Supporting information for

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1 Supporting information for What is the role of pyridinium in pyridine-catalyzed CO 2 reduction on p-gap photocathodes? Martina Lessio a and Emily A. Carter* b Contents: 1) Cluster calculations: general details 2) Density difference plot from cluster calculations 3) Adsorption energies from cluster calculations 4) Reduction potentials from cluster calculations 5) Periodic boundary condition (PBC) calculations: general details 6) Density difference plot from PBC calculations 7) Bader charge analysis from PBC calculations 8) Calculation of band edge positions from PBC calculations 9) References 10) Coordinates in Å and energies in hartrees of structures discussed in the text 1) Cluster calculations: general details We performed all cluster calculations with the ORCA 1 software package and density functional theory (DFT) 2,3 with the B3LYP exchange-correlation (XC) functional. 4 6 Geometries were relaxed choosing the Pople 6-31G** basis set 7,8 for all atoms except for Ga atoms that were modeled using the Stuttgart effective core potential (ECP; 28 electrons are subsumed into the core potential) and double-zeta valence basis set for the three remaining valence electrons. 9,10 More accurate energies were obtained by carrying out single point energy calculations on the optimized geometries with the aug-cc-pvdz basis set 11 for all atoms except Ga atoms that were modeled with the same ECP and valence basis set chosen for the geometry optimization. We used Grimme semi-empirical D2 dispersion corrections 12 in all calculations and we modeled solvation effects using the continuum Solvation Model based on solute electron Density (SMD). 13 We ensured that all the structures obtained upon geometry relaxation were minima by performing a frequency analysis and finding no imaginary frequencies. The cluster model for simulating the GaP(110) surface was built in the same way as described in previous work. 14 The only difference between previous work and our current work is that here we built our cluster model starting from a periodic slab obtained from a bulk GaP crystal optimized with a dispersion correction instead of a bulk crystal optimized without this correction. This choice of lattice vectors was made to be consistent with the use of this correction in our cluster calculations. Note that during geometry relaxation the terminating hydrogen atoms saturating dangling bonds at the edge of the cluster model were not allowed to relax. 14 Therefore, S1

2 we did not compute the frequencies associated with these atoms as they are not in a minimum position and will thus generate imaginary frequencies. 2) Density difference plot from cluster calculations Cluster models were used to verify the result presented in previous work showing that pyridinyl radical is not stable near a GaP surface: because of the driving force to re-form the aromatic pyridinium cation, the electron spontaneously transfers from pyridinyl to GaP, suggesting that the reverse process will be energetically uphill and therefore photoexcited electrons cannot be transferred from the GaP(110) surface to PyH Specifically this was done using a density difference plot generated by plotting the following charge density difference: ρ(gap + PyH ) - ρ(gap) - ρ(pyh ) where ρ(gap + PyH ) is the charge density of the GaP-PyH complex, ρ(gap) is the charge density of the bare GaP cluster and ρ(pyh ) is the charge density of the isolated PyH radical. 3) Adsorption energies from cluster calculations Cluster models were used to compute adsorption free energies on the neutral and negatively charged GaP(110) surface. Adsorption free energy values were computed using the following equation: G ads (x) = G -n cluster+x G -n cluster G x where G ads (x) is the adsorption free energy of species x, G -n cluster+x is the free energy of the complex formed by the GaP cluster with n extra electrons and the adsorbed species x, G -n cluster is the free energy of the bare GaP cluster with n extra electrons and G x is the free energy of an isolated x molecule. We performed calculations with n=0,1,2 to study the effect of negatively charging the electrode surface on the adsorption free energy of CO 2, H 2 O, o-dhp, Py and PyH +. Thermal corrections at room temperature were calculated from the computed frequencies using the ideal gas, the rigid rotor and harmonic oscillator approximations. Note that for all the calculations using the GaP cluster, we only included vibrational contributions because the cluster model is used to simulate the surface of a solid for which we would not have any rotational or translational contributions. 4) Reduction potentials from cluster calculations Cluster models were used to calculate reduction potentials associated with possible reduction pathways of PyH + on GaP(110). Reduction potentials (E 0 ) were computed from the reaction free energy in solution ΔG aq using the following equation: E 0 = - G aq /nf where n is the number of electrons involved in the reduction process and F is the Faraday constant. Reaction free energies in solution are often computed using thermodynamic cycles. S2

3 However, a recent study using the SMD solvation model showed that we can directly compute the reaction free energy in solution, saving computational time but without incurring in significant errors on the computed reduction potential values. 15 Thus, in this work we used the direct approach and the reaction free energy in solution for a generic reduction process Ox + 1e - Red was computed using the following equation: G aq = G aq (Red) G aq (Ox) G aq (e - ) where G aq is the free energy in solution at room temperature. G aq (e - ) was set equal to kcal/mol. This value comes from the absolute potential of the standard hydrogen electrode (SHE, V) 16 shifted by V to reference our reduction potential values vs. SCE and converted to kcal/mol. Thermal corrections at room temperature were computed as described in the previous section. Conversion of reduction potential values to the vacuum scale In Figure 2 of the main text, we report reduction potentials and the conduction band position both on the vacuum and on the electrochemical (SCE) scale. Reduction potentials on the SCE scale (E 0 SCE) were converted to the vacuum scale (E 0 Vacuum) by using the following equations: E 0 SHE = E 0 SCE V E 0 Vacuum = V - E 0 SHE where E 0 SHE is the reduction potential vs. SHE and V is the absolute potential of the SHE 16 as discussed above. We used analogous equations to convert the conduction band position in vacuum to the position on the electrochemical (SCE) scale. 5) Periodic boundary condition calculations: general details We performed all periodic boundary condition (PBC) calculations with the VASP code All nuclei (Ga, P, N, C and H) and frozen core electrons (1s2s2p3s3p3d for Ga, 1s2s2p for P, 1s for N, 1s for C) were modeled with the default projector augmented wave (PAW) potentials. 10 The remaining electrons were modeled with a plane wave basis with 800 ev kinetic energy cutoff. All the calculations were performed spin-polarized. We used different unit cell sizes and different k-point sampling grids depending on the specific application. With the computational parameters reported in the main text and in the following paragraphs, the total energy was always converged to within 1 mev per atom. 6) Density difference plot from PBC calculations The electron density difference plot from PBC calculations was generated using the PBE XC functional 20 and plotting the same density difference discussed for the density difference plot S3

4 obtained with cluster calculations. The Brillouin zone was sampled with a k-point 2x2x1 sampling grid using the Monkhorst-Pack scheme 21 and was integrated using the Gaussian smearing method with a smearing width equal to 0.05 ev. Our slab model for these calculations was a 2x3 unit cell with 12 GaP formula units per layer and five-layer thickness. The atoms in the central layer were frozen in their bulk positions during geometry relaxation to model a semi-infinite crystal. We placed adsorbates on both sides of the slab to prevent surface dipole formation. The vacuum region between slabs was larger than 20 Å to ensure no interaction between periodic images of the adsorbates in the normal direction to the GaP(110) surface. Finally, we placed only one adsorbate per surface in each unit cell leading to a 1/12 monolayer coverage. We verified that the structure we found for the GaP-PyH complex corresponded to a true energy minimum by performing a vibrational frequency analysis and finding no imaginary frequencies. Given the large number of atoms in the unit cell (144), we considered all the adsorbate atoms but only a limited number of the slab atoms for the vibrational frequency analysis. Specifically we considered the slab atoms directly interacting with the adsorbate, their nearest neighbors and their next-nearest neighbors within a 4 Å radius from the adsorbate for a total of 4 Ga atoms and 5 P atoms. A numerical Hessian obtained from analytic gradients and ±0.02 Å displacements was used to calculate the frequencies. 7) Bader charge analysis from PBC calculations The Bader charge analysis for the GaP-PyH complex was conducted using PBC calculations with both the PBE and PBE0 XC functionals. 22 For this analysis, we used the same parameters and slab model used for the electron density difference analysis from PBC calculations. Note that while the geometry was relaxed with the PBE XC functional, we only performed a single point calculation with PBE0 XC functional given the high computational cost of the hybrid calculation. Furthermore, given the large size of the system under study (144 atoms in the unit cell), we were able to run the PBE0 calculation only with a moderate precision on the FFT grid for the exact exchange (PRECFOCK tag in VASP). However, a test done with a smaller system revealed that a lower accuracy of the FFT grid for the exact exchange does not significantly affect the atomic charge values computed with the Bader analysis. For this test, we used a hydrogen atom adsorbed on GaP(110) simulated with a smaller slab model for a total of 58 atoms in the unit cell. This system was chosen as a test system because it is also characterized by a net charge transfer between the GaP slab and the adsorbate. In Table 1 we report the results of the Bader charge analysis performed on this test system with lower (PRECFOCK=Fast) and higher (PRECFOCK=Normal) precision on the FFT grid for the exact exchange. With both settings of PRECFOCK we obtained the same exact result in terms of charge transfer. PRECFOCK tag GaP slab total Bader charge H total Bader charge Fast Normal S4

5 Table 1. Bader charge analysis performed using a charge density obtained with different settings of the PRECFOCK tag in VASP. Bader volume analysis As discussed in the main text, the Bader charge analysis reveals a net transfer of 0.45e negative charge from the PyH radical to the GaP slab. This finding suggests that the electron could somehow be shared between the radical and the slab. However, we think this is a spurious result due to the volume assignment in the Bader charge analysis. In fact, in the Bader charge analysis, the resulting charge for each atom depends on the volume assigned to the latter because the charge is calculated by integrating the charge density distributed in this volume. In order to further investigate this aspect, we plotted and analyzed the sum of the Bader volumes associated with PyH atoms and the sum of the Bader volumes of all the surface atoms. These results are reported in the figures below (Figure 1 and Figure 2). From these figures, it can be seen that the total Bader volume associated with PyH is embedded in the total Bader volume associated with surface atoms. This indicates that part of the charge density that should have been attributed to the surface was likely attributed to PyH which results in an apparent limited charge transfer (only 0.45e). Figure 1. Sum of Bader volumes (yellow isosurface) of PyH atoms on the GaP(110) surface. Isosurface level= 0.001e/bohr 3. Figure 2. Sum of Bader volumes (yellow isosurface) of the surface atoms of the GaP(110) surface. Isosurface level= 0.001e/bohr 3. 8) Calculation of band edge positions from PBC calculations S5

6 Accurate band edge positions for GaP were computed following the procedure proposed by Toroker et al., 23 which requires computation of the band gap center (BGC) position with respect to the vacuum level and separately of the band gap. For this reason, we used both DFT (with the PBE XC functional) and the non-self-consistent GW method (G 0 W 0 ). The BGC position was simply derived from the work function, whose calculation requires the use of a periodic slab model. For this purpose, we simulated the GaP(110) surface with a smaller unit cell (1x2) than the one used for the GaP-PyH system simulation (2x3). Given the smaller size of the unit cell, we sampled the Brillouin zone with a more dense k-point grid (6x4x1), using the Monkhorst-Pack scheme. 21 Also in this case the Brillouin zone was integrated using the Gaussian smearing method with a smearing width equal to 0.05 ev. The 1x2 unit cell (4 GaP formula units per layer) used for this calculation had a 7 layer thickness. During geometry optimization, we kept the 3 central layers frozen in the bulk position to simulate a semi-infinite crystal. The vacuum space was set larger than 20 Å to avoid interaction between slabs. We verified that the optimized geometry was a minimum by performing a vibrational frequency analysis and finding no imaginary frequencies. We computed only the frequencies associated with atoms that were not kept frozen during geometry optimization. A numerical Hessian obtained from analytic gradients and ±0.02 Å displacements was used to calculate the frequencies. Using this slab model we obtained a 4.8 ev work function, which gave us the position of the BGC relative to the vacuum level: -4.8 ev. The band gap was calculated using accurate G 0 W 0 calculations on the GaP bulk phase. In these calculations, we used the primitive cell of GaP which contains only two atoms and thus reduces the computational cost. We first performed a PBE calculation to get a good guess for the wavefunction to be used as input for the G 0 W 0 calculations. In these calculations, the Brillouin zone was sampled with a Γ-point-centered 8x8x8 k-point grid. We used 192 bands and the number of frequency points (NOMEGA tag in VASP) in the G 0 W 0 calculation was set equal to 64. With these computational settings we reached convergence of the band gap value to within 0.1 ev. In Table 2 we report our results of direct and indirect band gap from G 0 W 0 calculations and we compare them to experimental values. Our computed values and the experimental values are in good agreement. As discussed in the main text, the difference between the computed and the experimental band gap values suggest a ~0.1 ev uncertainty on the computed band edge positions (Table 3). Type of transition E g from G 0 W 0 calculations E g from experiments Indirect 2.47 ev 2.22 ev Direct 2.62 ev 2.78 ev Table 2. GaP band gap (E g ) values from G 0 W 0 calculations and experiments. 24 S6

7 Band Edge DFT(PBE XC functional) G 0 W 0 method CB min ev ev VB max ev ev Table 3. Position of the GaP conduction band minimum (CB min ) and valence band maximum (VB max ) from DFT (PBE functional) and G 0 W 0 calculations. Note that the calculated band edge positions reported in Table 3 and in the main text can be considered to be at the ph of zero charge (ph ZC ), given that our calculations were performed with a neutral surface in vacuum. We were not able to find experimental data for ph ZC of GaP but ph ZC =7 is usually considered a good estimate as it corresponds to neutrality of the aqueous solution in contact with the electrode. Given this value, we can then shift the computed band edge positions according to the desired ph (e.g., experimental ph=5.2) using the following equation: 23 E(VB max / CB min )(ph) = E(VB max / CB min )(ph ZC ) (pH - ph ZC ) Finally, note that the CB min position will likely not be affected by the small cathodic potential applied in the Bocarsly experiments. The applied potential typically serves to move the Fermi level of the metal counter electrode below the potential for the water oxidation reaction 25 and, for the scenario where the band edges are not pinned, 26 could provide additional reducing potential for the photoexcited electrons in p-gap. However, in the ideal (defect-free) case, the band edges are pinned at the solution-semiconductor interface and the applied potential only affects the magnitude and the direction of the band bending. 25,26 In the Bocarsly experiments, the negative applied potential may therefore increase the downward bending of the band edges and enhance electron-hole separation at the solution-semiconductor interface, but it likely does not shift the CB min in a favorable direction to increase electron transfer to PyH +. 9) References (1) Neese, F. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012, 2 (1), (2) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864. (3) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 140, A1133. (4) Becke, A. D. Phys. Rev. A 1988, 38, (5) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37 (2), (6) Becke, A. D. J. Chem. Phys. 1993, 98, S7

8 (7) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28 (3), (8) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. a. J. Chem. Phys. 1982, 77 (7), (9) Bergner, A.; Dolg, M.; Küchle, W.; Stoll, H.; Preuß, H. Mol. Phys. 1993, 80 (6), (10) Leininger, T.; Berning, A.; Nicklass, A.; Stoll, H.; Werner, H.-J.; Flad, H.-J. Chem. Phys. 1997, 217, (11) Dunning, T. H. J. Chem. Phys. 1989, 90 (2), (12) Grimme, S. J. Comput. Chem. 2006, 27, (13) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 2009, 113 (18), (14) Keith, J. A.; Muñoz-García, A. B.; Lessio, M.; Carter, E. A. Top. Catal. 2015, 58, (15) Ho, J. Phys. Chem. Chem. Phys. 2015, 17 (4), (16) Isse, A. A.; Gennaro, A. J. Phys. Chem. B 2010, 114 (23), (17) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, (18) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, (19) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 48, (20) Perdew, J. P.; Ernzerhof, M.; Burke, K. Phys. Rev. Lett. 1996, 77, (21) Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, (22) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110 (13), (23) Toroker, M. C.; Kanan, D. K.; Alidoust, N.; Isseroff, L. Y.; Liao, P.; Carter, E. A. Phys. Chem. Chem. Phys. 2011, 13 (37), (24) Zallen, R.; Paul, W. Phys. Rev. 1964, 134 (6A), (25) Nozik, A. J.; Memming, R. J. Phys. Chem. 1996, 100 (31), (26) Bard, A. J.; Bocarsly, A. B.; Fan, F. R. F.; Walton, E. G.; Wrighton, M. S. J. Am. Chem. Soc. 1980, 102 (11), S8

9 Coordinates in Å and energies in hartrees of structures discussed in the text Note: if not indicated otherwise, all the structures are reported in Cartesian coordinates. Structures for density difference and Bader charge analyses Solvated PyH on GaP cluster Energy= H H H H H Ga Ga Ga Ga H H H H H H H Ga Ga Ga Ga Ga Ga H Ga Ga H Ga H H Ga Ga Ga H S9

10 H Ga Ga Ga Ga Ga Ga H Ga Ga H P P P H H P P P P H H P H H H H H H H H H P P P P H H H P P S10

11 P P H P P H P P H P P P P H C C C C C H H H H H N H PyH on GaP(110) periodic slab (fractional coordinates) Energy= Unit Cell Vectors Fractional Coordinates Ga Ga Ga Ga Ga Ga Ga S11

12 Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga S12

13 Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga P P P P P P P P P P P P P P P P P P P P P P P P P P P P P S13

14 P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P C C C C C C C C C C S14

15 N N H H H H H H H H H H H H Structures for GaP band edge position calculation GaP slab used for work function calculation (fractional coordinates) Energy= Unit Cell Vectors Fractional Coordinates Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga S15

16 Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga Ga P P P P P P P P P P P P P P P P P P P P P P P P P P P P GaP bulk used for band gap calculation (fractional coordinates) S16

17 Energy= Lattice Constant Unit Cell Vectors Fractional Coordinates Structures for reduction potential calculations Solvated PyH + Energy= C C C C C H H H H H N H Solvated Py Energy= C C C C C H H H H H N S17

18 Solvated GaP cluster Energy= H H H H H Ga Ga Ga Ga H H H H H H H Ga Ga Ga Ga Ga Ga H Ga Ga H Ga H H Ga Ga Ga H H Ga Ga Ga Ga Ga S18

19 Ga H Ga Ga H P P P H H P P P P H H P H H H H H H H H H P P P P H H H P P P P H P P H S19

20 P P H P P P P H Solvated H* atom on the GaP cluster Energy= H H H H H Ga Ga Ga Ga H H H H H H H Ga Ga Ga Ga Ga Ga H Ga Ga H Ga H H S20

21 Ga Ga Ga H H Ga Ga Ga Ga Ga Ga H Ga Ga H P P P H H P P P P H H P H H H H H H H H H P P P P H S21

22 H H P P P P H P P H P P H P P P P H H Solvated H* and Py* co-adsorbed on GaP cluster Energy= H H H H H Ga Ga Ga Ga H H H H H H H Ga Ga Ga S22

23 Ga Ga Ga H Ga Ga H Ga H H Ga Ga Ga H H Ga Ga Ga Ga Ga Ga H Ga Ga H P P P H H P P P P H H P H H H H S23