Supporting Information. Ab initio Based Kinetic Modeling for the Design of Molecular Catalysts: the Case of H 2 Production Electrocatalysts

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1 Supporting Information Ab initio Based Kinetic Modeling for the Design of Molecular Catalysts: the Case of H 2 Production Electrocatalysts Ming-Hsun Ho, Roger Rousseau, John A. S. Roberts, Eric S. Wiedner, Michel Dupuis, Daniel L. DuBois, R. Morris Bullock, and Simone Raugei Table of Contents Page 2 Table S1: Parameters used for the kinetic modeling Page 3 Table S2: Activation barriers and reaction barriers for intramolecular processes Page 4 Figure S1: Structure of the [Ni(P Ph 2N Ph 2) 2 H n ] q+ species considered in the present study Page 5, 6, 7 Figures S2 S4: Free energy landscapes for various protonation reactions Page 8 Figure S5: Molar fraction at the electrode surface of the most relevant catalytic species as a function of the applied potential Page 9 Figure S6: Effect of the exo protonation on the catalytic rate Page 10 Figure S7: Concentration profiles in the diffusion layer Page 11 Figure S8: Correlation between reaction free energy and activation barrier for various protonation reactions Page 12 Figure S9: Extended macrokinetic model Page 13 Figure S10: Free energy diagram with an acid BH + with pk a = 1.0 Page 14 Figure S11: Definition of the collective variables employed for studying protonation/deprotonation reactions. Page 15 Homoconjugation and turnover frequency Page 18 Calculation of steady state free energies

2 Table S1. Parameters used for the kinetic modeling. Diffusion coefficients, D, reduction potential in acetonitrile vs. the Fc + /Fc 0 couple, E 0, and pk a values for the endo and exo protonated pendant amine. Species D (10-5 cm 2 /s) E 0 (V) pk a (endo) pk a (exo) Ni Ni Ni e e e x x x NiH ee ee ee xx xx xx ex ex ex enih xnih [(DMF)H] DMF [(DMF) 2 H] H

3 Table S2. Activation barrier and reaction free energy (in kcal/mol) for the intramolecular processes considered in the present study. Process ΔG ΔG Source enih 2+ " Ni 2+ + H Ref. 1 e + " NiH This work enih 2+ " ee Ref. 1 xnih 2+ " ex This work x' + " x Ref. 1 x' 2+ " x Ref. 1 xnih' 2+ " xnih Ref. 1 xx' 2+ " xx Ref. 1 x' + B " x + B This work x' 2+ B " x 2+ B This work xnih' 2+ B " xnih 2+ B This work xx' 2+ B " xx 2+ B This work 1 Raugei, S.; Chen, S.; Ho, M.-H.; Ginovska-Pangovska, B.; Rousseau, R. J.; Dupuis, M.; DuBois, D. L.; Bullock, R. M. Chem.- Eur. J. 2012, 18 (21),

4 Figure S1. Structure of the [Ni(P Ph 2N Ph 2) 2 H n ] q+ species considered in the present study. For each species only the most stable isomer is shown. The phenyl (Ph) substituents on the P and N atoms are not shown for clarity. 4

5 Figure S2. Free energy landscape for endo protonation (a) and exo protonation (b) and lowestfree energy pathway for endo (c) and exo (d) protonation of the [Ni(P Ph 2N Ph 2) 2 ] 0 intermediate, Ni 0, by [(DMF)H] + in acetonitrile. 5

6 Figure S3. Free energy landscape for endo protonation (a) and exo protonation (b) and lowestfree energy pathway for endo (c) and exo (d) protonation of the exo singly-protonated Ni(0) intermediate, x+, by [(DMF)H]+ in acetonitrile. 6

7 Figure S4. Free energy landscape for endo protonation (a) and exo protonation (b) and lowestfree energy pathway for endo (c) and exo (d) protonation of the Ni(II) hydride intermediate, NiH+, by [(DMF)H]+ in acetonitrile. 7

8 Figure S5. Molar fraction at the electrode surface (see text for the definition) of the most relevant catalytic species as a function of the applied potential. The solid lines refer to catalysis started in solution of protonated 0.1 M of [(DMF)H] + ; the dashed lines refers to catalysis started in 1:1 [(DMF)H] + /DMF buffer solution at a concentration C buffer = 0.59 M, corresponding to an effective acid concentration of 0.1 M. 8

9 Figure S6. Effect of the exo protonation on the catalytic rate: (a) Full kinetic model; (b) exo protonation Ni + shutdown; (c) all protonation channels leading to xnih + shutdown; (d) exo protonation leading to xx 2+ shutdown; (e) all exo protonation channels shutdown. See Figure 5 for a legend of the reaction network of panels a-e. 9

10 Figure S7. Concentration profile in the diffusion layer (grey shaded area) of the Ni 2+, NiH +, xnih 2+, and xx 2+ species generated from 0.22 M solution of [(DMF)H] + and 0.43 mm [Ni(P Ph 2N Ph 2) 2 ] 2+ in acetonitrile at a potential of V in a simulated CV experiment (potential scan rate = 50 mv/s). Although thermodynamically unstable toward the release of H 2, the xx 2+ intermediate is kinetically stable and accumulates in the diffusion layer being the second most populated species in the diffusion layer (17%), after the non-protonated Ni(II) complex Ni 2+ (80%) as obtained from direct integration of the concentration of the species. 10

11 Figure S8. Correlation between reaction free energy and activation barrier for various protonation reactions. The data for [Ni(P Ph 2N Ph 2) 2 ] 2+ /[(DMF)H] + are from the present study. The data for [Ni(P Cy 2N Me 2) 2 ] 2+ /PhNH 3 + are taken from a previous study [J. Am. Chem. Soc. 2012, 134, 19409] and additional simulations performed for this study. Labels are as follows. [Ni(P Ph 2N Ph 2) 2 ] 2+ /[(DMF)H] + : (1) Ni 0 " e + ; (2) Ni 0 " x + ; (3) x + " ex 2+ ; (4) x + " xx 2+ ; (5) Ni + " x 2+ ; (6) NiH + " enih 2+ ; (7) Ni + " e 2+ ; (8) NiH + " xnih 2+. [Ni(P Cy 2N Me 2) 2 ] 2+ /PhNH 3 + : [1] x + " xx 2+ ; [2] x + " ex 2+ ; [3] NiH + " ex 2+ ; [4] NiH + " ee 2+ ; [5] Ni + " e 2+ ; [6] Ni + " x 2+. The acid and base are omitted from the chemical equations reported above. 11

12 Figure S9. Extended macrokinetic model employed for the analysis of the strength of the acid on the turnover rate. The bold arrows indicate the original kinetic model used to parameterize the extended model. 12

13 Figure S10. Free energy diagram representing the main species involved in the catalytic production of H 2 from acetonitrile solutions of an acid BH + with pk a = 1.0 under standard conditions (catalyst, BH + and B at 1 M concentration under 1 atm H 2 ) at an electrode potential equal to V. Reaction pathways among intermediates are indicated with dashed lines. See Figure S7 for further details. 13

14 Figure S11. Definition of the collective variables employed for studying protonation/deprotonation reactions by protonated dimethylformamide, [(DMF)H] + : (1) the distance between the O atom of [(DMF)H] + and the Ni center, d(ni-o), and (2) the asymmetric stretching coordinate defined by the N atom of the target pendant amine, the [(DMF)H] + protic H atom and the O atom of [(DMF)H] +, ν = d(n-h) d(o-h). 14

15 Homoconjugation and turnover frequency The analysis presented in the main text is based on a homoconjugation constant of the acid BH + equal to that of [(DMF)H] +. We discussed earlier how, in 1:1 BH + :B buffered acid solutions, homoconjugation reduces the concentration of free acid available for catalysis and results in catalytic rates for nominal concentrations of acid added lower than what they would have been in its absence. It is of interest to further explore how the homoconjugation equilibrium (see Eq. 3) influences catalysis. To this end, we performed a CV simulation for a wide range of homoconjugation constants and pk a values of the acid. The results of such analysis are reported in Figure S12 for a nominal acid concentration of 0.1 M, and show that homoconjugation is detrimental to catalysis also for unbuffered acid solutions. In fact, the sequestration by homoconjugation of the base B formed during catalysis slows down deprotonation and facilitates the accumulation of exo protonated isomers. Interestingly, in unbuffered acid solutions, a strong homoconjugation tendency increases the propensity of weaker acids to protonate the catalysts. This is highlighted by the dashed line in Figure S12, which shows the pk a value at which the highest turnover frequency is achieved for a given value of K homo. This observation is consistent with recent results by Wiedner and Helm, 1 who reported high TOF for H 2 production by [Ni(P Ph 2N Ph 2) 2 ] 2+ from acetonitrile solution of trifluoroacetic acid (pk a = 12.7 in acetonitrile), 2 which has a very large homoconjugation constant (K homo = M -1 ), 3 while negligible rates were observed for p-anisidinium (pk a = 11.9 in acetonitrile), 4 which has no propensity to homoconjugate. 5 As discussed previously, 1 the protonation reactions of the various catalyst species by the acid BH + are favored by homoconjugation, which lowers the effective pk a of the (!"") acid. Indeed, it is easy to show that, in the presence of a large excess of acid, the effective pk! is given by (see the appendix at the end of this section): (S1) pk! (!"") = pk! log 1 + K!"#" BH! Correction for homoconjugation of the pk a at which the maximum TOF is observed yields roughly constant values of the effective pk a (Figure S12, solid line). 15

16 Figure S12. Dependence of the turnover frequency on the homoconjugation constant, K homo, and the pk a value of the external acid BH + in 0.1 M acid solution. The free energy of the homoconjugation reaction (Eq. 3) is also provided (ΔG homo = -RT ln K homo ). In (a) the dashed line demarks, for a given value of the homoconjugation constant, the pk a at which the highest turnover frequency is achieved; the solid line demarks the effective pk a for a given value of the homoconjugation constant (see text). Appendix: Calculation of the effective pk a of an acid in the presence of homoconjugation Similarly to the ph of a weak acid in aqueous solution, we can formally define the ph of a weak acid BH + in acetonitrile from the dissociation equilibrium BH + D B + H +, where H + indicates the solvated proton in acetonitrile, and the acidic dissociation constant (S2) K! = B [H! ] [BH! ]. If the acid is weak and its the concentration C is high, we can approximate [BH + ] = C and [B] = [H + ], which yield the well-know formula (S3) ph = 1 2 pk! 1 log C. 2 16

17 A similar formula, where the pk a is replaced by an effective pk! (!"") constant, can be obtained in the case the acid homoconjugates with its conjugate base, BH + + B D B 2 H +, (S4) K!"#" = [B!H! ] [BH! ] B. This is easily shown by using eqs. S2 and S4 along with the equation for the mass balance (S5) C = [B] + [BH + ] + 2[B 2 H + ] and the equation for the electroneutrality of the solution (S6) C = [H + ] + [BH + ] + [B 2 H + ], where we assumed that the counterions are monovalent, in which case C is also the concentration of the balancing negative charges. Taking the difference of these two equations yields [H + ] = [B] + [B 2 H + ], which, using the eq. S4, provides (S7) B = [H! ] 1 + K!"#" [BH! ]. Finally, inserting eq. S7 in eq. S2 yields (S8) ph = 1 2 pk! log (1 + K!"#" C) 1 log C. 2 The comparison between eqs. S3 and S8 provides us with eq. S1. 17

18 Calculation of steady state free energies In the diffusion layer, the concentration of the catalytic intermediates varies with the distance from the electrode surface. As a consequence the reaction quotient Q (i) for a reaction i also varies with distance. For this reason, we introduce the distance dependent reaction quotient Q (i) (x) and the associated free energy value G! x = RT ln Q! (x). The difference G! x = G!! G! x = G!! + RT ln Q (!) (x) quantifies how steady state concentrations at distance x deviate from equilibrium concentrations. Plots of G! x for a few selected reactions at E = V are reported in Figure S13. Since the thermochemical processes can take place at any position x in the diffusion layer, in the main text we carry out the discussion in terms of the average G! values in the diffusion layer: G! = 1 L! dx G! x,! where L is the length of the diffusion layer. The free energy changes for the electrode electrochemical processes are defined only in terms of the concentration of the electrochemical active species at the electrode surface, i.e. Q (i) (0). The difference G! = G!! G! can be taken as a measure of the (average) deviation between the standard state reaction free energy and the reaction free energy under catalytic conditions. As discussed in the main text, for the most of the chemical transformations considered in the present study, G! values are within 1-2 kcal/mol of the corresponding G!! values. However, cases exist for which deviations are much larger (up to 9 kcal/mol). Figure S13 reports the free energy differences G! x for selected protonation reactions. As can be seen for the reaction Ni + + [(DMF)H] + D e 2+ + DMF, which can be taken as a representative example where G! G!!, G! x quickly approaches zero as we move away from the electrode surface. In the other cases illustrated in the figure, G! x values tend to a constant value appreciable different from zero. It is also interesting to point out that near the electrode surface, G! x values have generally the largest deviation from the standard state free energies. 18

19 Figure S13. Difference, ΔG i, between the standard state free energy, G!!, and the free energy under catalytic conditions, G!, in the diffusion layer as function of the distance from the electrode surface for selected protonation reactions. For simplicity the acid [(DMF)H] + and the base DMF are not shown in the schematic labels of the free energy curves. 19

20 References (1) Wiedner, E. S.; Helm, M. L. Organometallics 2014, 33 (18), (2) Kütt, A.; Leito, I.; Kaljurand, I.; Sooväli, L.; Vlasov, V. M.; Yagupolskii, L. M.; Koppel, I. A. J. Org. Chem. 2006, 71 (7), (3) Izutsu, K. Acid-Base Dissociation Constants in Dipolar Aprotic Solvents; Blackwell Science Inc: Oxford ; Boston : Brookline Village, Mass, (4) Kaljurand, I.; Kütt, A.; Sooväli, L.; Rodima, T.; Mäemets, V.; Leito, I.; Koppel, I. A. J. Org. Chem. 2005, 70 (3), (5) Roberts, J. A. S.; Bullock, R. M. Inorg. Chem. 2013, 52 (7),