Theoretical Design of Molecular Electrocatalysts with Flexible Pendant

Jan 20, 2013 - The design of hydrogen oxidation and production electrocatalysts is important for the development of alternative renewable energy sourc...
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Theoretical Design of Molecular Electrocatalysts with Flexible Pendant Amines for Hydrogen Production and Oxidation Laura E. Fernandez,† Samantha Horvath,‡ and Sharon Hammes-Schiffer*,‡ †

Department of Chemistry, 104 Chemistry Building, Pennsylvania State University, University Park, Pennsylvania 16802, United States ‡ Department of Chemistry, 600 South Mathews Avenue, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States S Supporting Information *

ABSTRACT: The design of hydrogen oxidation and production electrocatalysts is important for the development of alternative renewable energy sources. The overall objective is to maximize the turnover frequency and minimize the overpotential. We use computational methods to examine a variety of nickel-based molecular electrocatalysts with pendant amines. Our studies focus on the proton-coupled electron transfer (PCET) process involving electron transfer between the complex and the electrode and intramolecular proton transfer between the nickel center and the nitrogen of the pendant amine. The concerted PCET mechanism, which tends to require a lower overpotential, is favored by a smaller equilibrium Ni−N distance and a more flexible pendant amine ligand, thereby decreasing the energetic penalty for the nitrogen to approach the nickel center for proton transfer. Our calculations provide predictions about designing catalysts that incorporate these properties. These design principles will be useful for developing the next generation of hydrogen catalysts. SECTION: Energy Conversion and Storage; Energy and Charge Transport

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he design of H2 oxidation and production electrocatalysts is critical for the development of alternative renewable energy sources. The long-term objective is to design catalysts with high turnover frequencies and low overpotentials.1−3 A variety of electrocatalysts with a nickel metal center and ligands with pendent amines have been designed, synthesized, and experimentally characterized.4−8 For example, the Ni(P2N2)2 catalyst depicted in Figure 1 has been shown to exhibit high turnover frequencies for either H2 oxidation or production, depending on the substituents.6,8 Recently, we studied the proton-coupled electron transfer (PCET) reaction for these catalysts, focusing on the step involving electron transfer (ET) between the electrode and the complex and intramolecular proton transfer (PT) between the nitrogen atom of the pendant amine and the Ni center.9,10 Our calculations indicated that decreasing the equilibrium distance between the Ni and N atoms favors the concerted PCET mechanism, denoted EPT, by increasing the overlap between the reactant and product proton vibrational wave functions (i.e., the Franck−Condon factor associated with PT).11 On the basis of our calculations, we also predicted that more flexible pendant amines would facilitate the concerted mechanism by lowering the energetic penalty of bringing the Ni and N atoms closer together.10 The concerted mechanism is expected to require a lower overpotential by avoiding high-energy intermediates.12,13 Thus, the design of catalysts with smaller equilibrium Ni−N distances and more flexible pendant amines may assist in the development of © 2013 American Chemical Society

Figure 1. Molecular electrocatalysts studied herein, with metal center in magenta and pendant amine in blue. The substituents are denoted R and R′ with R on P and R′ on N except for M(PN), which has R and R′ on N. These structures are shown as unprotonated with +2 charge, although the charge is not given in the formulas for notational simplicity. For the Ni(P2N2)2 systems, the (bbcc) and (bbbb) conformations are denoted with bc and bb subscripts, respectively, and the bb structure is shown here. For the Ni(PNP)2, Ni(7P2N)2, and Ni(PN) systems, the subscripts bc, bb, and b, respectively, denote the structures shown here.

Received: December 6, 2012 Accepted: January 19, 2013 Published: January 20, 2013 542

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Ni(P2N2)2 system.9,10 We focused on the PCET process corresponding to [HNiII(P2N2)2]+ − e− → [NiI(P2HN2)(P2N2)]2+ for H2 oxidation and the reverse reaction for H2 production. In this process, the electron transfers between the Ni and the electrode, and the proton transfers between the Ni and the N of the pendant amine. This PCET process is also expected to play an important role in the catalytic cycle for the Ni(PNP)2, Ni(7P2N)2, and Ni(PN) catalysts. For simplicity and generality, we use the notation [HNiII···N]+ for the reduced state and [NiI···NH]2+ for the oxidized state in this PCET process for all of the catalysts studied herein. Although this PCET process may not be the rate-limiting step in the overall catalytic cycle, it is expected to strongly impact the required overpotential. In our previous study of the Ni(P2N2)2 catalysts,10 we calculated the relative electrochemical rate constants for the ET reactions in the sequential mechanisms and for the concerted PCET (i.e., EPT) mechanism as functions of the overpotential using a theoretical formulation developed in our group.23,24 In this formalism, the anodic or cathodic rate constant for the EPT mechanism is calculated as a thermal average over the Ni−N distance R:24

catalysts with both high turnover frequencies and low overpotentials. In this Letter, we examine several other related catalysts with pendant amines that may be more conducive to the concerted mechanism, and we propose modifications that may further favor this mechanism. These catalysts are depicted in Figure 1 with substituents denoted as (R,R′) and are labeled according to the notation that will be used for the remainder of this Letter. The Ni(PNP)2 complexes, which differ from the Ni(P2N2)2 complexes in having only two rather than four amine bases, catalyze the electrochemical oxidation of hydrogen in the presence of base.4 The Ni(7P2N)2 complexes, which incorporate seven-membered rings with an amine base, catalyze the electrochemical production of hydrogen in the presence of acid.7 Compared to the Ni(P2N2)2 catalysts, these catalysts could potentially have somewhat more flexible pendant amines or smaller equilibrium Ni−N distances. The M(PN) catalysts, where M is the metal center, differ from the Ni(P2N2)2 catalysts in that they are monodentate rather than multidentate and contain a very flexible, nonpositioned phosphinomethylamine ligand.14 These catalysts have only been synthesized with Pd and Pt metal centers and with the R substituents as phenyl. In the presence of acid, these complexes function as hydrogen production catalysts.14 We utilized theoretical methods to examine the catalysts depicted in Figure 1 with various substituents. We studied the M(PN) complexes with Ni metal centers, although such catalysts have not been synthesized yet. The chelate rings of each bidentate cyclic ligand in the Ni(P2N2)2, Ni(PNP)2, and Ni(7P2N)2 catalysts can be in either a boat or chair conformation, denoted with “b” and “c” subscripts, respectively. For the M(PN) complexes, we also use the boat and chair terminology to describe the conformation with the pendant amine oriented toward or away from the metal center, respectively, although this ligand is expected to rotate freely in solution. The boat conformation is expected to be the catalytically active conformation for the PCET step involving intramolecular PT between the pendant amine and the metal center.15 We performed density functional theory (DFT) calculations to determine the structures, vibrational frequencies, reduction potentials, and Ni pKa’s for the catalysts studied. All calculations were performed with the Gaussian 09 electronic structure program16 using the B3P86 density functional17,18 in conjunction with the SDD pseudopotential for Ni,19 the 631G** basis set for the transferring hydrogen,20 and the 631G* basis set for all other atoms.21,22 The starting geometries were obtained from crystal structures for the Ni(PNP)2 system,4 the Ni(7P2N)2 system,7 and the M(PN) system.14 The crystal structures were manually altered to the boat conformation and/or to incorporate the appropriate substituents to obtain the starting conditions for the systems studied. Table S1 in the Supporting Information provides a comparison between the distances obtained from the geometry optimizations of the bare, unprotonated (M2+) catalysts and the available crystal structures. As observed for previous studies of the Ni(P2N2)2 catalysts,9 the calculated and experimental distances are in reasonable agreement. Comparisons of calculated and experimental reduction potentials for some of these complexes are also provided in the Supporting Information for benchmarking purposes. Previously, we examined the sequential and concerted PCET mechanisms of a specific portion of the catalytic cycle for the

k EPT(η) =

∫ k EPT(R ;η)P(R) dR

(1)

where η is the overpotential, k (R;η) is the EPT rate constant for given values of R and η, and P(R) is the probability distribution function for the distance R. The rate constant kEPT(R;η) is expressed as a summation over all reactant and product electron−proton vibronic states, where each term is proportional to the square of the overlap between the reactant and product proton vibrational wave functions. As shown in Figure 2, the rate constant typically increases dramatically as R EPT

Figure 2. Schematic depiction of the rate constant k(R) in red, the probability distribution function P(R) in blue, and their product in purple, as functions of the Ni−N distance R. The overall rate constant is the integral of the product, k(R)P(R), over R. The y-axis has no label because the quantities have different units and are scaled arbitrarily so they can be viewed on the same graph.

decreases because this overlap increases. The probability function P(R) is often chosen to correspond to a classical harmonic oscillator and depends on the equilibrium proton donor−acceptor distance, R̅ , and an effective force constant, keff, which can be converted to an effective frequency ωeff. The integral of the product of the two terms increases as R̅ decreases (i.e., as the center of P(R) shifts to smaller R) and as ωeff decreases (i.e., as the width of P(R) increases). Thus, we 543

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predict that the concerted mechanism will become more favorable as the equilibrium Ni−N distance and the frequency of the Ni−N vibrational motion decrease. Given this background, we calculated the equilibrium Ni−N distance and the associated frequency for the reduced and oxidized states, [HNiII···N]+ and [NiI···NH]2+, respectively, for the Ni catalysts depicted in Figure 1. The equilibrium distances were obtained by geometry optimization of the protonated species. The associated frequencies were obtained with the method described in ref 24. In this approach, the deviation of the Ni−N distance R from its equilibrium value is expressed as a linear combination of normal mode coordinates with expansion coefficients ci determined by projecting all normal mode vectors onto the Ni−N axis. Evaluation of the time correlation function of this deviation, which is assumed to behave as a classical harmonic oscillator, leads to an expression for the effective force constant that includes contributions from all normal modes with force constants ki: keff = [∑ic2i /ki]−1. Note that this effective force constant corresponds to the second derivative of the electronic energy curve generated along the Ni−N distance R with all other degrees of freedom optimized for each value of R.24 For the purposes of discussion below, this effective force constant is converted to an effective frequency ωeff using the reduced mass of the Ni and N atoms. In other words, P(R) represents the Boltzmann distribution for the Ni−N vibrational motion. According to the theory of PCET,11 concerted PCET reactions occur at a geometry intermediate between the geometries of the reduced and oxidized species. Thus, the values used in the probability distribution P(R) correspond to averages of the R̅ and keff values determined for the reduced and oxidized species. Further information about the probability distribution functions used in electrochemical PCET theory is available elsewhere.9,10 Table 1 provides the distances and associated frequencies for all of the catalysts studied, and Figures 3A and 3B depict the resulting probability distribution functions for the species with Me and Ph substituents, respectively, at the position labeled R′ in Figure 1. The equilibrium Ni−N distance, R̅ , is ∼3.3 Å for the Ni(P2N2)2,

Figure 3. Probability distribution functions P(R) along the Ni−N distance R for catalysts with (A) ligand substituents R′ = Me and (B) ligand substituents R′ = Ph. The Ni(P2N2)2 (black), Ni(PNP)2 (red), and Ni(7P2N)2 (orange) catalysts have similar probability distribution functions, while the Ni(PN) catalysts (blue and green) have probability distribution functions with larger equilibrium Ni−N distances and smaller associated frequencies. Modifying the substituents R = Ph to R = Me in the Ni(PN) catalyst leads to a smaller equilibrium Ni−N distance (blue to green curve in (A)).

Ni(PNP)2, and Ni(7P2N)2 catalysts and ∼4.0 Å for the Ni(PN) catalysts with R = Ph. The associated frequencies are significantly lower for the Ni(PN) catalysts than for the other three types of catalysts. Figure 3 illustrates that the probability functions for the Ni(P2N2)2, Ni(PNP)2, and Ni(7P2N)2 catalysts are very similar (black, red, and orange curves in Figure 3). In contrast, the probability function for the Ni(PN) catalyst with R = Ph (blue curves in Figure 3) is qualitatively different: it is centered at a larger Ni−N distance and is broader. Despite the greater flexibility of the Ni(PN) catalyst, which leads to the broader probability distribution function, the Ni−N equilibrium distance is so much larger that the concerted mechanism is expected to be less favorable for the Ni(PN) catalysts than for the other three types of catalysts, assuming that all other factors are similar. As discussed above, our objective is to design a catalyst that favors the concerted PCET mechanism, which relies upon the decrease of both the Ni−N equilibrium distance and the associated effective frequency. The van der Waals interactions between the Ni and N influence the equilibrium Ni−N distance but are similar for all of these catalysts. Analysis of the structure of the optimized protonated Ni(PN) (Ph,Me) catalyst indicates that steric effects between the Ph substituents and the pendant amine may exacerbate the energetic penalty for the nitrogen to move closer to the nickel center. Thus, we performed calculations on the Ni(PN) (Me,Me) catalyst, which would be expected to decrease these unfavorable steric interactions.

Table 1. Calculated Equilibrium Ni−N Distances, Effective Frequencies, and Inner-Sphere Reorganization Energies for Catalysts in Boat Conformationsa species c

Ni(P2N2)2 (Ph,Ph)bc Ni(P2N2)2 (Me,Me)bbc Ni(PNP)2 (Et,Bu)bc Ni(PNP)2 (Et,Me)bc Ni(7P2N)2 (Ph,Ph)bb Ni(PN) (Ph,Ph)b Ni(PN) (Ph,Me)b Ni(PN) (Me,Me)b

R̅ (Å)

ωeff (cm−1)

λi (eV)b

3.28 3.25 3.29 3.29 3.28 4.00 3.99 3.71

252 234 235 221 238 165 141 138

0.84 0.67 0.51 0.51 0.98 0.77 0.53 0.53

a

These values were obtained by averaging the equilibrium distances, R̅ , and the effective force constants, keff, for the reduced and oxidized complexes. The effective force constant, keff, was converted to the effective frequency, ωeff, using the reduced mass of Ni and N (11.28 amu). The R̅ , keff, and ωeff values for the reduced and oxidized complexes, as well as the averages, are provided in Table S6 of the Supporting Information. bThe inner-sphere reorganization energy25 is ox ox red calculated as λi = 1/2[Eox(Rred eq ) − Eox(Req) + Ered(Req) − Ered(Req )] with the individual terms defined in refs 9 and 24 and explained in the Supporting Information. cValues reported previously in ref 9. 544

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efficiency would be worthwhile. Note that we have examined only one part of the overall catalytic cycle, and another step may require a larger overpotential or slow down the overall turnover frequency. Extensive theoretical studies of the complete reaction profiles for the Ni(P2N2)2 catalysts have been published elsewhere.15,29,30 Nevertheless, the types of targeted calculations presented in this Letter elucidate trends and underlying principles that can be used to guide catalyst design toward lower overpotential. A key objective in the more efficient oxidation and production of hydrogen is the design of catalysts with both high turnover frequencies and low overpotentials. A variety of nickel catalysts with pendant amines have exhibited promising turnover frequencies but still require relatively high overpotentials. This Letter examines the PCET process involving ET between the electrode and the catalyst and intramolecular PT between the nickel center and the nitrogen of the pendant amine. The concerted mechanism, which tends to require a lower overpotential, is favored by a smaller equilibrium Ni−N distance and a more flexible ligand, which decreases the energetic penalty for the nitrogen to approach the nickel center. Our calculations illustrate that these two characteristics are often competing against each other because greater flexibility of the pendant amine is typically associated with a larger equilibrium Ni−N distance. Based on these calculations, however, we predict that reducing the bulkiness of the substituents on the other ligands may result in a smaller equilibrium Ni−N distance for such flexible amine ligands. These types of design principles will be useful for developing the next generation of hydrogen catalysts.

Note that the M(PN) (Ph,Me) catalyst has been synthesized with Pd and Pt metal centers,14 and the M(PN) (Me,Me) catalyst has not been synthesized at all yet. As shown in Table 1, altering these Ph substituents to Me groups decreases the equilibrium Ni−N distance from 4.0 to 3.7 Å and decreases the effective frequency slightly from 141 to 138 cm−1, although these frequencies are considered to be virtually identical within the accuracy of the calculations. Thus, both the distance and frequency decrease in a manner expected to favor the concerted mechanism. The trends in the distances were also reproduced with the ωB97X-D functional,26,27 which includes dispersion corrections, and the larger 6-31+G* basis set,20−22,28 which includes diffuse basis functions, as indicated by Table S4 in the Supporting Information. As shown in Figure 3A, the probability distribution function for the Ni(PN) (Me,Me) catalyst (green curve) favors smaller Ni−N distances compared to that for the Ni(PN) (Ph,Me) catalyst (blue curve). This distribution function still needs to be shifted to smaller Ni−N distances, however, to be competitive with the other catalysts in terms of favoring the shorter Ni−N distances that facilitate the concerted PCET mechanism, assuming that all other factors remain equal. In addition to modification of the probability distribution function P(R), modification of the rate constant k(R) will also alter the overall rate constant, as illustrated in Figure 2. The rate constant k(R) depends on factors such as the shapes of the proton potential curves and the reorganization energies.11 We expect the qualitative shapes of the proton potential curves to be similar for all of the catalysts depicted in Figure 1 because the proton is transferred between Ni and N in all cases, although the environment may impact these potentials somewhat. To examine other possible differences, we calculated the inner-sphere (solute) and outer-sphere (solvent) reorganization energies for these catalysts. The nonadiabatic rate constant for concerted PCET depends on these reorganization energies through both a prefactor and a contribution to the effective free energy barrier in the exponential, and typically the rate constant increases as the reorganization energy decreases.11 As shown in the Supporting Information, the outer-sphere reorganization energies do not vary significantly among the various types of catalysts. As shown in Table 1, however, the inner-sphere reorganization energies are lower for the Ni(PN) catalysts than for the Ni(P2N2)2 catalysts with equivalent substituents. Moreover, for both of these catalysts, the innersphere reorganization energy is lower with R′ = Me than with R′ = Ph. A comparison of the reorganization energies for the sequential and concerted mechanisms of Ni(P2N2)2 catalysts was given in ref 9. These results enable a qualitative analysis of the concerted PCET rate constant for the hypothetical Ni(PN) (Me,Me) catalyst compared to that of the experimentally studied Ni(P2N2)2 catalysts. Specifically, the smaller inner-sphere reorganization energy for the Ni(PN) (Me,Me) catalyst may increase the rate constant k(R) enough to override the larger equilibrium Ni−N distance. In the context of Figure 2, the red curve representing k(R) is increased, and the blue curve representing P(R) is broadened and shifted to larger R values (see shift from black to green curve in Figure 3A), leading to the possibility that the integral of the purple curve representing the product, k(R)P(R), in Figure 2 is larger, thereby favoring the concerted mechanism. Given the success of the Ni(P2N2)2 catalysts, these calculations suggest that the synthesis of the Ni(PN) (Me,Me) complex and the testing of its catalytic

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ASSOCIATED CONTENT

S Supporting Information *

Details of computational methods; comparisons between calculated and experimental structures, reduction potentials, and pKa’s; comparisons between calculated Ni−N distances for select catalysts obtained using different computational approaches; calculated reorganization energies; expanded version of Table 1; and coordinates of optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Monte Helm, Alexander Soudackov, Brian Solis, Morris Bullock, and Wendy Shaw for helpful discussions. This research was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.

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REFERENCES

(1) Fontecilla-Camps, J. C.; Volbeda, A.; Cavazza, C.; Nicolet, Y. Structure/Function Relationships of [NiFe]- and [FeFe]-Hydrogenases. Chem. Rev. 2007, 107, 4273−4303. (2) DuBois, D. L.; Bullock, R. M. Molecular Electrocatalysts for the Oxidation of Hydrogen and the Production of Hydrogen − The Role

545

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of Pendant Amines as Proton Relays. Eur. J. Inorg. Chem. 2011, 1017− 1027. (3) Hammarström, L.; Hammes-Schiffer, S. Artificial Photosynthesis and Solar Fuels. Acc. Chem. Res. 2009, 42, 1859−1860 and references within this special issue. (4) Curtis, C. J.; Miedaner, A.; Ciancanelli, R.; Ellis, W. W.; Noll, B. C.; Rakowski DuBois, M.; DuBois, D. L. [Ni(Et2PCH2NMeCH2PEt2)2]2+ as a Functional Model for Hydrogenases. Inorg. Chem. 2003, 42, 216−227. (5) Wilson, A. D.; Newell, R. H.; McNevin, M. J.; Muckerman, J. T.; Rakowski DuBois, M.; DuBois, D. L. Hydrogen Oxidation and Production Using Nickel-Based Molecular Catalysts with Positioned Proton Relays. J. Am. Chem. Soc. 2006, 128, 358−366. (6) Fraze, K.; Wilson, A. D.; Appel, A. M.; Rakowski DuBois, M.; DuBois, D. L. Thermodynamic Properties of the Ni-H Bond in Complexes of the Type [HNi(P2RN2R′)2](BF4) and Evaluation of Factors That Control Catalytic Activity for Hydrogen Oxidation/ Production. Organometallics 2007, 26, 3918−3924. (7) Helm, M. L.; Stewart, M. P.; Bullock, R. M.; Rakowski DuBois, M.; DuBois, D. L. A Synthetic Nickel Electrocatalyst with a Turnover Frequency Above 100,000 s−1 for H2 Production. Science 2011, 333, 863−866. (8) Wilson, A. D.; Shoemaker, R. K.; Miedaner, A.; Muckerman, J. T.; DuBois, D. L.; Rakowski DuBois, M. Nature of Hydrogen Interactions with Ni(II) Complexes Containing Cyclic Phosphine Ligands with Pendant Nitrogen Bases. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 6951− 6956. (9) Fernandez, L. E.; Horvath, S.; Hammes-Schiffer, S. Theoretical Analysis of the Sequential Proton-Coupled Electron Transfer Mechanisms for H2 Oxidation and Production Pathways Catalyzed by Nickel Molecular Electrocatalysts. J. Phys. Chem. C 2012, 116, 3171−3180. (10) Horvath, S.; Fernandez, L. E.; Soudackov, A. V.; HammesSchiffer, S. Insights Into Proton-Coupled Electron Transfer Mechanisms of Electrocatalytic H2 Oxidation and Production. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 15663−15668. (11) Hammes-Schiffer, S.; Soudackov, A. V. Proton-Coupled Electron Transfer in Solution, Proteins, and Electrochemistry. J. Phys. Chem. B 2008, 112, 14108−14123. (12) Mayer, J. M. Proton-Coupled Electron Transfer: A Reaction Chemist’s View. Annu. Rev. Phys. Chem. 2004, 55, 363−390. (13) Huynh, M. H. V.; Meyer, T. J. Proton-Coupled Electron Transfer. Chem. Rev. 2007, 107, 5004−5064. (14) Waggoner, N. W.; Spreer, L. S.; Boro, B. J.; DuBois, D. L.; Helm, M. L. Group 10 Complexes Containing Phosphinomethylamine Ligands: Synthesis, Structural Analysis and Electrochemical Studies. Inorg. Chim. Acta 2012, 380, 14−21. (15) Raugei, S.; Chen, S.; Ho, M.-H.; Ginovska-Pangovska, B.; Rousseau, R. J.; Dupuis, M.; DuBois, D. L.; Bullock, R. M. The Role of Pendant Amines in the Breaking and Forming of Molecular Hydrogen Catalyzed by Nickel Complexes. Chem.Eur. J. 2012, 18, 6493−6506. (16) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. (17) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (18) Perdew, J. P. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B 1986, 33, 8822−8824. (19) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. Energy-Adjusted Ab Initio Pseudopotentials for the First Row Transition Elements. J. Chem. Phys. 1987, 86, 866−872. (20) Hariharan, P. C.; Pople, J. A. The Influence of Polarization Functions on Molecular Orbital Hydrogenation Energies. Theoret. chim. Acta 1973, 28, 213−222. (21) Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self-Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian-Type

Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56, 2257−2261. (22) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. Self-Consistent Molecular Orbital Methods. XXIII. A Polarization-Type Basis Set for Second-Row Elements. J. Chem. Phys. 1982, 77, 3654−3665. (23) Venkataraman, C.; Soudackov, A. V.; Hammes-Schiffer, S. Theoretical Formulation of Nonadiabatic Electrochemical ProtonCoupled Electron Transfer at Metal-Solution Interfaces. J. Phys. Chem. C 2008, 112, 12386−12397. (24) Auer, B.; Fernandez, L. E.; Hammes-Schiffer, S. Theoretical Analysis of Proton Relays in Electrochemical Proton-Coupled Electron Transfer. J. Am. Chem. Soc. 2011, 133, 8282−8292. (25) Klimkäns, A.; Larsson, S. Reorganization Energies in Benzene, Naphthalene, and Anthracene. Chem. Phys. 1994, 189, 25−31. (26) Chai, J.-D.; Head-Gordon, M. Systematic Optimization of LongRange Corrected Hybrid Density Functionals. J. Chem. Phys. 2008, 128, 084106. (27) Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615−6620. (28) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. Efficient Diffuse Function-Augmented Basis Sets for Anion Calculations. III.* The 3-21+G Basis Set for First-Row Elements, Li-F. J. Comput. Chem. 1983, 4, 294−301. (29) O’Hagan, M.; Shaw, W. J.; Raugei, S.; Chen, S.; Yang, J. Y.; Kilgore, U. J.; DuBois, D. L.; Bullock, R. M. Moving Protons with Pendant Amines: Proton Mobility in a Nickel Catalyst for Oxidation of Hydrogen. J. Am. Chem. Soc. 2011, 133, 14301−14312. (30) O’Hagan, M.; Ho, M.-H.; Yang, J. Y.; Appel, A. M.; Rakowski DuBois, M.; Raugei, S.; Shaw, W. J.; DuBois, D. L.; Bullock, R. M. Proton Delivery and Removal in [Ni(P 2RN 2R ′ ) 2 ] 2+ Hydrogen Production and Oxidation Catalysts. J. Am. Chem. Soc. 2012, 134, 19409−19424.

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