Felizitas
Gottwald
a,
Christopher
Penschke
a and
Peter
Saalfrank
*ab
aUniversität Potsdam, Institut für Chemie, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam-Golm, Germany. E-mail: peter.saalfrank@uni-potsdam.de
bUniversität Potsdam, Institut für Physik und Astronomie, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam-Golm, Germany
First published on 29th July 2024
Covalent organic frameworks (COFs) are a promising class of metal-free catalysts, offering a high structural and functional variety. Here, we systematically study imine-linked COFs with donor (D) and acceptor (A) groups using density functional theory (DFT). Using water splitting as a model reaction, we analyze the effects of protonation of the catalyst, the orientation of the imine linkage leading to different constitutional isomers, and solvation. In agreement with experimental results, we show that protonation decreases the band gap. In addition, COFs in which the donor is closer to the nitrogen atom of the imine group (DNCA) have lower band gaps than those in which the donor is closer to the carbon atom (DCNA). Three different D/A COFs are compared in this work, for which energies for the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) and corresponding electrochemical overpotentials are computed. We show that reaction energies are very similar for DCNA and DNCA COFs. The differences in hydrogen evolution rates between the constitutional isomers observed experimentally in (photocatalytic) HER (Yang et al., Nat. Commun., 2022, 13, 6317), are proposed to be at least in part a consequence of differences in charge distribution.
However, optimizing the COFs for specific catalytic applications requires a detailed understanding of the relationship between structure and properties. The large number of possible donor, acceptor, and linkage groups necessitates systematic studies. Even for a given combination of building units, structural variation may also be possible regarding the orientation of donor and acceptor groups with respect to the linkage. For example, when employing imine linkages, there are two constitutional isomers, depending on whether the carbon atom of the imine group is closer to the donor (DCNA) or to the acceptor (DNCA) groups, respectively. This has recently been shown to significantly affect hydrogen evolution rates20 in photocatalytic water splitting. In that work, we achieved good agreement between observed and calculated band gaps for both isomers of one particularly active donor–acceptor combination, called DCNA-1 and DNCA-1. In ref. 20 it was observed that the HER production rate in particular for protonated DCNA-1, called DCNA-1_AC there (with protonation done by ascorbic acid) was excellent, while DNCA-1_AC performed less good. In ref. 20, also two other classes of D/A imine-linked COFs with different D and A combinations were investigated (see below), DCNA-2/DNCA-2 and DCNA-3/DNCA-3, which both showed good HER performance in their protonated forms and with DCNA-X_AC (X = 2,3) peforming better than DNCA-X_AC.
Here, we extend our previous computational studies to compare the mentioned three different donor–acceptor combinations in detail. In addition to band gaps and band positions for unprotonated and protonated species, we also calculate reaction energies of the hydrogen evolution and oxygen evolution reactions, and corresponding overpotentials relevant in particular for electrochemistry. Furthermore, we study the effect of solvation on these COFs. As one determinant for the HER efficiency of various D/A COFs, differences in charge distributions will be identified. The possible performance of the studied COFs in OER, not realized experimentally so far, will also be addressed.
The oxygen evolution reaction (OER) can be described by four one-electron steps (* represents the catalyst):
A: * + H2O → *OH + H+ + e− |
B: *OH → *O + H+ + e− |
C: *O + H2O → *OOH + H+ + e− |
D: *OOH → * + O2 + H+ + e− |
The reaction path of the OER under alkaline conditions is, from a thermodynamic viewpoint, related to the acidic path shown above via the dissociation of water to protons and hydroxide ions, which is represented by the pH correction term discussed below.
The hydrogen evolution reaction (HER) proceeds via two one-electron steps:
E: * + H+ + e− → *H |
F: *H + H+ + e− →* + H2 |
To compute Gibbs free reaction energies for individual steps in presence of finite pH and voltage, U, we employ Nørskov's computational hydrogen electrode model.32 That is (ref. 32 and 33)
ΔGe = ΔG + ΔpH − eU | (1) |
The overpotential η is calculated as η = UL − Ueq, with Ueq as the voltage required to reach equilibrium, i.e., ΔGe of the overall reaction (OER or HER) is 0 (this is independent of the catalyst used), and UL as the voltage at which all individual steps are exergonic. Barriers between the reaction steps are neglected. Note that, while UL and Ueq are affected by the pH value, the pH correction term cancels out when calculating the overpotential (assuming a constant pH value throughout the reaction). Overpotentials are determined both for OER, ηOER and HER, ηHER, respectively. Note that within the computational hydrogen electrode approach, reaction energies of E and F at U = 0 and pH = 0 have the same absolute values, just with an opposite sign. Thus, the overpotential for the HER corresponds to the absolute value of the Gibbs free energy of step E (or, equivalently, F).
While our analysis emphasizes electrochemical reactions with OER being the anodic half reaction and HER the cathodic one, the energetics are relevant for photocatalytic water splitting as well. In this case electrons are photoexcited from the valence to the conduction band and drive the HER while the OER is driven by holes in the valence band.
Graphical representations of structures and spin densities were prepared using Jmol34 and VESTA,35 respectively.
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Fig. 2 Schematic representations of the central motif (donor, imine linkage, and acceptor) of (a) DCNA-1, (b) DNCA-1, (c) DCNA-2, (d) DNCA-2, (e) DCNA-3, (f) DNCA-3. |
To be suitable for water splitting, band gaps of photo(electro)catalysts should be larger than 1.23 eV, the energy required for the overall reaction. All investigated COFs fulfill this minimal requirement. Band gaps of unprotonated DNCA-COFs are lower compared to the corresponding DCNA-COFs by 0.2 to 0.7 eV (see Fig. 3(a)). PBE and HSE results both show this trend, but PBE underestimates the values compared to HSE, as expected. The HSE results are in very good agreement with experimental results.20 Also the experimental trends for gaps with DCNA-1 ∼ DCNA-2 < DCNA-3 and DNCA-1 < DNCA-2 < DNCA-3 are nicely followed.
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Fig. 3 Band gaps of (a) DA-COFs and (b) protonated DA-COFs obtained from experiment20 (black circles) and calculated using PBE (red triangles) and HSE (blue squares). |
In further agreement with experimental results,20 protonation results in lower band gaps (see Fig. 3(b)). Similar to the non-protonated COFs, HSE results are in very good agreement with experimental values, while PBE underestimates them. Note that apart from the diminished band gaps, the overall trends observed for the protonated species are similar to those found for the non-protonated COFs.
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Fig. 4 OER intermediates at (a)–(c) imine, (d)–(f) amine, (g)–(i) triazine, and (j)–(l) phenyl groups, optimized at the PBE+D3 level of theory. H: white; C: grey; N: blue; O: red. |
The different binding sites also lead to differences in the Gibbs free energy profiles of the OER (see Fig. 5). The figures show these profiles at pH = 0 and U = 0, for DCNA-X and DNCA-X, with the three different adsorption sites (donor, acceptor, imine) in each case. Step A, which involves adsorption of an OH group, is endergonic in all cases, but significantly more so when the reaction takes place at amine or triazine groups. The following step B, leading to an adsorbed O atom, is exergonic at triazine groups, but endergonic at imine, amine and phenyl groups. Step C, involving adsorption of another OH, is strongly endergonic at all groups, in particular at triazine groups. Finally, step D, in which O2 is formed and the catalyst is regenerated, is exergonic at amine groups, close to thermoneutral at triazine groups, and endergonic at phenyl and imine groups. Step A is the one with the highest increase in energy (corresponding to the rate-determining step) at all groups. Because this step is most favorable at imine groups, they are the most probable reaction sites (based on purely thermodynamical considerations).
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Fig. 5 OER reaction profiles of (a) DCNA-1, (b) DNCA-1, (c) DCNA-2, (d) DNCA-2, (e) DCNA-3, (f) DNCA-3. |
Independent of adsorption site and catalyst, the reaction energy for the entire half reaction, H2O → O2+ 4 H++ 4e− is 4.32 eV. Note that this value is much lower than the expected 4.92 eV due to the overbinding of the oxygen molecule (see, for instance,36). However, this applies to all COFs equally and does not affect comparability between them. When applying the equilibrium voltage of Ueq = 4.32/4 = 1.08 V, each individual step will be stabilized by 1.08 eV. Since step A is rate-limiting and most favourable when adsorption takes place at imine sites, the corresponding (minimal) overpotentials (see Table 1) are rather similar for the different donor–acceptor combinations. However, they are lower for DNCA-COFs compared to the DCNA-COFs, demonstrating the importance of the constitutional isomerism. Note that OH and O preferentially bind to the C and N atom of the imine group, respectively. Consequently, the transformation of OH to O in step B would also involve a change in binding site and a corresponding energy barrier. However, step B requires around 1 eV less than step A, so even with the inclusion of this barrier, step A likely remains rate-determining.
COF | η HER | η HER AC | η OER |
---|---|---|---|
DCNA-1 | 0.26 | 0.01 | 0.64 (0.59) |
DNCA-1 | 0.24 | 0.05 | 0.41 (0.63) |
DCNA-2 | 0.22 | 0.31 | 0.56 (0.51) |
DNCA-2 | 0.23 | 0.23 | 0.37 (0.50) |
DCNA-3 | 0.17 | 0.11 | 0.64 (0.60) |
DNCA-3 | 0.14 | 0.03 | 0.54 (0.60) |
If we correct the energy of the oxygen molecule such that the experimental value of the overall water splitting reaction is obtained (4.92 eV), step D becomes the rate-limiting step at imine groups. The overpotentials change by up to 0.22 eV (see the values in parentheses in Table 1), reducing the differences between the various COFs. In this case, the overpotentials for DCNA-2, DNCA-2, and DNCA-3 are slightly lower at phenyl groups compared to imine groups.
We investigated hydrogen adsorption at the imine groups and the donor and acceptor groups. Imine groups are the most stable adsorption sites, showing slightly exothermic binding energies of −0.06 to −0.17 eV. All other sites show endothermic adsorption energies, increasing from triazine (0.15 to 0.22 eV) to phenyl (0.51 to 0.68 eV) to amine (1.67 to 1.91 eV). These trends also apply to the protonated COFs, but the adsorption energies are generally lower (stronger binding). The exception are imine and phenyl groups in DCNA-2 and the imine group in DNCA-2, which show slightly higher adsorption energies (weaker binding) compared to the corresponding non-protonated COFs.
Using Gibbs free energies instead of electronic energies increases the energy of the adsorbed state with respect to free H2. The enthalpic and entropic corrections are similar for the pure and protonated COFs. Thus, while step E is endergonic in most cases, this is generally much more pronounced for the pure COFs (0.14 eV up to 0.26 eV). The Gibbs free energy profiles for the HER of DCNA-1 and DNCA-1 are shown in Fig. 7 (black lines without any solvation effects).
At the protonated COFs 1 and 3, step E is only slightly endergonic or slightly exergonic (DNCA-3_AC). Thus, the overpotentials (see Table 1) are particularly low for COFs 1 and 3. Differences between DCNA and DNCA structures are small. This is apparently in contrast to the experimentally observed large HER activity differences between the constitutional isomers,20 and the better performance of DCNA-1_AC compared to DCNA-2_AC and DCNA-3_AC. This may be either because of other factors affecting the catalytic activity (e.g., the separation of charge carriers or the precise positioning of the conduction band), or because our computational models are too simple. We will explore some of these aspects in the following sections.
In Fig. 6(a), we show the conduction and valence band edges of DCNA-X and DNCA-X (X = 1,2,3) with and without overpotential corrections. Uncorrected band edges are obtained with HSE, the overpotentials are taken from Table 1. Fig. 6(b) gives the same information for the protonated species, DCNA-X_AC and DNCA-X_AC. (For overpotentials of the OER reaction, the values of the unprotonated species of Table 1, ηOER, were taken for simplicity.) Also shown are the electrochemical potentials for H+/H2 and O2/H2O at pH = 7 (blue and red horizontal lines) and a range of pH values between 0 and 14 (shaded areas), at T = 298.15 K. Note that all values are given w.r.t. the vacuum energy. On this absolute scale, the electrochemical potential for H+/H2 at pH = 0 is −4.44 V37 (rather than 0 V as for the normal hydrogen electrode potential), while that of O2/H2O at pH = 7 is −4.44 V −1.23 V = −5.67 V. At finite pH, these values are up-shifted by kTln(10)pH.
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Fig. 6 Band edges relative to vacuum energy for (a) unprotonated DCNA-X without (filled symbols) and with overpotential correction (open symbols). (b) The same for protonated DCNA-X_AC. Band edges were calculated with HSE, overpotentials are taken from Table 1. (For ηOERAC in (b), the ηOER were taken for simplicity.) Also shown are the electrochemical potentials for H+/H2 and O2/H2O at pH = 7 (blue and red horizontal lines) and a range of pH values between 0 and 14 (lower and upper boundaries of the shaded areas), all at T = 298.15 K. |
From the conduction band edges we note that all COFs fulfill the energy criterion for HER, εCBM − ηHER > U (H+/H2), at least for not too basic pH values, in agreement with experimental findings. Note that the corrected band edges are closer to the HER potential for the protonated species. In the sense of a Golden Rule type argument, which predicts electron transfer rates to be large when initial and final states are close in energy, this may help to explain the better performance of the protonated species. The experimentally observed differences between DCNA-1_AC, DCNA-2_AC, and DCNA-3_AC, however, cannot be rationalized on the basis of this criterion either.
Inspecting overpotential-corrected valence band edges we note that OER will be difficult for most COFs studied in this work, at least when based on a simple energy criterion εVBM + ηOER < U (H2O/O2). At pH = 7, only DCNA-1_AC as well as DCNA-3 and DNCA-3 in protonated and unprotonated form are predicted to be possible candidates. Note that this result is not qualitatively affected when using the overpotentials corrected as described above (using the experimental value of the Gibbs free energy of the water splitting reaction).
Solvation leads to stronger binding of hydrogen to the COF, reducing the energy required for step E of the HER (see Fig. 7). The effect is approximately twice as large when using the PCM compared to explicit solvation, or, in other words, the differences in energy between no solvent and explicit solvent and between explicit solvent and implicit solvent are very similar. The energy difference is much higher for DCNA-1 (ca. 0.1 eV) compared to DNCA-1 (ca. 0.05 eV). Thus, while both show very similar reaction energies in the absence of solvation, the reaction energy (and, consequently, the overpotential) in water is much smaller for DCNA-1 compared to DNCA-1. However, the overpotentials of both isomers are small compared to the separation between conduction band and hydrogen evolution potential, especially at the low pH values used in experiment (cf.Fig. 6). The observed differences in hydrogen evolution rates is, therefore, unlikely to be based on the differences in overpotentials. Nevertheless, the impact of solvation on the HER overpotentials highlights the important role of electrostatic effects.
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Fig. 7 Free energies of the hydrogen evolution reaction at (a) DCNA-1 and (b) DNCA-1, calculated without solvent (black), with a single water molecule (cyan), and with implicit solvation (pink). |
COF | Imine | Donor | Acceptor |
---|---|---|---|
DCNA-1 | −0.21 | −0.11 | −0.06 |
DNCA-1 | −0.20 | +0.01 | −0.25 |
DCNA-2 | −0.22 | −0.15 | −0.01 |
DNCA-2 | −0.21 | +0.01 | −0.21 |
DCNA-3 | −0.25 | −0.09 | −0.09 |
DNCA-3 | −0.19 | +0.04 | −0.27 |
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Fig. 8 Spin densities (yellow) after hydrogen adsorption at (a) DCNA-1 and (b) DNCA-1. An isosurface level of 0.01 eV Å−3 was used. The arrow indicates the adsorbed hydrogen. Donor and acceptor groups as defined for the charge analysis in Table 2 are indicated in red and green, respectively. |
Our analysis thus demonstrates that the changes in electron density occur near the donor and acceptor groups for DCNA-1 and DNCA-1, respectively. This suggests that the isomers behave differently in terms of charge separation and/or charge transport during the HER, which affects their catalytic performance.
Metal–organic frameworks (MOFs) are also frequently studied as electrocatalysts for water splitting. For example, Das et al.39 investigated metallophthalocyanine-based MOFs using PBE+D3. The lowest HER overpotential that they reported is 0.08 V, which is comparable to our HER overpotentials for COFs 1 and 3 (see Table 1, ηHER AC). The lowest overpotential for the OER in their work is 0.58 V, which is also very similar to our values (Table 1, ηOER). DNCA-1 and DNCA-2 have even lower OER overpotentials than the values reported in ref. 39, but the valence band position of these two COFs limits their suitability for the OER.
Thus, in terms of band alignment and overpotentials, the performance of the COFs presented here is on par with other recently studied water-splitting catalysts. However, charge separation and carrier mobility are also important characteristics affecting the catalytic performance, which may be improved using two-dimensional hetero-structures (see, for example, ref. 40).
The COFs investigated here fulfill the additional energy criterion for the HER half reaction based on conduction band edges, as suggested by experiment. For the OER half reaction, however, only few of the COFs fulfill an analogous criterion based on valence band edges.
Imine groups are the most active sites for both reactions. This suggests a competition between the OER and HER reactions, but the presence of multiple imine groups and the fact that the OER overpotentials are only moderately higher at phenyl groups may still enable both reactions to take place at the same COF. Overpotentials for the OER and HER are rather similar at the different COFs. This suggests that the experimentally observed large differences in hydrogen production rates during HER between DCNA and DNCA COFs are not based on differences in the stabilization of adsorbed hydrogen, but rather on other photochemical descriptors. Based on the charge density differences and spin densities, we propose that the separation and/or transport of excited charge carriers are more decisive factors. In particular for photocatalysis, also differences in oscillator strengths for relevant optical excitations may be of importance.20,41 Based purely on the combination of band positions and overpotentials, protonated DCNA-3 is expected to show the best overall water splitting performance, followed by DCNA-1 (which shows the highest HER rates in experiment).
Our calculations also showed the importance of taking into account solvation effects. The reaction energies of the HER (and, consequently, overpotentials) are affected even by the presence of a single explicit water molecule. Using an implicit solvation model leads to even stronger changes in reaction energies. Further work is needed to address this in more detail by using more explicit water molecules and combining explicit and implicit solvation.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4cp02019g |
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