Engineering the electronic and optical properties of 2D porphyrin paddlewheel metal-organic frameworks

Metal organic frameworks (MOFs) are promising photocatalytic materials due to their high surface area and tuneability of their electronic structure. We discuss here how to engineer the band structures and optical properties of a family of two-dimensional (2D) porphyrin-based MOFs, consisting of M tetrakis(4 carboxyphenyl)porphyrin structures (M TCPP, where M = Zn2+ or Co2+) and metal (Co2+, Ni2+, Cu2+ or Zn2+) paddlewheel clusters, with the aim of optimising their photocatalytic behaviour in solar fuel synthesis reactions (water splitting and/or CO2 reduction). Based on density functional theory (DFT) and time-dependent DFT simulations with a hybrid functional, we studied three types of composition/structural modifications: a) varying the metal centre at the paddlewheel or at the porphyrin centre to modify the band alignment; b) partially reducing the porphyrin unit to chlorin, which leads to stronger absorption of visible light; and c) substituting the benzene bridging between the porphyrin and paddlewheel, by ethyne or butadiyne bridges, with the aim of modifying the linker to metal charge transfer behaviour. Our work offers new insights on how to improve the photocatalytic behaviour of porphyrin- and paddlewheel-based MOFs.

Porphyrin-like organic units are particularly attractive as components of MOF photocatalysts, due to their remarkable light absorbing properties, which is also the basis of natural photosynthetic systems [21][22][23]. Several porphyrin-based MOFs have been investigated for photocatalysis. For example, Fateeva et al. reported a water-stable porphyrin-based MOF with Al-carboxylate clusters as metal nodes, capable of performing photocatalytic production of hydrogen from water, in the presence of Pt nanoparticles [19]. A MOF consisting of Zn metalloporphyrins connected to Zr6O8 clusters through carboxylic groups, coupled with an organometallic [Fe2S2] complex, has also shown photocatalytic activity for hydrogen evolution [26] to exhibit visible-light photocatalytic activity for hydrogen evolution, without the presence of metal co-catalysts. In that case, the proximity of the Ru cluster to the porphyrin (∼11 Å) was found to facilitate the electron transfer from the photoexcited porphyrins to the metal clusters.
There has been recent interest in creating two-dimensional (2D) photocatalytic MOFs, which could benefit from very accessible active sites and short paths for the photogenerated charge carriers to reach the solid-water interface. Wang et al. [20] have proposed ultrathin porphyrin-based MOFs consisting of Ti7O6 clusters and free-based porphyrins connected by H2TCPP linkers, which exhibited excellent photocatalytic hydrogen evolution in the presence of Pt as co-catalyst. Porphyrin-based quasi-2D lanthanide MOFs with different thicknesses where synthesised by Jiang et al. [27], demonstrating that the thinner materials had higher Brunauer-Emmett-Teller (BET) surface area, light harvesting ability, carrier density, separation efficiency, and therefore better photocatalytic performance.
Despite the remarkable progress in recent years, porphyrin-based MOFs still need efficiency improvement in the light absorption and charge separation processes to become viable photocatalysts. The optical behaviour of porphyrin-based MOFs is still not well understood at a fundamental level, which hinders the optimisation process. Computer simulations based on density functional theory (DFT) can be very useful in rationalising the electronic and optical properties of MOFs [28]. Previous DFT simulation work from our group [29,30] on 3D porphyrin-based MOFs similar to those synthesised by Fateeva et al. [19] has shown that the choice of metal at the porphyrin centre or at the metal clusters can be used to optimise the band alignment for the photocatalytic process. Also, we showed that when Al cations in the PMOFs are replaced by Fe cations, the position of the conduction band edge is lowered significantly, and that the Fe/Al composition in a mixed metal system can be used to tune the band edge positions.
The paddlewheel cluster comprises of two divalent metal ions bridged together by four carboxylate ligands. Each paddlewheel is then linked to four porphyrin units (Figure 1). A MOF with this layer structure was synthesised by Choi et al. [32] in bulk form, with layers exhibiting AB stacking. Zhao et al. [33,34] showed how to grow this material anisotropically, with the help of surfactants, to create 2D nanosheets with only 8±3 layers. Spoerke and co-workers [35] also reported the synthesis and characterisation of 2D structures consisting of Zn-paddlewheels and Zn-porphyrins and showed that these structures can serve as active component in photovoltaic systems. The presence of porphyrin in a 2D pattern, and the possibility of tuning the electronic properties by changing the paddlewheel metal, make this family of materials potentially interesting for photocatalysis. One possible concern is the poor hydrolytic stability of some

Methodology
Calculations of the periodic models were performed using density functional theory (DFT) as implemented in the VASP program [40,41]. The simulation cell consists of one Zn 2+ centred porphyrin linker and one metal paddlewheel node (Figure 1). Vacuum regions separating the layers from their periodic images have a width of ~20 Å. Ni, Cu, Zn and up to 1s for C, N, O) and its valence electrons and a kinetic energy cut-off of 400 eV was fixed for the plane-wave basis set expansion. A Γ-centred k-grid of 4×4×1 k-points was used, which leads to 6 irreducible reciprocal lattice points. During relaxation, the cell parameters are allowed to relax while keeping the cell volume constant, so that the vacuum gap is preserved. The forces on the atoms were minimised until they were less than 0.02 eV Å -1 .
All calculations were spin-polarised and we considered all possible spin states and Using the Gaussian16 code [51], time-dependent DFT calculations (TD-DFT) were also performed in order to examine the excited states in some selected cases. For these calculations, the MOF systems were represented by cluster models consisting of one porphyrin and one paddlewheel unit, where all the cleaved C bonds were saturated with H atoms (figures S1, S2 and S3 in the SI). The geometries of the clusters were fixed to those obtained from the periodic calculations. For consistency, we used the same HSE06 functional as in the VASP calculations. Triplet states were used to describe the magnetic nature of the copper paddlewheel clusters. The calculations were all-electron (i.e. no pseudopotentials were employed) and a 6-311G(d,p) basis set was used to expand the wavefunctions.

Framework geometry and magnetic ground states
We first discuss how the nature of the paddlewheel metal affects the geometric and electronic properties of the framework.  [56], although they found that the local magnetic moments were aligned antiferromagnetically within the paddlewheel, whereas in our calculation we found that the ferromagnetic alignment is more stable.  [56]. If we perform our calculation for the Nipaddlewheel system with water molecules added in axial position making each Ni centre pentacoordinated, then we find that the high-spin antiferromagnetic state is the most stable, followed by the high-spin ferromagnetic ground state, which in this case is only 0.06 eV higher in energy.
In any case, we have found that the band alignment presented below does not change much with the nature of the magnetic ground state. The results below refer to the magnetic ground states found theoretically in this work for the paddlewheel units with tetra-coordinated metal centres.
The cell parameter of the Zn-paddlewheel framework (16.80 Å) can be compared with the experimental value obtained by X-ray diffraction for stacked 2D porphyrin-paddlewheel nanosheets with the same composition, which was 16.71 Å [57]. The discrepancy (0.5%) is small considering the approximations in the DFT simulation, both related to the exchangecorrelation functional and to ignoring vibrational effects. Furthermore, the experimental value refers to the bulk material, whereas the simulation corresponds to a single-layer material. The variation of both the cell parameter and the M-M distance is consistent with the trend of ionic radii for Co 2+ , Ni 2+ , Cu 2+ and Zn 2+ , which is not monotonous along the period but has a minimum value for Ni 2+ [58].

Effect of changing the paddlewheel metal on the band positioning
We now discuss the suitability of the band structure alignment for the photocatalysis of solar fuel synthesis from H2O or CO2, as a function of the nature of the metal in the paddlewheel.
For this analysis, we need to align the band edges with respect to the vacuum potential, to obtain their absolute positions, and compare with the redox potentials for the photocatalytic reaction. The valence and conduction bands must straddle the redox potentials for the given reaction. For example, for water-splitting, the valence band edge should be below the energy of the oxygen evolution reaction (OER): while the conduction band edge should be above the energy of the hydrogen evolution reaction (HER): The difference between these redox potentials is 1.23 eV and therefore the band gap needs to be higher than this value. The optimal band gap for water-splitting is ~2 eV [59]    It is shown that the valence band, which is mainly contributed by the porphyrin unit, is approximately at -5.5 eV, which is below the OER as required. The nature of the paddlewheel metal mainly affects the position of the conduction band edge. Whereas the lowest unoccupied molecular orbital (LUMO) of the porphyrin is always at the same energy (~-3 eV), the empty 3d levels of the paddlewheel transition metal centres can go below that value, lowering the band gap. For the Ni-Zn system, a lower-lying, empty Ni 3d level narrows the band gap to 1.6 eV, where in the Co-Zn system, the lowest empty Co 3d level is at the same energy as the porphyrin's LUMO, so the band gap is not narrowed. For water-splitting photocatalysis, the best metal in the paddlewheel is Cu, whose empty 3d levels bring the band gap to 2.2 eV. The Co-Zn system also has suitable band positions, albeit with a larger gap, which might be useful for photocatalytic CO2 reduction reactions.
Taking the Cu-Zn system as reference, we can form a picture of how the photocatalytic water-splitting reaction could occur in a system like this.  Table S1 for the list of excited states and Table   S2 for the relative charges of the porphyrin and paddlewheel units). However, this first excitation has zero oscillator strength, i.e. the charge transfer cannot be achieved via direct excitation. The lowest bright excitation (T44) is a transition localized within the porphyrin unit, and corresponds to the so-called Soret band (or B band) of the porphyrin, which typically appears in the far visible or ultraviolet (UV) region of the spectrum [21, [60][61][62]. These calculations suggest two limitations of these porphyrin-based MOFs in photocatalytic applications. First, most of the adsorption happens at energies in the far visible or UV range of the spectrum, so it would not be possible to take advantage of most of the energy from solar radiation, which lies in the visible region. Second, since the oscillator strength of the charge transfer state is very low, we need to engineer the structure to make charge transfer more feasible. Therefore, in the next sections we will consider possible modifications to these MOFs, which could enhance their photocatalytic properties.

Effect of changing the metal from Zn to Co at the porphyrin centre
We now briefly consider the substitution of Zn by Co at the porphyrin centre, for which we have investigated the band positions in a system with Co at the centre of the porphyrin and Cu in the paddlewheel. The conduction band for this Cu-Co system is 0.3 eV below the LUMO of the porphyrin, which is similar to what is observed for the Cu-Zn system (Figure 3). However, the highest filled 3d levels of the Co centres are significantly higher in energy than the highest filled 3d levels of Zn. The proximity between the high-lying filled Co 3d levels and the HOMO of the porphyrin will help stabilize a photogenerated hole, since the Co(II) centre can be readily oxidised to Co(III) (in contrast with the case of Zn, whose low-lying filled 3d levels prevent the oxidation). The presence of Co as a redox centre in porphyrins has been widely used in the experimental design of porphyrin-based photocatalysts [63,64].
Although Co-porphyrins seem more interesting for photocatalysis than Zn-porphyrins, in what follows we will consider other modifications of the porphyrin-based MOFs, while keeping the Zn at the porphyrin centre, for ease of calculations (the Co centres introduce additional magnetic degrees of freedom). The effect of other metal centres at the porphyrin on the electronic structure of porphyrin-based MOFs has been investigated in more detail in Ref. [29].

Effect of partially reducing the porphyrin unit to chlorin
Until this point, we have explored substitutions of the metals at the paddlewheel and porphyrin units. Another route to modify the electronic properties and optical behaviour of these MOFs is to partially reduce the porphyrin unit to form chlorin. Chlorins fall in the generic class of hydroporphyrins, that is, porphyrin derivatives in which one or more bonds are saturated by addition of hydrogen, resembling a photosynthetic chromophore found in nature [65]. It is known that chlorin exhibits stronger light absorption at lower energies compared to porphyrin Therefore, our analysis below refers to the ordered configuration represented by a single unit cell. The partial reduction leads to a narrower band gap (1.9 eV), but otherwise the electronic structure is similar to that of the unreduced Cu-Zn-TCPP system ( Figure 5). Although the valence band is now slightly above the OER level, it is possible in practical applications to realign such small differences using a bias voltage [29,30].

Figure 5. Comparison between band alignments of a) Cu-Zn-TCPP and b) Cu-Zn-chlorin systems. The bands of metal at paddlewheel, metal at the centre and organic part (C, N and H atoms of porphyrins) are shown in green, magenta and black, respectively. The energy levels of relevant half-reactions involved
in water splitting and CO2 reduction to CH4 and CH3OH are also shown.
Excited states calculations were performed for these Cu-Zn-chlorin systems (energies of all calculated states and Bader charges of selected states are listed in Tables S3 and S4 of the SI). The first excited state (T1), as in the unmodified porphyrin system, is a charge transfer state, but with zero oscillator strength. The Soret band is also found at roughly the same energy in the porphyrin-and chlorin-based MOFs. However, the chlorin-based MOF has a relatively bright state at lower energies (T16 at 2.3 eV) which is not present in the porphyrin-based system. This is consistent with previous work showing that chlorin increases light absorption in the lower-energy Q bands, thus improving photophysical behaviour under visible light [66,67].
This is clearly observed in the absorption spectra of the cluster model of the Cu-Zn-chlorin system (Figure 6), which shows the presence of a peak in the visible range. This peak corresponds to the Q bands, which in the case of the unreduced Cu-Zn-TCPP system is still appreciable but it has a very small intensity.

Figure 6. Light absorption spectra calculated using TD-DFT for the cluster models of the porphyrinbased (Cu-Zn-TCPP) and chlorin-based (Cu-Zn-chlorin) systems. The inset expands the spectrum in the region of the Q band.
All these results suggest that the partial reduction of porphyrin to chlorin units in these and other MOFs could enhance the photocatalytic performance under visible light, but to the best of our knowledge this avenue has not been experimentally explored.

Changing the bridge between the porphyrin and paddlewheel
Finally, we consider the effect of modifying the bridging species between the porphyrin and the paddlewheel units. We investigate the substitution of the benzene rings by ethyne (C2) or butadiyne (C4) bridges (Figure 7). We have shown in previous work that it is possible to modify the properties of porphyrin-based structures by varying the nature of the bridging species linking the porphyrins, and in this way tune the band gap values [68].  It is interesting to discuss the effect of the different bridges on the charge transfer. The excited states for the system with the C2 bridge show that there are now several relatively bright states involving charge transfer from the porphyrin to the paddlewheel (see Table S5 and Table S6  The length of the bridging unit length can also be expected to modify LMCT behaviour from excited states localized in the porphyrin. To illustrate this, we present here a simple model based on Marcus theory [69,70], where we consider the porphyrin and the paddlewheel as two separate fragments. When light is absorbed at the bright states of the porphyrin, before any charge transfer takes place, the excitation will decay to the first excited state of the porphyrin (Kasha's rule). We make use Marcus theory to describe the electron transfer between the excited porphyrin fragment (donor) and the paddlewheel fragment (acceptor). To consider the electrostatic interaction between the charged fragments (porphyrin + and paddlewheel -), we have simply added a classical electrostatic term to the energy of the charge transfer state, considering the distance between these fragments (and assuming a full electron transfer).

Figure 9. Marcus parabolas and energy levels showing the transfer process in a) the C2 linker and b) the C4 linker. The excited state is shown in red and the charge transfer state in blue.
In our model calculations, we find that the charge transfer state is always above the first excited state (∆ 0 > 0). In this case, the barrier (with respect to the charge transfer state) is given by ∆ ‡ = (∆ 0 − ) 2 /4 , where is the reorganization energy (the change in energy of the first excited state when moved to the geometry of the charge transfer state, which in this simple model is independent of the length of the bridging unit). The energy of the chargetransfer state, and then the value of ∆ 0 , is 0.3 eV lower for the C2 linker than that for the C4 linker, due to the stronger electrostatic attraction for the shorter bridge. This means that in the C2 system the kinetic barrier to go from state to the other will also be lower, as shown in Figure   9. Our analysis suggests that the introduction of shorter bridging units between the porphyrin and the metal clusters should lower the kinetic barriers for the LMCT process. This is consistent with the experimental work from Lan et al. [26], who concluded that electron transfer from the photoexcited porphyrins to Ru clusters was facilitated by the proximity of the Ru cluster to the porphyrin in their MOF.

Conclusions
We have presented a computer simulation study of two-dimensional, porphyrin(chlorin)-based

Excited states of Cu-paddlewheel / Zn-porphyrin system
The model we have employed for the TD-DFT calculation of excited states in the Cu-Zn-TCPP system is shown in Figure S1.
The excited states energies and oscillator strengths obtained for this model are presented in Table S2, and the atomic (Bader) charges in Table S3.

Excited states after partial reduction of porphyrin to chlorin
The structural model used is shown in Figure S2. The excited states energies and oscillator strengths obtained for this model are presented in Table S3 and the Bader charges are in Table S4.

Excited states of system with C2 bridge
The model for the system with a C2 bridge between the porphyrin and the paddlewheel is shown in Figure S3. The excited states energies and oscillator strengths are presented in Table   S6, and the Bader charges in Table S7.