Strain engineering for tuning the photocatalytic activity of metal-organic frameworks – Theoretical study of the UiO-66 case

: In recent years, the class of metal-organic framework (MOF) materials emerged. These materials' unique properties can be assigned to their structure, containing inorganic nodes connected with organic linkers. Due to their porosity and flexibility, MOFs have become suitable for various energy-related applications, including gas storage, hydrogen production and heterogeneous catalysis, and photocatalysis. Using DFT+ U calculations, we show that the substitution of metal centers in inorganic nodes and the strain engineering of UiO-66 alters the electronic and optical properties of this material. We show that applying mechanical strain on UiO-66 enables the control of absorption coefficient in the UV-Vis spectrum and the photocatalytic processes' selectivity when reactants for several photocatalytic processes are present. The presented findings could lead to general strategies for designing novel MOFs for sustainable energy conversion applications. smearing width of σ = the levels' occupation Monkhorst-Pack Γ-centered -point employed for the relaxation calculations. relaxation of all atoms in the simulation cell was unrestricted. relaxation procedure was until the Hellmann-Feynman forces on all atoms were 0.01 −1 in all of the presented calculations.


Introduction
In recent years there has been an ongoing challenge of using clean energy sources. One of the most abundant and versatile clean energy sources is Solar energy. There are many possibilities of using this renewable source. Besides photoelectrochemical and photovoltaic systems [1,2], one of the main uses of Solar energy is heterogeneous photocatalysis. The photocatalytic processes include three main steps3: 1) Absorption of photon 2) Creation of electron-hole pair (exciton) which can migrate to catalytic centers, and 3) Redox reactions with substrates.
Regarding these steps in a photocatalytic process, a material used as a photocatalyst should possess strong solar radiation absorption, a very long lifetime of excited states, and good charge mobility to prevent rapid recombination [3,4]. Ever since the discovery of TiO2 as a suitable catalyst for water photosplitting [5], there has been an expansion in the research and development of new synthetic photocatalysts. The main focus has recently been placed on a new class of materials known as metal-organic frameworks (MOFs) [6,7]. Due to their specific structure, which contains metal nodes connected with organic linkers, MOFs showed great potential for energy storage and conversion-related applications, such as capacitors and Li-ion batteries [8][9][10]. Different pore sizes inside MOFs and exchangeable building units make this material suitable for gas storage and hydrogen production [11,12]. Also, MOFs' high porosity leads to an increased number of active sites, making them convenient for catalytic processes [13], including photocatalytic ones [14][15][16].
When we look at different metal-organic framework structures, we can see that the metal nodes usually consist of monovalent and divalent, but also trivalent and four va-lent metals such as Zr 4+ , Ti 4+ . The most stable structures often have four valent metals [17]. In that kind of system, metal clusters can contain up to twelve metal ions. When it comes to the connection between the building units, there is great diversity, particularly in materials containing Zr ions. Nevertheless, in these MOFs, clusters are predominantly built from highly symmetrical units in the form of Zr6O8. Considering the topology, MOFs can have different numbers of connecting points [6,8,12].
UiO-66 is one of the most investigated MOFs to this day, justified by its chemical, thermal and mechanical stability [18]. In its original form, it has Zr metal centers and the fcc structure [19]. Possible modifications of UiO-66(Zr) using either the functionalization of linkers or replacements of Zr centers with other metals were reported [20,21]. Wu et al. [22] systematically investigated the modification of UiO-66(Zr) using both strategies and found that the longer-lived excited states in Ce-based UiO-66, UiO-66(Ce) than in UiO-66 MOFs with other metals, ascribed to the facile charge separation in the case of UiO-66(Ce). The authors further showed that the functionalization of the linkers (1,4-benzene-dicarboxylate) enables modification of the electronic structure of UiO-66(Ce), enabling the tuning of the photocatalytic activity.
Due to very open structures, MOFs belong to the soft materials class [23], and small mechanical strain can be applied to them without irreversible structural changes. Their flexibility was recently employed for the development of strain-based sensors with unprecedented performances [24]. Here we show that the strain engineering in MOFs can be an excellent tool for modifying the electronic structure and the band gap, allowing the modification of optical and photocatalytic properties. For this purpose, we compare the effects of strain on UiO-66(Zr) and UiO-66(Ce), demonstrating the effects in the latter case. Using mechanical strain, we show that one can exclude undesired photochemical processes and obtain high selectivity, which is a great challenge in practice.

Geometry
The optimized structures of UiO-66(Zr) and UiO-66(Ce) (Figure 1) have triclinic primitive cells with a0 = 14.834 Å for Zr and a0 = 15.440 Å for the Ce case. This difference is dominantly due to the M-O bond lengths, amounting to 2.216 Å for Zr-O and 2.395 Å for the Ce-O bond. Upon analyzing the optimized structures, we see that the M-O bonds behave differently in these two cases. Namely, the Zr-O bond is rather rigid, and its change upon the application of strain is relatively small. For the applied strain of −3%, the Zr-O bond is changed to 2.191 Å. However, in the Ce case, the Ce-O bond contracts to 2.312 Å. As a result, the optimized structures with the negative strain (contraction, Figure 2) look qualitatively different. In the case of Zr-based MOF, due to the rigidity of the Zr-O bond, the contraction is compensated with the deformation of the linker. In contrast, for the Ce-based MOF, the deformation of the Ce-O bond compensates the applied strain. The situation is similar for the positive strain (expansion of the lattice).

Electronic structure
Upon optimizing the crystal structures, we turn to analyzing the electronic structures of studied MOFs ( Figure 3). Densities of States (DOS) show a bandgap in all the cases, which is effectively tuned by the applied strain (Table 1). For UiO-66(Zr), the calculated bandgap for the unstrained structure is 2.98 eV, which is lower than the experimental value (3.76 eV [25]) and the HSE06//PBEsol result [22]. This difference is expected due to the level of theory that we have used. For UiO-66(Ce), the HSE06//PBEsol result is 2.66 eV [22]. The DOS profiles agree with the hybrid calculations, showing that for UiO-66(Zr) the Zr 4d states are well above the bottom of the conduction band. However, for UiO-66(Ce) the Ce 4f states form the conduction band. In the case of UiO-66(Ce), the bandgap is much more sensitive to the applied strain. The lattice contraction causes the increase of the bandgap, while the expansion of the lattice increases the bandgap (Table  1). It is interesting to observe that the applied strain does not cause much change in the Zr 4d states but greatly affects the Ce 4f states, which we will discuss later. As the Ce 4f states form the conduction band, this also reflects on the optical properties of UiO-66(Ce), presented in the next section.

Optical properties
UiO-66(Zr) is a white-colored substance with optical absorption below 300 nm and an absorbance maximum around 250 nm [27]. Compared to our result (Figure 3a), the absorption maximum is shifted to higher energy as the experimental bandgap is larger than the one we calculated. However, the qualitative agreement is rather good. As the strain affect the bandgap of UiO-66(Zr) very little (except for the largest negative strain, Table 1), optical spectra are little affected by strain. However, for UiO-66(Ce), the effect of strain on the optical absorption is appreciable. Negative strain (lattice contraction) causes the blueshift of the optical spectra, while the positive strain (lattice expansion) causes the redshift of the optical spectra (Figure 3b). Moreover, the absorption coefficient is larger for UiO-66(Ce) compared to UiO-66(Zr) (Figure 3). Besides the tuning of the bandgap via applied strain, a possibility to tune the optical absorption using strain is another strong indication that the strain engineering can be applied as a tool for controlling the photocatalytic properties of MOFs.

Tuning selectivity of the photocatalytic process via strain
Finally, we present the results of the band alignment procedure for UiO-66(Zr) (Figure 5a) and UiO-66(Ce) (Figure 5b). For the Standard Hydrogen Electrode (SHE) absolute value, we took 4.44 eV [28]. The potentials of other redox couples in Figure 5 are then recalculated to the vacuum scale. We note that there is an uncertainty of the value of the absolute potential of SHE, so the final result of the band alignment procedure has an uncertainty of approx. ±0.2 eV [29]. Besides the potentials of H + /H2 and O2/H2O couples, we also added the couples corresponding to the CO2 reduction process, using the summary of standard electrode potentials reported by Wu et al. [22].  We see that the valence band (VB) top is weakly affected by the applied strain for both investigated MOFs. However, for UiO-66(Ce), the conduction band (CB) bottom shifts significantly with the applied strain. This result gives a possibility to tune the photocatalytic activity of UiO-66(Ce) using strain. For example, for the unstrained Ce-based MOF, four reduction processes presented in Figure 5b can occur. However, if a positive strain is applied, the CB bottom shifts downwards, and the processes with more positive redox potentials (at vacuum scale) are switched off one by one. Finally, for the strain of +3%, only the reduction of CO2 to CH4 can occur (among presented redox couples), and it is combined with anodic O2 formation. Such a level of selectivity is generally difficult to obtain, while the use of strain for the control of photocatalytic activity also enables that one material can be used for different processes, which can be switched on or off as desired. This level of control is not possible if other strategies for the control of the catalytic activity are applied, such as chemical modification of the linker.

Discussion
As we have shown, the concept of using strain for the control of the electronic structure of MOFs works nicely for the UiO-66(Ce). The induced modifications of the electronic structure reflect onto the optical properties and ultimately the photocatalytic ones. In the case of UiO-66(Ce), a downshift of the CB bottom is seen, and we look into it in more detail. Figure 6 presents DOSes of Ce atoms for different applied strains. As one can see, the f orbitals of Ce atoms degenerate with positive strain, and the band becomes narrower. This occurrence is not seen for the CB of UiO-66(Zr) (Figure 3). If one recalls the results of the structural relaxation of strained structures (Figure 2 The resulting modifications of the electronic structure of UiO-66(Ce) also have a strong impact on the optical properties ( Figure 4). Putting the results in a wider context, the results suggest that mechanical strain can be used to modulate the optical absorption, color and conductivity of UiO-66(Ce). This observation opens the possibility for wider use of UiO-66(Ce), from smart optical materials to strain and chemical sensors. However, we want to link the effects of strain on the photocatalytic activity and selectivity control.
For this purpose, we constructed the 3D diagram showing the dependence of the CB bottom and the VB top positions and the potentials of three selected redox couples (the anodic process is O2 formation, while reduction processes are H2 formation and CO2 reduction to methanol) on the applied strain and pH (Figure 7). We assume that the CB bottom and the VB top positions depend only on the strain, while the redox potentials depend only on pH. H2 and O2 evolution processes involve one proton per transferred electron, so the calculated plane slope versus pH axis is 0.059 eV per pH unit. CO2 reduction to methanol follows the equation: CO2 + 6e − + 6H + = CH3OH + H2O (1) so the slope versus pH axis is also 0.354 eV per pH unit at room temperature. We choose to discuss the CO2 reduction to methanol due to the importance of methanol in contemporary energy technologies. As can be seen from Figure 7, pH modulates the relative positions of redox couple potentials vs. the CB bottom of UiO-66(Ce), allowing one to identify the pH-strain domain in which the potential of the H + /H2 couple shifts above the CB bottom while the potential of CO2/CH3OH couple is still below the CB bottom. In this way, one excluded the H2 formation, while CO2 reduction still proceeds. While this discussion only demonstrates the general principle of strain-controlled photocatalysis by UiO-66(Ce), we note that in this particular case, this pH-strain region corresponds to small positive strains for pH just below 7. Hence, besides altering MOFs (photocatalytic) properties using the change of metal centers and chemical modification of linkers, we suggest that strain should be added to this list and combined with the former two strategies to exploit the application potential of MOFs fully.

Materials and Methods
The first-principles DFT calculations were performed using the Vienna ab initio simulation code (VASP) [30][31][32][33]. We used the generalized gradient approximation (GGA) in the parametrization by Perdew, Burk and Ernzerhof [34] and the projector augmented wave (PAW) method [35,36]. The on-site Coulomb interactions were added to the d states of Zr and f states of Ce using the DFT+U scheme of Dudarev et al. [37]. We have systematically investigated the effects of the value of U on the bandgap and opted for U = 6 eV in both cases. The cut-off energy of 500 eV and Gaussian smearing with a width of σ = 0.025 eV for the electronic levels' occupation were used. A Monkhorst-Pack Γ-centered 3×3×3 k-point mesh was employed for the relaxation calculations. The relaxation of all the atoms in the simulation cell was unrestricted. The relaxation procedure was performed until the Hellmann-Feynman forces on all atoms were below 0.01 eV Å −1 . Spin-polarization was considered in all of the presented calculations. We used 6×6×6 k-point mesh for the DOS calculations in combination with the Blöch tetrahedron method [38]. For the band alignment, we used the method of Butler et al. [39] with the same con-verge criteria for the vacuum potential as in the ref. [22]. Optical spectra were calculated from the frequency-dependent microscopic polarizability matrix in the projector-augmented wave (PAW) methodology [40]. VESTA code was used for visualization [41].

Conclusions
We propose the use of strain for the control of the photocatalytic activity and selectivity of MOFs. The general principle is demonstrated for the case of UiO-66(Ce) using DFT+U calculations. While we are aware of the limitations of our theoretical approach, the concept itself shows that the mechanical strain is an eligible tool for controlling MOFs' electronic structure, optical properties, and, ultimately, photocatalytic performance. It is suggested that the combination of strain and pH can be used to control the selectivity of the photocatalytic process to a great extent, as exemplified in the case of CO2 reduction to methanol. However, the results should be sought in a wider context, as the strain engineering could open a large range of potentially new MOFs applications.  Data Availability Statement: The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.