# Dye Anchoring on CuCrO2 Surfaces for p-Type Dye-Sensitized Solar Cell Applications: An Ab Initio Study

Dimple Dimple, Sébastien Lebègue, Mariachiara Pastore

► To cite this version:

Dimple Dimple, Sébastien Lebègue, Mariachiara Pastore. Dye Anchoring on CuCrO2 Surfaces for p-Type Dye-Sensitized Solar Cell Applications: An Ab Initio Study. ACS Applied Energy Materials, 2021, 4 (6), pp.6180-6190. 10.1021/acsaem.1c00970. [https://doi.org/10.1021/acsaem.1c00970](https://doi.org/10.1021/acsaem.1c00970). [doi: 10.1021/acsaem.1c00970](https://doi.org/10.1021/acsaem.1c00970)

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# Dye anchoring on CuCrO₂ surfaces for p-type DSSCs applications: an ab initio study

Dimple Dimpleª, Sébastien Lebègueª and Mariachiara Pastoreª,\*

ªUniversité de Lorraine & CNRS,
LPCT, UMR 7019, F-54000 Nancy, France

May 11, 2021

<footnote>\*corresponding author: mariachiara.pastore@univ-lorraine.fr</footnote>
<figure><img src="image_2.png" /></figure>

TOC
Abstract

The possibility of stably anchoring dye molecules on the exposed surface of a p-type semiconductor is crucial to have efficient dye-sensitized photoelectrodes. Here, we theoretically characterize the adsorption mechanism of carboxylic and phosphonic anchoring groups onto the (012) surface of stoichiometric and reduced CuCrO₂ delafossite. Density Functional Theory is employed to accurately predict the preferred adsorption modes and their energies, both in gas phase and solution (water and acetonitrile). On the stoichiometric (012) surface, we found a strong selectivity toward the molecular monodentate binding modes at the highly active Cr-sites, stabilized by strong Hydrogen-bonds with the surface oxygens, for both anchoring groups; deprotonated bidentate bridging anchoring is only identified when the proton transferred to the surface is kept far away from the molecule during the structural relaxation process. On the other hand, the bidentate anchoring becomes the preferred adsorption mode when Cu⁺ vacancies are considered at the topmost layer of the surface slab. The identification of stable bidentate bridging anchoring modes on the CuCrO₂ surface might have important implications for the device stability, as well as for the efficiency of the interfacial hole injection and suggest it as an alternative material to NiO for p-type DSSCs.

**keywords:** DSSCs; p-type semiconductors; Cu(I) delafossite; CuCrO₂; dye anchoring; Cu vacancies; DFT modeling

1 Introduction

Dye-sensitized solar cells (DSSCs) hold great promise as efficient photovoltaic devices, alternative to traditional Silicon-based technologies.¹ Thus, since their first inception in 1991 by O'Regan and Grätzel,² considerable research efforts have been addressed to the development of high-performing, low-cost and durable DSSCs. So far, the highest DSSCs power conversion efficiency is ~ 14% using an n-type TiO₂ photoanode as the working electrode.³ Alternatively, one can build a p-type DSSC, working in a reverse way, where the photoactive electrode is a dye-sensitized mesoporous transparent p-type semiconductor. The first example of a p-type DSSC was reported, indeed, in 1999 by Lindquist and co-workers using a porphyrin dye as a photosensitizer, nanoporous NiO as a p-type semiconductor to load the dye, and a liquid $I^−/I_3^−$ electrolyte redox mediator to undertake electron transport between the counter electrode and the photocathode.⁴ Subsequently, p-type DSSCs have been gaining tremendous interest due to their potential applications in the preparation of *tandem* dye-sensitized solar cells in cooperation with conventional n-type DSSCs.⁵,⁶ Despite the extensive research efforts to develop efficient
p-type electrodes, however, their solar-energy-to-electric-energy conversion efficiency is still one order of magnitude smaller than the n-type DSSCs, with the reported record efficiency of 2.5% for a NiO-based solar cell.⁷

The under performance of NiO-based DSSCs with respect to n-type counterparts is ascribed to a multitude of factors: (1) the $I^/-I_3^-$ redox couple, commonly used in DSSCs, yields low photovoltages due to the small energy difference with the valence band (VB) offset of NiO; (2) the low hole mobility of NiO, with a diffusion coefficient of $10^{-8}-10^{-7} \text{ cm}^2\text{s}^{-1}$,⁸ being more than two orders of magnitude lower than the electron diffusion coefficient of $\text{TiO}_2$, may favor fast back recombination process; (3) the quite low dielectric constant of NiO ($\epsilon$=9.7), compared to that of $\text{TiO}_2$ ($\epsilon$ =80), can cause the injected hole to be strongly bound with the electron residing on the dye, thus limiting the charge generation as suggested for ZnO ($\epsilon$=8) based n-type DSSCs.⁹ Such drawbacks in the use of NiO as sensitized photocathode are pushing toward the development of alternative p-type photocathodic materials, like, for instance, copper (Cu)-based delafossite oxides,¹⁰ oxysulfides¹¹,¹² and spinels materials.¹³

In particular, in the recent years, p-type Cu delafossite oxides have been hogging the lime-
light owing to their superior optoelectronic properties when compared to NiO.<sup>10,14-20</sup> The gen-
eral formula of these delafossite oxides is $\text{Cu}^+\text{M}^{3+}\text{O}_2$, where $\text{M}^{3+}$= $\text{B}^{3+}$, $\text{Al}^{3+}$, $\text{Ga}^{3+}$, $\text{In}^{3+}$,
$\text{Cr}^{3+}$, etc). In such delafossites, the mixing of Cu-3d states and O-2p states forming the VB
leads to a higher hole mobility. Tailoring the edge of the VB by mixing molecular orbitals of
the cations was proposed as a valuable strategy by Hosono and co-workers and demonstrated
for $\text{CuAlO}_2$ as the first p-type transparent delafossite.<sup>21</sup> In the quest for higher-performing p-
type delafossite oxides, $\text{CuCrO}_2$ has been the focus of recent interest due to its high density
of states of 3d chromium orbitals near the maximum of the VB and the covalent mixing be-
tween chromium and oxygen ions.<sup>22,23</sup> These two properties promote a larger hole mobility
and hence a greater conductivity is expected in this material. In 2012, Chen's group<sup>16</sup> reported
the hydrothermal synthesis of small $\text{CuCrO}_2$ nanocrystals and applied them as photocathodes
in p-type DSSCs. The deeper VB edge position of $\text{CuCrO}_2$ (+0.84 V vs. Normal Hydrogen
Electrode (NHE)) compared to NiO (+0.56 V vs. NHE) was confirmed using a Mott-Schottky
analysis.<sup>16</sup> In recent studies, Ahmadi et al.<sup>24</sup> reported a record value ($280 \text{ S.cm}^{-1}$) for the elec-
tric conductivity in CuCrO₂ co-doped with Mg and N. Resiner and coworkers had shown that CuCrO₂ photocathodes outperforms NiO yielding a higher onset potential of +0.75 V and an increased photocurrent (15 µA·cm⁻²).²⁵ Also, Powar et. al¹⁴ observed a high transient lifetime between the photo-generated dye anion and the electron vacancy (hole) in CuCrO₂ (140 ± 15 µs) compared to NiO DSSCs (24 ± 0.4 µs), which indicates an overall reduced recombination rate for CuCrO₂.

Despite the optimal opto-electronic properties of Cu-delafossites, their use in DSSCs did not result yet in an overall significant increase of photocurrent and device's efficiency.¹⁰,²⁶ To this end, boosting the performance of photocathodes requires acquiring fundamental knowledge on the structure, energetics and charge generation properties of the dye/oxide interface. Apart from the individual optoelectronic properties of dyes and semiconductors, a salient feature of efficient photoelectrodes is the formation of strong and stable dye-surface linkages, realized through the use of anchoring groups on the dye, which should also assure an efficient electronic coupling between the molecule and the metal oxide.²⁷ Historically, the two commonly employed anchoring groups in DSSCs are: carboxylic acid (–COOH) and phosphonic acid (–PO₃H₂). Different adsorption modes are likely to exist, with possibly different implications for the interfacial charge separation and the long-term stability.²⁷ Along with experimental investigations, a number of theoretical works have focused on the dye adsorption modes on the anatase TiO₂ surface.²⁸,³¹ In the case of carboxylic anchoring, most of the calculations pointed to the bidentate bridging mode with proton transfer to the surface as the most stable one, while monodentate anchoring was usually found to be less stable; it is worthwhile to note, however, a certain dependency of the relative stability of these two adsorption modes on the employed level of theory. As far as phosphonic acid is concerned, while there is no clear experimental assignment of the most stable adsorption mechanism, theoretical works identified either monodentate or bidentate bridging modes as the preferred ones.²⁹ Typical calculated adsorption energies in vacuo for –COOH and –PO₃H₂ onto the most stable (101) TiO₂ anatase surface are of ca. 1.2 and 1.8 eV, respectively,³⁰ with the latter giving stronger binding (higher device stability) at the price of a reduced electronic coupling (lower photocurrents). To date, on the other hand, a limited number of theoretical studies have been conducted to investigate the ad-
sorption mechanism of anchoring groups or dyes on p-type semiconducting surfaces.<sup>32-34,36,37</sup>

While there is an overall agreement on the identification of the bidentate bridging mode as the preferred one for both carboxylic and phosphonic groups anchoring to the (100) NiO surface at 0 K, the calculated binding energies reported in the literature strongly vary depending on the slab models and level of theory employed, with values ranging from about 0.8 to more than 3 eV.<sup>32-34</sup> Very recently Pavone and co-workers<sup>37</sup> reported a DFT study on the grafting of carboxylic and phosphonic groups onto pristine and Mg-doped CuGaO<sub>2</sub> surfaces, identifying monodentate configurations on the Ga sites as the most stable one, with calculated adsorption energies in vacuo of ca. 0.8 and 1.0 eV for CH<sub>3</sub>-COOH and CH<sub>3</sub>-PO<sub>3</sub>H<sub>2</sub>, respectively. Interesting, no stable bidentate or tridentate (for the phosphonic group) adsorption modes were obtained.

To the best of our knowledge, on the other hand, nothing is known, from both a theoretical and experimental point of view, about the adsorption of carboxylic and phosphonic acids on CuCrO<sub>2</sub> surfaces, despite its promising performances in DSSCs. Here we tackle this issue, reporting a systematic Density Functional Theory (DFT) investigation of the adsorption mechanism of CH<sub>3</sub>-COOH and CH<sub>3</sub>-PO<sub>3</sub>H<sub>2</sub> on the high-index (012) CuCrO<sub>2</sub> surface, considering implicit solvation effects and also taking into account the impact of Cu<sup>+</sup> vacancies on the different adsorption modes as well as on their stability. In earlier studies, Cu vacancies have been discussed mainly to understand the p-type conductivity of delafossites.<sup>22,38-40</sup> Herein, we present Cu<sup>+</sup> vacancy point defect and highlight their importance in stabilizing bidentate bridging (BB) modes.

## 2 Computational Methodology

Spin-polarized periodic density-functional theory (DFT) calculations were performed with the Vienna Ab initio Simulation Package (VASP) code.<sup>41,42</sup> The exchange correlation potential was described by Perdew-Burke-Ernzerhof<sup>43</sup> (PBE) functional within the generalized gradient approximation (GGA). The projector augmented wave method was used as the basis set.<sup>44,45</sup> For bulk CuCrO<sub>2</sub>, a full optimization of the cell parameters was carried out by using a cutoff energy of 550 eV and a 13×13×2 Γ-centered k-point sampling. Geometric relaxation was
deemed to be converged when the forces on all the atoms were less than 0.001 eV/Å. To describe the strong-correlated nature of the Cu and Cr 3d electrons, we applied the rotationally invariant DFT+U approach of Dudarev<sup>46</sup> as implemented in VASP.<sup>47</sup> Based on the previous work of Scanlon et. al,<sup>48</sup> we choose effective U values of 5.2 eV for the Cu-3d states and 4.0 eV for the Cr-3d states.

An orthorhomic supercell with lattice parameters a= 12.06 Å and b= 17.93 Å has been purposefully used for the surface adsorption calculations. The Brillouin zone was sampled with a 3×2×1 Γ-centered k-mesh. A vacuum thickness of more than 16 Å has been used to decouple the periodic images between adjacent surfaces in the thickness direction along c-axis. The DFT-D2 van der Waals (vdWs) correction proposed by Grimme<sup>49</sup> has been adopted to describe the long-range dispersive interactions as implemented in VASP.<sup>50</sup> Dipole and quadrupole corrections were applied along the direction perpendicular to the surface in order to eliminate spurious electrostatic interactions between periodic images.

In order to compare the adsorption energies, we have employed the PBE, PBE+D2, PBE+U and PBE+U+D2 methods in the vacuum. The binding energies were computed as the difference between the total energies of the combined adsorbate/substrate system and the (012) CuCrO<sub>2</sub> surface plus an isolated molecule,

$$ \Delta E_{ads} = E_{adsorbate/substrate} - (E_{substrate} + E_{adsorbate}) \quad (1) $$

For implicit solvation calculations, we used VASPsol,<sup>51</sup> a package that incorporates solvation calculations into VASP within a self-consistent linear polarizable continuum model (PCM). The solvation energies in implicit water ($\epsilon_{water}$=80.0) and acetonitrile ($\epsilon_{acetonitrile}$=37.5), the latter being a commonly employed solvent in DSSCs, were evaluated by performing single-point energy calculations on the structures optimized in vacuo, keeping the defaults setting parameters.<sup>52</sup>
# 3 Results and Discussion

This section is organized as follows: first, a brief description of bulk CuCrO₂ delafossite and its (012) surface properties will be given. Next, the choice of the supercell used is presented, and finally, the adsorption modes of the CH₃-COOH and CH₃-PO₃H₂ molecules on the (012) CuCrO₂ surface slab will be discussed.

## 3.1 Bulk CuCrO₂ and its (012) surface

Bulk CuCrO₂ exists in two polytypes, namely: a rhombohedral 3R and a hexagonal H-type, depending on the stacking of in-plane copper (Cu⁺) atoms and its edge-shared (regular) octahedron by chromium oxide (CrO₆) layers with $d_{Cr-O}$= 2.03 Å along the z-direction. These planes are connected by dumbbell-like O-Cu-O ($d_{Cu-O}$= 1.85 Å) bridges. Experimentally, CuCrO₂ crystallizes at room temperature in the 3R polytype with the R$\overline{3}$m space group symmetry.⁵³ We modeled the crystal structure of 3R CuCrO₂ in an hexagonal setting as shown in Figure 1 (a). The calculated lattice constants and structural parameters using the PBE and PBE+U levels of theory are tabulated in Table 1. These parameters are in good agreement with those reported in other theoretical and experimental studies.⁵³,⁵⁴ Moreover, bulk CuCrO₂ is reported as a triangular lattice antiferromagnetic (AFM)⁵⁵ insulator with a band gap > 3 eV⁵⁶ and a magnetic moment of 3.0 µB. Although we found similar kind of anti-ferromagnetism in the ground state, the calculated difference between the anti-ferromagnetic and ferromagnetic ground state energy was about 0.1 eV, consistently with previous results.⁵⁷ Therefore, in the present work, we have purposefully chosen the ferromagnetic state due to its smaller unit-cell requirement and simplicity (Figure 1 (a)).

Our simulated PXRD (powder x-ray diffraction) along with the experimental reference data¹⁶,⁵⁸ shows that different possible facets exist (such as (006), (012), (104), (110) etc.) for bulk CuCrO₂, although the preferred orientation is along its (012) high index plane as shown in Figure 1 (b).
<table><caption>Table 1: Optimized PBE and PBE+U structural parameters of bulk 3R-CuCrO₂: lattice constants (a and c in Å), volume, V (in Å³), bond lengths, d (in Å) and magnetic moment, μ (in μB); results of earlier experimental and theoretical studies are also reported for the sake of comparison.</caption><thead><tr><th></th><th>a(Å)</th><th>c(Å)</th><th>V (Å³)</th><th>d<sub>Cu-O</sub>(Å)</th><th>d<sub>Cr-O</sub>(Å)</th><th>μ(μ<sub>B</sub>)</th></tr></thead><tbody><tr><td>PBE</td><td>3.02</td><td>17.15</td><td>135.24</td><td>1.86</td><td>2.01</td><td>3.00</td></tr><tr><td>PBE+U</td><td>3.06</td><td>17.15</td><td>138.72</td><td>1.85</td><td>2.03</td><td>3.00</td></tr><tr><td>Exp.</td><td>2.98<sup>a,b</sup>,2.97<sup>c</sup></td><td>17.11<sup>a,b</sup>,17.06<sup>c</sup></td><td>131.2<sup>a</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>Th.</td><td>2.99<sup>d</sup>, 3.03<sup>e</sup></td><td>17.31<sup>d</sup>, 17.17<sup>e</sup></td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

Ref. a,⁵⁴ b,⁵³ c,⁵⁹ d,⁶⁰ and e⁶¹

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>Figure 1: (a) Bulk CuCrO₂ delafossite (3R) crystal structure where copper atoms (green) lie in-plane and stack alternatively with edge-shared chromium oxide layers in the z-direction. (b) The simulated PXRD plot along with experimental reference shows the different possible facets of CuCrO₂.</figcaption></figure>

Thus, we cleaved the (012) surface by taking into consideration its symmetry and stoichiometry in a periodic orthorhombic supercell as shown in Figure 2. We considered a surface slab composed of five layers (60 Cr, 60 Cu and 120 O atoms), in which the ferromagnetic ordering of bulk CuCrO₂ is preserved. To avoid spurious interaction between periodic replica, a vacuum space of ≈ 16 Å along the direction perpendicular to the surface was considered in the
simulations. The calculated surface energy for this symmetric and stoichiometric CuCrO₂ slab, obtained as the difference between the energy of the slab and that of bulk divided by twice the surface area of the slab,¹⁸ is 0.914 J.m⁻² and 0.962 J.m⁻² at the PBE and PBE+U levels of theory, respectively.

The surface morphology of the (012) CuCrO₂ surface is akin to a corrugated (non-planar) surface and is a mixture of all the cations (Cu⁺ and Cr³⁺) and anions (O²⁻) species available in the bulk component of CuCrO₂ as shown in Figure 2. The surface and sub-surface Cu⁺ atoms present the same bond coordination with the oxygen atoms, thus explaining their low reactivity to coordinate the molecule, as we shall discuss later. On the other hand, the surface Cr³⁺ and oxygen species are different from their respective sub-surface layers. The sub-surface Cr³⁺ atoms linked with six nearest neighboring oxygen atoms form a CrO₆ regular octahedral geometry, whereas on the surface, it is coordinated with just three oxygen atoms and exists in a distorted semi-octahedral form with d<sub>Cr-O<sub>B</sub></sub> = 2.03 Å and d<sub>Cr-O<sub>A</sub></sub> = 1.93 Å, where the surface oxygen atoms are of two types (O<sub>A</sub> and O<sub>B</sub>) on the (012) surface. Half the fraction of oxygen atoms, O<sub>B</sub>, form the usual linkage as available for the sub-surface oxygen atoms i.e. each oxygen atom is linked with their nearest neighbors of three Cr and one Cu atoms (see Figure 2); the other half fraction, O<sub>A</sub>, form bonds with two Cr and one Cu atom.
<figure><img src="image_5.png" /></figure>

Figure 2: The (012) surface in a periodic orthorhombic supercell with its cell parameters after cleaving bulk CuCrO₂. A distorted semi-octahedral of CrO₆ formed with cleavage which is different from sub-layer regular octahedral. The surface Oₐ-site and Oₐ-site represent the two different types of surface oxygen atoms. Oₐ are the surface oxygen atoms that form the active sites as they are linked with two Cr and one Cu atom. Oₐ are surface oxygen atoms that form the usual bond linkage as available for the sub-surface oxygen atoms i.e. each oxygen atom linked with their nearest neighbors of three Cr and one Cu atom.

## 3.2 Acetic acid on (012) CuCrO₂

The –COOH anchoring group is probably the most widely employed in DSSCs, since it assures high electronic coupling between the dye and the semiconductor, essential to allow fast interfacial hole/electron transfers. When interacting with a semiconductor substrate, the acidic proton can be either transferred to the oxide surface (both in a bidendate and monodentate anchoring mode) or be retained on the molecule and possibly interact with a surface oxygen via hydrogen-bonding.²⁷,⁶² If we consider the (012) CuCrO₂ surface, as schematized in Figure 3, in principle, two monodentate modes can exist, depending on whether the covalent bond is established with the Cu (M–CuH) or Cr (M–CrH) atom. The sub-index “H”indicate that –OH group can form H–bonding with an oxygen surface atom. Upon deprotonation and proton transfer to the surface, three possible bidentate bridging modes can occur: BB–Cu-Cu, BB–Cr-Cr and
BB-Cu-Cr, depending on the metal atoms to which the carboxylate anion is linked to.

Starting from the five guess adsorption configurations displayed in Figure 3, after structure relaxation, we ended up with only three stable adsorption modes, as shown in Figure 4: two monodentate coordinations on the Cr atom, M-Cr<sub>H</sub>, where the proton is shared by the molecule and by a nearby surface oxygen atom, and M-Cr, resulted from the optimization of the bidentate BB-Cu-Cr mode, and one bidentate bridging anchoring, BB-Cr-Cr. In other terms, covalent coordination to Cu atoms is unstable, as it could be expected on the basis of the fact that the surface Cu atoms are fully coordinated, presenting the same coordination of the bulk ones. Upon relaxation, indeed, the M-Cu<sub>H</sub> and the BB-Cu-Cu modes were converted into the M-Cr<sub>H</sub> and BB-Cr-Cr ones, respectively and the O-Cu bond in the BB-Cu-Cr was broken yielding the deprotonated monodentate M-Cr configuration. It is important to stress here that, following the approach employed in Ref.,<sup>37</sup> in building the initial guess structures of the BB modes, to avoid the transferred proton to go back to the molecule as in the case, for example, of the deprotonated monodentate M-Cr, we placed the H<sup>+</sup> sufficiently far from the anchoring group. This allowed us to identify all possible grafting modes, less stable at neutral or acidic pH, that might be present, however, when organic bases are added to the electrolyte.<sup>63,64</sup> The corresponding selected structural parameters of the optimized CH<sub>3</sub>-COOH@CuCrO<sub>2</sub> modes, together with their binding energies, obtained at the PBE+U+D2 level of theory, are listed in Table 2 and Table 3, respectively.

As indicated by the optimized structural parameters in Table 2, the O-Cr bond distances are rather short, around 2 Å, with the shortest value of 1.97 Å exhibited by the M-Cr structure. Similar values were reported in Ref.<sup>37</sup> for the CuGaO<sub>2</sub> surface. In the case of the M-Cr<sub>H</sub> configuration, interestingly, the proton is almost uniformly shared by the carboxylic and the surface oxygen atoms, with bond distances of 1.37 Å and 1.10 Å. This explains the relatively high stabilization of this monodentate adsorption on the CuCrO<sub>2</sub> surface, with a binding energy being more than two-fold in magnitude with respect to that of the monodentate and bidentate adsorption modes of acetic acid on NiO (001) and on the (012) CuGaO<sub>2</sub> surface.<sup>37</sup> As is apparent by comparing the dispersion-corrected binding energies in Table 3 with the ones reported in Table S1 in Supporting Information, inclusion of Grimme's correction has a major role in
<figure><img src="image_6.png" /><figcaption>Figure 3: Schematic representation of all possible binding modes for a carboxylic acid (—COOH) anchoring on CuCrO₂ (012) surface: monodentate (M) modes (M-Cu<sub>H</sub> and M-Cr<sub>H</sub>), bidentate bridging (BB) modes (BB-Cu-Cu, BB-Cr-Cr and BB-Cu-Cr). The sub index “H”indicates H-bonding (dashed line) between the OH group and a surface oxygen atom.</figcaption></figure>

stabilizing the molecule anchoring on the surface, and our best estimates of the adsorption energies (PBE+U+D2) indicate the monodentate M-Cr<sub>H</sub> as the preferred adsorption mode in gas phase, with an adsorption energy of 0.3 eV higher than the bidentate BB-Cr-Cr mode (-1.66 vs. -1.36 eV, in Table 3). Differently to what reported in Ref. 37, where no stable bidentate adsorption was found, we predict the anchoring on two Cr atoms, BB-Cr-Cr, to have quite a large binding energy in gas phase and to be further stabilized with respect to the monodentate configurations when implicit solvation is accounted for. Both in acetonitrile and water solution, indeed, the stability of the molecular monodentate adsorption mode slightly reduces due to the dielectric screening of the strong H-bond with the surface and the M-Cr<sub>H</sub> and BB-Cr-Cr configurations become isoenergetics. Inclusions of the solvent, clearly also stabilizes the dissociated monodentate mode, M-Cr, presenting a dangling C-O bond.

Under growth conditions of delafossites, the dominant intrinsic p-type defects are the Cu⁺ vacancies.<sup>40,65</sup> Therefore, in order to refine our structural model of the CuCrO₂ (012) surface and investigate the effect of native Cu vacancies on the -COOH adsorption mechanism and energetics, we created single Cu defects on the two uppermost surface layers, in proximity of the adsorbed molecule; we will hereafter refer to this surface as “reduced surface”. The presence of a single Cu⁺ vacancy on our slab gives a defect percentage of 1.7%, which is reasonable con-
sidering the experimental value (4 ± 2 %) obtained for CuGaO₂ via XPS (X-ray Photoelectron Spectroscopic) measurements.⁴⁰ A comparison between the total and partial density of states of the pristine and reduced surfaces shows that the Cu vacancy does not introduce significant intra-gap states (see Figure S3 in Supporting Information). Moreover, by looking at the difference in the Bader's charges between the clean and defective slabs (Figure S4 in Supporting Information), one can notice that the charges on the Cr atoms are only marginally changed by the presence of the defect, with a difference of charge of 0.04 electrons. The different positions of the Cu⁺ vacancy considered here are displayed in Figure 5, and the corresponding binding energies listed in Table 3. We examined both monodentate (M-Cr<sub>H</sub>) and bidentate-bridging (BB-Cr-Cr) adsorption configurations, creating a defect on the left (V<sub>1</sub><sup>L</sup> and V<sub>2</sub><sup>L</sup> on the first and second layer, respectively) and right sides (V<sub>1</sub><sup>R</sup> and V<sub>2</sub><sup>R</sup> on the first and second layer, respectively). When considering the four defects in the case of the M-Cr<sub>H</sub> mode, the first interesting finding is the possible stabilization of a bidentate anchoring form (V<sub>1,H</sub><sup>R</sup> BB' in Figure 5) when the Cu atom which is removed is linked to the surface oxygen H-bonded with the molecule. This defect, indeed, yields to structural changes in the monodentate coordination, with strengthening of the covalent bond between the surface oxygen and the proton (1.01 Å vs. 1.10 Å in Table 2) and weakening of the -COO-H bond (1.69 Å vs. 1.37 Å). The O atom, losing the coordination to the Cu, now can strongly bind to the proton of the -COOH anchoring group and, if a bidentate BB-Cr-Cr guess structure is created, by rotation of the COO anchoring, the proton is not transferred back to the molecule after optimization, resulting in the highly stable bidentate form shown in Figure 5. Notably, this configuration turns out to be the most stable one in gas phase, with a binding energies of -2.19 eV, among the ones optimized on both clean and defective CuCrO₂ surfaces (Table 3). The corresponding dissociative monodentate, V<sub>1</sub><sup>R</sup> M, as it could be expected, is slightly less stable in vacuo (-2.06 eV) but becomes isoenergetic to the BB' mode in solution, where the calculated adsorption energy is of about -1.80 eV. This defect position, therefore, remarkably stabilizes the carboxylic anchoring to the metal oxide surface, in both a bidentate and monodentate-deprotonated mode. The others defect positions, on the other hand, do not significantly affect the adsorption mechanism and energetics of the monodentate form, that remains around -1.60/-1.35 eV in gas phase/solution. Concerning the
bidentate structures, also in this case, a Cu vacancy on the first layer on the right side, that is
close to the surface oxygens bound to the Cr atoms coordinating the molecule, induce a slight
stabilization of the adsorption energy (about 0.2 eV) associated to a ca. 0.1 Å shortening in the
the COO-Cr bonds. These results thus suggest that surface Cu vacancies promote stabilization
of bidentate-anchoring modes which are less likely to occur on the clean surface. The calcu-
lated adsorption energies are comparable in magnitude with the ones calculated for the bidentate
bridging carboxylic anchoring on NiO and TiO₂,²⁷,³² and the possibility of having a bidentate
coordination might be beneficial for the electronic coupling and the interfacial electron transfer
processes.⁶⁶⁻⁶⁹

<figure><img src="image_7.png" /></figure>

Figure 4: Optimized structures of the CH<sub>3</sub>-COOH anchoring group on the CuCrO<sub>2</sub> (012) surface. Labels according to the anchoring mode [mondodentate (M) and bidentate bridging (BB)] and to the surface atoms involved in the adsorption process. Sub index “H” indicates H-bonding (dashed line) between the OH group and the surface oxygen atom upon relaxation in M cases. Color legend: Cu (green), Cr (blue), O (red), C (brown), and H (light pink).
<table><caption>Table 2: Selected optimized (PBE+U+D2) structural parameters (units in Å) for CH₃-COOH anchored on clean and defective CuCrO₂ (012) in their different adsorption modes.</caption><thead><tr><th rowspan="2">Anchoring mode</th><th colspan="6">Bond distances (Å)</th></tr><tr><th>d<sub>C-O1</sub></th><th>d<sub>C-O2</sub></th><th>d<sub>O2-H</sub></th><th>d<sub>O1-Cr</sub></th><th>d<sub>O2-Cr</sub></th><th>d<sub>H-Os</sub></th></tr></thead><tbody><tr><td>Isolated molecule</td><td>1.22</td><td>1.37</td><td>0.98</td><td></td><td></td><td></td></tr><tr><td colspan="7"><em>Clean CuCrO<sub>2</sub> (012)</em></td></tr><tr><td>M-Cr<sub>H</sub></td><td>1.29</td><td>1.27</td><td>1.37</td><td>2.03</td><td></td><td>1.10</td></tr><tr><td>M-Cr</td><td>1.23</td><td>1.32</td><td></td><td></td><td>1.97</td><td></td></tr><tr><td>BB-Cr-Cr</td><td>1.28</td><td>1.28</td><td></td><td>2.05</td><td>2.05</td><td></td></tr><tr><td colspan="7"><em>Defective CuCrO<sub>2</sub> (012)</em></td></tr><tr><td>V<sub>1</sub><sup>L</sup> M</td><td>1.28</td><td>1.28</td><td>1.34</td><td>2.03</td><td></td><td>1.12</td></tr><tr><td>V<sub>1</sub><sup>R</sup> M</td><td>1.30</td><td>1.25</td><td>1.69</td><td>1.99</td><td></td><td>1.01</td></tr><tr><td>V<sub>2</sub><sup>L</sup> M</td><td>1.29</td><td>1.27</td><td>1.38</td><td>2.03</td><td></td><td>1.10</td></tr><tr><td>V<sub>2</sub><sup>R</sup> M</td><td>1.29</td><td>1.27</td><td>1.41</td><td>2.02</td><td></td><td>1.09</td></tr><tr><td>V<sub>1</sub><sup>R</sup><sub>H</sub> BB'</td><td>1.29</td><td>1.28</td><td></td><td>2.03</td><td>2.04</td><td></td></tr><tr><td>V<sub>1</sub><sup>L</sup> BB</td><td>1.28</td><td>1.28</td><td></td><td>2.02</td><td>2.02</td><td></td></tr><tr><td>V<sub>1</sub><sup>R</sup> BB</td><td>1.28</td><td>1.28</td><td></td><td>2.04</td><td>2.04</td><td></td></tr><tr><td>V<sub>2</sub><sup>L</sup> BB</td><td>1.28</td><td>1.28</td><td></td><td>2.05</td><td>2.05</td><td></td></tr><tr><td>V<sub>2</sub><sup>R</sup> BB</td><td>1.27</td><td>1.28</td><td></td><td>2.09</td><td>2.04</td><td></td></tr></tbody></table>

<table><caption>Table 3: Calculated adsorption energies, ΔE<sub>ads</sub> (eV) for CH₃-COOH anchored on clean and defective CuCrO₂ (012) in their different adsorption modes calculated at the DFT PBE+U+D2 level of theory in gas phase, and in implicit solution (water and acetonitrile)</caption><thead><tr><th rowspan="3">Anchoring modes</th><th>Gas Phase</th><th>Water</th><th>Acetonitrile</th></tr><tr><th colspan="3">ΔE<sub>ads</sub></th></tr><tr><th colspan="3"><em>Clean CuCrO<sub>2</sub> (012)</em></th></tr></thead><tbody><tr><td>M-Cr<sub>H</sub></td><td>-1.66</td><td>-1.33</td><td>-1.38</td></tr><tr><td>M-Cr</td><td>-0.16</td><td>-0.53</td><td>-0.51</td></tr><tr><td>BB-Cr-Cr</td><td>-1.36</td><td>-1.37</td><td>-1.40</td></tr><tr><th colspan="4"><em>Defective CuCrO<sub>2</sub> (012)</em></th></tr><tr><td>V<sub>1</sub><sup>L</sup> M</td><td>-1.58</td><td>-1.26</td><td>-1.31</td></tr><tr><td>V<sub>1</sub><sup>R</sup> M</td><td>-2.06</td><td>-1.78</td><td>-1.82</td></tr><tr><td>V<sub>2</sub><sup>L</sup> M</td><td>-1.64</td><td>-1.33</td><td>-1.38</td></tr><tr><td>V<sub>2</sub><sup>R</sup> M</td><td>-1.67</td><td>-1.36</td><td>-1.40</td></tr><tr><td>V<sub>1</sub><sup>R</sup><sub>H</sub> BB'</td><td>-2.19</td><td>-1.77</td><td>-1.84</td></tr><tr><td>V<sub>1</sub><sup>L</sup> BB</td><td>-1.23</td><td>-1.23</td><td>-1.25</td></tr><tr><td>V<sub>1</sub><sup>R</sup> BB</td><td>-1.59</td><td>-1.45</td><td>-1.49</td></tr><tr><td>V<sub>2</sub><sup>L</sup> BB</td><td>-1.37</td><td>-1.36</td><td>-1.39</td></tr><tr><td>V<sub>2</sub><sup>R</sup> BB</td><td>-1.25</td><td>-1.27</td><td>-1.30</td></tr></tbody></table>
<figure><img src="image_8.png" /></figure>

Figure 5: Formation of a single atom Cu-vacancy around the adsorbed anchoring CH₃-COOH molecule on the top two surface layers CuCrO₂ (012). The label V₁¹/₂¹M/BB represents the Cu-vacancy site where 1/2 is the first/second layer, L/R is the left/right to the anchored site and M/BB represent monodentate/bidentate-bridging mode. The yellow highlighted site pointed with arrow symbol represents the Cu defect-site.

## 3.3 Phosphonic acid on (012) CuCrO₂

The possible anchoring modes of the phosphonic acid on the CuCrO₂ (012) surface, according to the degree of deprotonation, are depicted in Figure 6. In principle, the neutral form, -PO₃H₂, can form one covalent bond with Cr (M-Cr₂H) or Cu (M-Cu₂H), where the “2H” notation indicates that the two protons are retained by the molecule and can form H-bonds with the surface oxygen atoms. The monodeprotonated form, [-PO₃H]⁻, can bind in a bidentate bridging fashion to two Cr (BB-Cr-CrH) or two Cu (BB-Cu-CuH), as well as to a CuCr pair (BB-Cu-CrH). Finally, if both the protons are transferred to the surface, [-PO₃]²⁻, in principle
ple, two tridentate modes are possible (T-Cu-Cu-Cr and T-Cu-Cr-Cr). Note that a tridentate coordination of the phosphonic group was found to be stabilized at room temperature in water on the (100) NiO surface.32 As discussed above for the carboxylic group, also in this case, for the BB and T modes, the H atoms have been attached to surface oxygen atoms as far as possible from the anchoring group.

<figure><img src="image_9.png" /><figcaption>Figure 6: Schematic representation of all possible binding modes for a phosphonic acid (–PO$_3$H$_2$) anchoring on the CuCrO$_2$ (012) surface: monodentate (M) modes (M-Cu$_{2}$H and M-Cr$_{2}$H), bidentate bridging (BB) modes (BB-Cu-Cu$_H$, BB-Cr-Cr$_H$ and BB-Cu-Cr$_H$) and tridentate (T) modes (T-Cu-Cu-Cr and T-Cu-Cr-Cr).</figcaption></figure>

The only three stable adsorption configurations obtained after full structural relaxation of the considered guess structures are shown in Figure 7. As discussed in the previous section for -COOH, the chemical grafting to Cu sites is unstable and, upon relaxation, M-Cu$_{2}$H and B-Cu-Cu$_H$ were converted into M-Cr$_{2}$H and BB-Cr-Cr$_H$, respectively. The corresponding optimized structural parameters together with the binding energies (ΔE$_{ads}$) of all the stable modes are listed in Table 4 and Table 5, respectively. Monodentate, M-Cr$_{2}$H, and bidentate, BB-Cr-Cr$_H$, anchoring modes are, interestingly, very close in energy in both gas phase (-2.19 and -2.11 eV, respectively) and solution (-1.73/-1.82 and -1.86/-1.92 eV in water/ACN, respectively) and,
as expected, their adsorption energy significantly exceeds (ca. 0.5 eV) that calculated for the carboxylic anchoring group (Table 3). This magnitude of binding energy is more than two-fold in magnitude with respect to the monodentate M-Cr<sub>2H</sub> mode occurred on the NiO (001) and CuGaO<sub>2</sub> (012) surface<sup>37</sup> when Grimme's correction was taken into consideration. Structural relaxation of the tridentate T-Cr-Cr-Cu configuration (Figure 6) clearly ended up in a weakly stable dissociated bidentate Cr-Cr structure (BB-Cr-Cr), due to the impossibility to keep the coordination to the Cu atom. Inclusion of solvent dielectric screening stabilizes this configuration, which, however, with a calculated adsorption energy of about -0.8 eV (at the PBE+U+D2 level) is not likely to occur.

Moving to the reduced (012) surface (Figure 8) and following the same scheme of Cu vacancies creation for both monodentate (M-Cr<sub>2H</sub>) and bidentate bridging (BB-Cr-Cr<sub>H</sub>) modes discussed in the previous section, we again observe stabilization of the molecular monodentate mode when the defect is created on the right side and on the top layer ($V_1^R$ M in Figure 8). The adsorption energy increases from -2.19 to -2.51 eV in gas phase and from about -1.8 to -2.3 eV in solution, as a consequence of peculiar structural rearrangements similar to the ones discussed above for the carboxylic group. As shown by the optimized bond distances reported in Table 4, one of the two strong H-bonds (H<sub>1/2</sub>-O<sub>s</sub>1.49 Å), the one corresponding to the oxygen contiguous to the Cu vacancy, becomes a true covalent bond (1.02 Å) with consequent deprotonation of the molecule (O<sub>2</sub>-H<sub>2</sub> from 1.06 to 1.65 Å). This rearrangement is somewhat counterbalanced on the other OH group, by shortening of the covalent O<sub>1</sub>-H<sub>1</sub> bond (from 1.06 to 1.01 Å) and elongation of the O<sub>s</sub>-H<sub>1</sub> bond (from 1.49 to 1.71 Å). Starting from this monodentate deprotonated structure, a bidentate mode can be easily stabilized, $V_{1H}^R$ BB, with a gain of 0.4 eV in the binding energy (-2.91 and ca. -2.70 eV in gas phase and solution, respectively, Table 5). Interestingly, this is by far the most stable adsorption configuration predicted for the phosphonic acid, suggesting again that surface Cu defects promote a stable bidentate coordination to the CuCrO<sub>2</sub> surface. On the other hand, the deprotonated bidentate anchoring, BB-Cr-Cr<sub>H</sub>, is not significantly stabilized/destabilized by neighboring Cu vacancies, with only a negligible 0.05 eV increase in the binding energy when the defect is on the right side and on the top surface layer ($V_1^R$ BB in Table 5).
<figure><img src="image_10.png" /><figcaption>Figure 7: Optimized structures of the CH<sub>3</sub>−PO<sub>3</sub>H<sub>2</sub> anchoring group on CuCrO<sub>2</sub> (012) surface. Labels according to the anchoring mode [mondodentate (M) and bidentate bridging (BB)] and to the surface atoms involved in the adsorption process. Sub index "H" indicates H bonding (dashed line) between the OH group and surface oxygen atom upon relaxation in M cases. Color legend: Cu (green), Cr (blue), O (red), C (brown), P (lavender) and H (light pink).</figcaption></figure>

<table><caption>Table 4: Selected optimized (PBE+U+D2) structural parameters (units in Å) for CH<sub>3</sub>PO<sub>3</sub>H<sub>2</sub> anchored on clean and defective CuCrO<sub>2</sub> (012) in different adsorption modes.</caption><thead><tr><th rowspan="2">Anchoring modes</th><th colspan="9">Bond distances (Å)</th></tr><tr><th>d<sub>P-O1</sub></th><th>d<sub>P-O2</sub></th><th>d<sub>P-O3</sub></th><th>d<sub>O1-H1</sub></th><th>d<sub>O2-H2</sub></th><th>d<sub>O3-Cr</sub></th><th>d<sub>O1-Cr</sub></th><th>d<sub>H1-Os</sub></th><th>d<sub>H2-Os</sub></th></tr></thead><tbody><tr><td>Isolated molecule</td><td>1.62</td><td>1.61</td><td>1.48</td><td>0.98</td><td>0.98</td><td></td><td></td><td></td><td></td></tr><tr><td colspan="10" style="text-align: center; font-style: italic;">Clean CuCrO<sub>2</sub> (012)</td></tr><tr><td>M-Cr<sub>2H</sub></td><td>1.58</td><td>1.58</td><td>1.54</td><td>1.06</td><td>1.06</td><td>2.04</td><td></td><td>1.49</td><td>1.49</td></tr><tr><td>BB-Cr-Cr<sub>H</sub></td><td>1.54</td><td>1.60</td><td>1.54</td><td></td><td>1.01</td><td>2.04</td><td>2.04</td><td></td><td>1.77</td></tr><tr><td>BB-Cr-Cr</td><td>1.51</td><td>1.58</td><td>1.58</td><td></td><td></td><td>1.97</td><td>1.97</td><td></td><td></td></tr><tr><td colspan="10" style="text-align: center; font-style: italic;">Defective CuCrO<sub>2</sub> (012)</td></tr><tr><td>V<sub>1</sub><sup>L</sup> M</td><td>1.58</td><td>1.58</td><td>1.53</td><td>1.06</td><td>1.06</td><td>2.04</td><td></td><td>1.50</td><td>1.50</td></tr><tr><td>V<sub>1</sub><sup>R</sup> M</td><td>1.61</td><td>1.51</td><td>1.57</td><td>1.01</td><td>1.65</td><td>1.99</td><td></td><td>1.71</td><td>1.02</td></tr><tr><td>V<sub>2</sub><sup>L</sup> M</td><td>1.58</td><td>1.58</td><td>1.54</td><td>1.06</td><td>1.06</td><td>2.05</td><td></td><td>1.49</td><td>1.49</td></tr><tr><td>V<sub>2</sub><sup>R</sup> M</td><td>1.58</td><td>1.58</td><td>1.53</td><td>1.06</td><td>1.06</td><td>2.08</td><td></td><td>1.50</td><td>1.50</td></tr><tr><td>V<sub>1</sub><sup>R</sup> BB</td><td>1.57</td><td>1.52</td><td>1.59</td><td></td><td>1.76</td><td>1.99</td><td>1.97</td><td></td><td>1.01</td></tr><tr><td>V<sub>1</sub><sup>L</sup> BB</td><td>1.55</td><td>1.61</td><td>1.54</td><td></td><td>1.01</td><td>2.03</td><td>2.04</td><td></td><td>1.78</td></tr><tr><td>V<sub>1</sub><sup>R</sup> BB</td><td>1.54</td><td>1.68</td><td>1.54</td><td></td><td>1.01</td><td>1.54</td><td>1.54</td><td></td><td>1.77</td></tr><tr><td>V<sub>2</sub><sup>L</sup> BB</td><td>1.54</td><td>1.60</td><td>1.54</td><td></td><td>1.01</td><td>2.05</td><td>2.05</td><td></td><td>1.76</td></tr><tr><td>V<sub>2</sub><sup>R</sup> BB</td><td>1.54</td><td>1.61</td><td>1.55</td><td></td><td>1.01</td><td>2.04</td><td>2.08</td><td></td><td>1.79</td></tr></tbody></table>
<table><caption>Table 5: Calculated adsorption energies, ΔE<sub>ads</sub> (eV) for CH<sub>3</sub>−PO−(OH)<sub>2</sub> anchored on clean and defective CuCrO<sub>2</sub> (012) in their different adsorption modes calculated at the DFT PBE+U+D2 level of theory in gas phase, and in implicit solution (water and acetonitrile)</caption><thead><tr><th rowspan="3">Anchoring modes</th><th>Gas Phase</th><th>Water</th><th>Acetonitrile</th></tr><tr><th colspan="3">ΔE<sub>ads</sub></th></tr><tr><th colspan="3">Clean CuCrO<sub>2</sub> (012)</th></tr></thead><tbody><tr><td>M-Cr<sub>2H</sub></td><td>-2.19</td><td>-1.73</td><td>-1.82</td></tr><tr><td>BB-Cr-Cr<sub>H</sub></td><td>-2.11</td><td>-1.86</td><td>-1.92</td></tr><tr><td>BB-Cr-Cr</td><td>-0.30</td><td>-0.84</td><td>-0.82</td></tr><tr><th colspan="4">Defective CuCrO<sub>2</sub> (012)</th></tr><tr><td>V<sub>1</sub><sup>L</sup> M</td><td>-2.09</td><td>-1.67</td><td>-1.75</td></tr><tr><td>V<sub>1</sub><sup>R</sup> M</td><td>-2.51</td><td>-2.26</td><td>-2.33</td></tr><tr><td>V<sub>2</sub><sup>L</sup> M</td><td>-2.17</td><td>-1.72</td><td>-1.81</td></tr><tr><td>V<sub>2</sub><sup>R</sup> M</td><td>-1.99</td><td>-1.59</td><td>-1.67</td></tr><tr><td>V<sub>1</sub><sup>R</sup><sub>H</sub> BB</td><td>-2.91</td><td>-2.72</td><td>-2.79</td></tr><tr><td>V<sub>1</sub><sup>L</sup> BB</td><td>-1.80</td><td>-1.78</td><td>-1.83</td></tr><tr><td>V<sub>1</sub><sup>R</sup> BB</td><td>-2.16</td><td>-1.93</td><td>-2.01</td></tr><tr><td>V<sub>2</sub><sup>L</sup> BB</td><td>-1.95</td><td>-1.85</td><td>-1.91</td></tr><tr><td>V<sub>2</sub><sup>R</sup> BB</td><td>-1.80</td><td>-1.74</td><td>-1.80</td></tr></tbody></table>
<figure><img src="image_11.png" /><figcaption>Figure 8: Formation of the Cu mono-vacancy around the adsorbed anchoring CH<sub>3</sub>–PO<sub>3</sub>H<sub>2</sub> molecule on the top two surface layers CuCrO<sub>2</sub> (012). The label V<sub>1/2</sub><sup>L/R</sup> M/BB represents the Cu-vacancy site where 1/2 is the first/second layer, L/R is the left/right to the anchored site and M/BB represent monodentate/bidentate-bridging mode. The yellow highlighted site pointed with arrow symbol represents the Cu defect-site.</figcaption></figure>

# 4 Conclusion

Here we have investigated the possibility of using the CuCrO₂ delafossite oxide as an alternative material to NiO for p-type DSSCs. We have modeled the anchoring mechanism of the carboxylic and phosphonic groups as well as their stability, in vacuo and in implicit solution, on pristine and defective (Cu⁺ vacancies) CuCrO₂ (012) surface models. To this aim, DFT calculations at the PBE, PBE+D2, PBE+U and PBE+U+D2 level of theory have been carried out, systematically considering all the possible adsorbed configurations for each protonation state of the acidic groups. Overall, the present results indicate that, the two anchoring groups stably
adsorb on the CuCrO₂ (012) surface, with comparable binding energies, and even larger, to that calculated for NiO. The phosphonic group is found, in line with the results obtained on other metal oxide surfaces, to have a larger adsorption energy. More interestingly, while monodentate adsorption is preferred on clean surfaces, unless the protons are forced to remain on the substrate by putting them far from the molecule, bidentate bridging modes are largely stabilized on defective slabs, when the Cu⁺ vacancy is adjacent to the surface O atom interacting by a H-bond with the molecule. This particular defect position allows the surface oxygen to cova lently bind the proton coming from the molecule, resulting in the deprotonation of the anchoring group and in the consequent stabilization on a bidentate coordination to two Cr sites. The pos sibility to form bidentate linking between the dye and the metal oxide surface has been shown to be beneficial for the efficiency of the interfacial electron transfer processes and thus for the overall DSSC performances. These findings, providing for the first time atomistic insights on the mechanism of dye adsorption on CuCrO₂ (012) surfaces, might indicate possible routes for the optimization and the selection of alternative anchoring groups for Cu(I)-delafossite- based DSSCs.

**Supporting Information**

Optimized structures and atom labeling of CH₃-COOH and CH₃-PO₃H₂. Total and partial density of states (DOS, PDOS) of the pristine and defective surface slab. Bader's charges on some representative Cr atoms for the pristine and defective slabs. PBE, PBE+U and PBE+D2 adsorption energies calculated in vacuo for the carboxylic and the phosponic acid groups on both the clean and defective surfaces.

**5 Acknowledgment**

This work has been carried out in the framework of the ANR JCJC HELIOSH2 project (ANR-17-CE05-0007-01). HPC resources from the mésocentre EXPLOR of Université de Lorraine and LPCT local computational resources are greatly acknowledged.
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