Automated assessment of redox potentials for dyes in dye-sensitized photoelectrochemical cells

Sustainable solutions for hydrogen production, such as dye-sensitized photoelectrochemical cells (DS-PEC), rely on the fundamental properties of its components whose modularity allows for their separate investigation. In this work, we design and execute a high-throughput scheme to tune the ground state oxidation potential (GSOP) of perylene-type dyes by functionalizing them with different ligands. This allows us to identify promising candidates which can then be used to improve the cell's efficiency. First, we investigate the accuracy of different theoretical approaches by benchmarking them against experimentally determined GSOPs. We test different methods to calculate the vertical oxidation potential, including GW with different levels of self-consistency, Kohn–Sham (KS) orbital energies and total energy differences. We find that there is little difference in the performance of these methods. However, we show that it is crucial to take into account solvent effects as well as the structural relaxation of the dye after oxidation. Other thermodynamic contributions are negligible. Based on this benchmark, we decide on an optimal strategy, balancing computational cost and accuracy, to screen more than 1000 dyes and identify promising candidates which could be used to construct more robust DS-PECs.


Contents
Experimental data set S-3 S2 R 2 sensitivity analysis S-5 S3 Calculation steps of the GSOP strategies and calculated GSOP values S-6 S4 PDI-0000 outlier analysis S-8 S5 Different contributions to the GOSP in the adiabatic approach (the Gibbs free energy of the oxidation reaction) S-10 S6 Suitable dyes for the trial system containing the Ru-based water oxidation catalyst designed by Duan et al. S1 and TiO 2 anode. S-14 References S-18 S-2 S1 Experimental data set The experimental data has been collected from different sources, presented in the Table S1.
For computational convenience both core (numbered C atoms of the aromatic core) and imide substituents are slightly modified ( Figure S1). All the imide substituents at NDI and PDI derivatives are replaced with a hydrogen atom. We compared experimentally obtained oxidation potentials of two NDIs substituted at the core with alkyl chains of different length.
In a paper by Röger and Würthner, we note the difference between oxidation potential of two tetraalkylamino NDIs. S2 The two NDI derivatives bearing the cyclic diaminoethyl and hexylamino had oxidation potentials of -0.01 V and 0.01 V, respectively. Therefore, the shortening of the alkyl chain resulted in a decrease of the oxidation potential of 0.02 eV.
Thalacker, Röger and Würthner reported S3 oxidation potential for di-substituted NDI core with octylamino groups of 0.60 V and di-substituted NDI core with one octylamino and one 4-tert-butylphenylamino group of 0.62 V. In this case the oxidation potential increased for 0.02 V with the introduction of an aryl group at one of the substitution spots. The NDI core is substituted in the following order, first position 2, than 6, 3 and 7. If represented as a list, the first element of the list corresponds to substitution on position 2, the second element corresponds to substitution position 6, etc.; if we use numbers to represent substituents as in Figure S1, we can represent NDI derivatives in a short notation as NDI-11 for 2,6-di-alkylthio-substituted NDI. The PDI core is substituted in the analogous way at the positions 1, 7, 6 and 12. The PDI-55c and PDI-55t are conformational isomers, where c and t stand for cis (on the same side) and trans (on the other side), which means that PDI-55c is substituted at the positions 1 and 6 while PDI-55c at the positions 7 and 12. The experimental values came from different sources; we used raw experimental data obtained in very similar conditions. All values are obtained with cyclic voltammetry (CV) in dichloromethane (DCM) with a scan rate of 100 mV s −1 (except NDI-59, 20 mV s −1 ) and with tetrabutylammonium hexafluorophosphate (N Bu 4 P F 6 ) as a supporting electrolyte. For NDI-77 and NDI-66 the oxidation potentials are determined against an SCE electrode and for other dyes against the ferrocene/ferricenium couple F c/F c + as internal standard (Ag/AgCl reference electrode).
Here we define absolute potential for used reference electrodes. The reported value for the F c/F c + potential is 0.46 V versus SCE in DCM solution (0.1 M N Bu 4 P F 6 ). S10,S11 The standard value of SCE versus normal hydrogen electrode (NHE), which is by Bard S12 considered the same as standard hydrogen electrode (SHE) is 0.24 V. Finally, we can relate the SHE reference electrode potential to the absolute scale. Sticking to the Fermi-Dirac statistics for the electron convention, calculated absolute potential for the SHE reference electrode is 4.28 V. S13,S14 Therefore, knowing the relations between the electrodes, the absolute potential for the SCE electrode is 4.52 V and for F c/F c + 4.98 V.

S2 R 2 sensitivity analysis
We want to check the sensitivity of the R 2 to the error of ± 0.05 eV to the experimental values. We do that by adding random values from the interval (-0.05, 0.05) eV to the experimental values to randomize the data set. We then iteratively calculate the value of R 2 between the calculated values and randomised data and calculate the MAD for the R 2 .
We repeat this process increasing the number of iterations to avoid initialisation noise. The

S3 Calculation steps of the GSOP strategies and calculated GSOP values
Direct approach with COSMO includes two steps: 1. Solution-phase geometry optimization with frequencies for the neutral, G 0 sol (g 0 sol ) and 2. Solution-phase geometry optimization with frequencies for the oxidized, G + sol (g + sol ) molecule. From these calculations we can directly obtain the Gibbs free energies, as in Equation (S1).
are solution-phase Gibbs free energies of the oxidized and neutral molecular species, respectively.
Thermodynamic cycle approach with COSMO (or COSMO-RS) requires nine calculations shown below to obtain components of equation (S2), where i denotes neutral (0) and oxidized (+) molecule. The ∆G T C COSM O is calculated as in equation (S3): For the neutral molecule: 1. Gas-phase geometry optimization with frequencies, G 0 gas (g 0 gas ) and E gas (g 0 gas ) 2. Single point on gas-phase geometry in solution, ∆G 0 solv (g 0 gas ) 3. Solution-phase geometry optimization, geometry (g 0 sol ) 4. Single point on solution-phase geometry in gas, E gas (g 0 sol ) For oxidized molecule: 1. Gas-phase geometry optimization with frequencies with charge G + gas (g + gas ) 2. Single point on gas-phase geometry in solution with charge, ∆G + solv (g + gas ) 3. Single point on gas-phase geometry in gas, E gas (g + gas ) 4. Solution-phase geometry optimization with charge, geometry (g + sol ) 5. Single point on solution-phase geometry in gas, E gas (g + sol ) Thermodynamic cycle with COSMO-RS used for screening includes six steps in total.
For this approach three calculations are needed to calculate the solution-phase Gibbs free energy G i sol,CRS (g i gas ) for i = 0, + state (Equation (S4)). The Gibbs free energy of oxidation is given in Equation (S5) G i sol,CRS (g i gas ) = E i sol (g i gas ) + ∆G i CRS,solv (g i gas ) 1. Geometry optimisation in gas-phase with semiempirical quantum mechanical (SQM) techniques, g i gas 2. Single point on gas-phase geometry in solution (COSMO) on DFT level, E i sol (g i gas ) 3. COSMO-RS calculation G i sol,CRS (g i gas )

S4 PDI-0000 outlier analysis
Following the automated procedure for ∆G DC COSM O and ∆G T C COSM O strategy to calculate adiabatic GSOP, molecule PDI-0000 appears as an outlier. We analyse the effective contributions to the GSOP for the two strategies such as thermal contributions, geometry relaxation due to solvation and due to oxidation. These effects are not very different compared to other molecules, therefore do not have large effect on the value of the GSOP. There is a slight differ-  Table S4. Würthner S15 mentions that the tetraphenoxy-substituted PDI preferred conformation in gas is unclear as many conformational isomers exist in a small energy range, therefore the conformation in solution will highly depend on solvent effects. For similar molecules it has been shown S8 that the molecule is twisted with the torsion angle around 25 degrees between two naphtalene planes which are forming the PDI core. The procedure we applied, does not employ conformational search and we assume that the molecule ended up in one of the local minima. In addition, we notice that the bonding energy in solvent calculated with COSMO (DC and TC strategies) for the oxidized molecule on oxidized geometry is larger than for the oxidized molecule on neutral geometry by 0.23 eV, while the energy difference induced only by geometry change due to oxidation is 0.05 eV as shown in Table S8, which describes the sensitivity of the molecule's electronic energy to the solvent S-9 model. Therefore, we conclude that the discrepancy from the experimental value originates in the molecule's sensitivity to the environment in combination with the conformational uncertainties. S-12 S6 Suitable dyes for the trial system containing the Rubased water oxidation catalyst designed by Duan et al. S1 and TiO 2 anode.