sub> – flat</td><td>-0.74</td><td>-0.80</td><td>-0.47</td></tr><tr><td>BB'<sub>2D</sub> – ortho</td><td>-0.66</td><td>-1.25</td><td>-0.88</td></tr></tbody></table>

### 3.3 Phenylphosphonic acid

Phosphonic anchoring groups are well-known to possess high affinity toward metal oxide surfaces,¹¹⁴,¹¹⁵ offering stable anchoring in water and highly oxidative environments. According to the degree of de-protonation, -PO₃H₂ can react with the metal surface to form one, two, or three tungsten-oxygen covalent bonds and one or two H-bonds. The calculated adsorption energies of all the configurations considered and displayed in Figure 5 are gathered in Table 3, while Table S8 in Supporting Information compiles some relevant structural parameters for isolated and WO₃-
grafted PA. The calculated surface deformation energies and the surface deformation parameters upon anchoring PA on clean and defective surfaces are reported in Tables S9 and S10, respectively.

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Optimized structure of phenylphosphonic acid on a) clean and b) defective (001) WO₃ surface. The light grey, black, and light red spheres represent the W, reduced W₆c and O atoms of WO₃ surface, respectively. The dark red, green, light blue and white spheres represent the OₚA, C, P and H atoms of PA molecule, respectively. Dashed lines indicate H bonding between the OH group and surface O atom.</figcaption></figure>

The particular W<sub>5c</sub> – W<sub>5c</sub> distances on the stoichiometric (001) WO<sub>3</sub> surface do not allow bidentate or tridentate binding as found on (101) TiO<sub>2</sub> anatase<sup>116</sup> and (100) NiO surfaces.<sup>117</sup> The possible M configurations are reported in Figure 5a, for the molecular and mono-deprotonated forms. In the undissociated case, for the monodentate anchoring with two H-bonds with O<sub>t</sub> surface atoms the calculated adsorption energy in solution along *a* (M<sup>a</sup>) and *b* (M<sup>b</sup>) are very similar, with
the latter favored by about 0.2 eV (−1.26 and −1.42 eV respectively). This is essentially due to
the contribution of the surface deformation energy, that for **M**<sup>a</sup> turns out to be higher by about
0.15 eV than for **M**<sup>b</sup>, thus reducing the interaction energy (Tables S9 in Supporting Information).
In both cases, the underneath W<sub>5c</sub> − O<sub>2p</sub> bond length stretched to 1.77 Å with the consequent
shortening of the O<sub>2p</sub> − W<sub>6c,2</sub> bond length to 2.24 Å. Thus, the O<sub>1p</sub> − W<sub>5c</sub> − O<sub>2p</sub> angle decreases
by about 6.3 and 4.7°, for **M**<sup>a</sup> and **M**<sup>b</sup>, respectively. Then, a weakly stable (−0.19 eV)
monodentate mono-deprotonated form was also found, **M**<sub>1D</sub><sup>b</sup>, in which one H-bond stabilizes the
covalent O − W linking.

In the sub-stoichiometric WO₃ surface, for the molecular M binding mode, we have considered
the PA attached to either W₅c or to reduced W₆c surface atoms (Figure 5b). First, when the
molecule adsorbs on W₅c, along *b* direction, **M**<sup>b</sup>, the calculated adsorption energy is −1.21 eV,
slightly lower than the value obtained when PA binds to reduced W₆c atom along *a*, **M**'<sup>a</sup>,
amounting to −1.32 eV. Then, the most stable anchoring mode is a bidentate bridging
configuration for the mono-deprotonated form, **BB**'<sub>1D</sub><sup>a</sup>, where the molecule is covalently bound
to a W₅c and to a reduced W₆c site, while the hydroxyl forms H-Bond with a O<sub>t</sub> surface atom. This
anchoring mode is by far the most stable one (ΔE<sub>ads</sub> = −1.60eV), in line with what was found
for anatase TiO₂.<sup>116</sup> As is apparent in Table S1 in Supporting Information, a similar picture is
obtained by using the rev-vdW-DF2 functional, with a predicted slightly higher adsorption energy
(-1.97 eV in water). We note that similar stabilization of bidentate coordination on defective
surfaces was also recently reported for delafossite CuCrO₂.<sup>77</sup> The corresponding structural features
is illustrated in Figure S4-b. Finally, when the molecule is fully deprotonated, contrary to the TiO₂
and NiO case, no tridentate coordination is possible due to unfavorable disposition of coordinative
W atoms on the surface, and only a much less stable bidentate anchoring was found ($BB'_{2D}$), with an adsorption energy of -0.79 eV.

<table><caption>**Table 3.** Calculated adsorption energies upon anchoring phenylphosphonic acid on the clean and defective (001) $WO_3$ in vacuum and implicit solvent.</caption><thead><tr><th rowspan="2">Anchoring modes</th><th colspan="2">In vacuum</th><th>In implicit solvent</th></tr><tr><th>ΔE<sub>disp</sub> (eV)</th><th>ΔE<sub>ads</sub> (eV)</th><th>ΔE<sub>ads</sub> (eV)</th></tr></thead><tbody><tr><td colspan="4" style="text-align: center; font-weight: bold;">Clean surface</td></tr><tr><td>M<sup>a</sup></td><td>-0.56</td><td>-2.12</td><td>-1.26</td></tr><tr><td>M<sup>b</sup></td><td><strong>-0.62</strong></td><td><strong>-2.27</strong></td><td><strong>-1.42</strong></td></tr><tr><td>M<sup>b</sup><sub>1D</sub></td><td>-0.59</td><td>-0.51</td><td>-0.19</td></tr><tr><td colspan="4" style="text-align: center; font-weight: bold;">Defective surface</td></tr><tr><td>M<sup>'a</sup></td><td>-0.67</td><td>-2.10</td><td>-1.32</td></tr><tr><td>M<sup>b</sup></td><td>-0.63</td><td>-2.02</td><td>-1.21</td></tr><tr><td>BB<sup>'a</sup><sub>1D</sub></td><td><strong>-0.68</strong></td><td><strong>-2.40</strong></td><td><strong>-1.60</strong></td></tr><tr><td>BB<sup>'a</sup><sub>2D</sub></td><td>-0.77</td><td>-1.24</td><td>-0.79</td></tr></tbody></table>

### 3.4 Summary and Conclusive Remarks

Understand the grafting behavior of anchoring groups on metal oxides such as $TiO_2$ and $WO_3$ is of high interest to design new efficient dye-sensitized photoelectrochemical cells. Until now the covalent anchoring of carboxylic acids to (101) $TiO_2$ anatase surfaces has been intensively investigated and most of the ab initio calculations identified the bidentate bridging mode with proton transfer to the surface as the preferred one. Calculated binding energies of monodentate modes were usually reported to be lower, although, a remarkable dependency of the relative
stability of these two adsorption modes on the level of theory can be highlighted. Concerning the
phosphonic acid, while the experimental assignment of the adsorption mechanism is not available,
theoretical calculations pointed to either monodentate or bidentate bridging modes as the most
stable ones. Typical calculated binding energies in vacuo for bidentate coordination of carboxylic
and phosphonic acids onto the most stable (101) TiO₂ anatase surface are of about 1.2 and 1.8 eV,
respectively.⁷⁶ On the other hand, molecular and dissociative adsorption, in both monodentate and
bidentate bridging mode, of catechol onto (101) TiO₂ anatase was reported to be less stable, with
calculated adsorption energies of about 0.8-0.9 eV; although defective surfaces were shown to
highly stabilize a bidentate chelating mode at about 2.5 eV.¹¹⁸

Here we have undertaken a detailed investigation on the binding mode of three anchoring groups,
on clean and oxygen-defective (001) WO₃ surfaces using first principles calculations and including
solvation effects and dispersion corrections. Based on the present results, both BA and PA
anchoring groups are preferably adsorbed in molecular monodentate mode on clean surfaces, while
the mono-deprotonated bidentate bridging binding mode becomes the preferred configuration on
defective surface, in line with the findings reported by some of us for p-type (012) CuCrO₂
surfaces.⁷⁷ In the case of Cat molecule, favoring in all cases a flat orientation with respect to the
surface plane, two configurations (BH – flat and M₁D – flat) were found to be very close in
energy in solution on clean surfaces, while it coordinates in mono-deprotonated monodentate mode
on defective surfaces. A summary of the most stable adsorption energies, in implicit solvent, of
the considered anchoring groups, on both clean and defective surface is displayed in Figure 6. As
is apparent, these values are comparable to those discussed above for adsorption on TiO₂ anatase
for the three anchoring groups, even if due to an unfavorable distance between adjacent W sites
on the (001) facet, bidentate coordination can only be realized on oxygen-deficient surfaces. It is
worthwhile to stress that the possibility to realize a bidentate anchoring between the dye and the
metal oxide surface has been shown to be important for maximizing the efficiency of the interfacial
electron transfer processes¹¹⁹ as well as for the overall device stability and performance. The
present results, providing for the first time atomic-scale details on the dye anchoring mechanism
on monoclinic WO₃ substrates, nicely rationalize the experimental evidence of a lower binding
strength and surface coverage of carboxylic and phosphonic acids groups onto WO₃ substrates
with respect to TiO₂ surfaces.⁶⁸ Our findings thus suggest novel design rules for the optimization
and the selection of alternative anchoring functionalities, better matching the surface W-W
patterns, for optimized WO₃-based DSSCs and hybrid photocatalysts.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Calculated adsorption energies of benzoic acid, catechol and phenylphosphonic acid on clean and defective surfaces in implicit solvent.</figcaption></figure>
**Supporting Information.** Calculated adsorption energies using PBE+D3_BJ and rev-vdW-DF2 functionals in vacuo and solution for Benzoic acid, catechol and phenylphosphonic acid on both clean and defective surfaces; Surfaces deformation energies calculations and parameters changes in the 2 first layers of clean and defective surfaces upon molecules adsorption; Optimized structural parameters of isolated clean and defective (001) WO₃ surfaces, isolated molecules, and anchored configurations on both clean and defective surfaces (PDF). Coordinates of the optimized configurations on clean and defective (001) WO₃ surfaces in POSCAR format (ZIP).

**Acknowledgement.** M.P. and M. B. are grateful to the financial support given by the COMETE project (COنception in silico de Matériaux pour l'Environnement et l'Energie), which is co-funded by the European Union under the program 'FEDER-FSE Lorraine et Massif des Vosges 2014-2020.

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