Inner-sphere Reorganization Energy Research Articles

Proton-Coupled Electron Transfer Involving Localized Electronic Defects on Solid Surfaces

Proton-coupled electron transfer (PCET) is a critical elementary step in many (photo)electrocatalytic transformations. PCET reactions on semiconducting metal oxide surfaces involve proton transfer that is charge compensated by electronic defects, such as electrons or holes. When highly localized as small polarons, these electronic defects are coupled with local bond distortions that accompany the excess or depleted charge. Using anatase TiO2 as a model system, I will describe recent first-principles modeling studies of interfacial PCET on metal oxide surfaces. The PCET reaction free energies involving the cleavage of O–H bonds on TiO2 surfaces varies widely depending on whether the charge-compensating electronic defects are conduction d-band electrons or valence p-band holes. Differences in PCET thermochemistry are accounted for using a Marcus theory framework based on defect energy levels and inner-sphere reorganization energies. The PCET rate constants associated with the cleavage of O–H bonds in the presence of a nitroxyl radical oxidant are calculated using vibronically nonadiabatic PCET theory, where both the transferring electron and proton are treated quantum mechanically. Input parameters to the rate constant expressions are calculated using hybrid periodic density functional theory calculations. These studies highlight the effects of local electronic defects on the PCET reactivity of semiconductor surfaces.

Reorganization Energies for Interfacial Proton-Coupled Electron Transfer to a Water Oxidation Catalyst.

The reorganization energy (λ) for interfacial electron transfer (ET) and proton-coupled ET (PCET) from a conductive metal oxide (In2O3:Sn, ITO) to a surface-bound water oxidation catalyst was extracted from kinetic data measured as a function of the thermodynamic driving force. Visible light excitation resulted in rapid excited-state injection (kinj > 108 s-1) to the ITO, which photo-initiated the two interfacial reactions of interest. The rate constants for both reactions increased with the driving force, -ΔG°, to a saturating limit, kmax, with rate constants consistently larger for ET than for PCET. Marcus-Gerischer analysis of the kinetic data provided the reorganization energy for interfacial PCET (0.90 ± 0.02 eV) and ET (0.40 ± 0.02 eV), respectively. The magnitude of kmax for PCET was found to decrease with pH, behavior that was absent for ET. Both the decrease in kmax and the larger reorganization energy for an unwanted competing PCET reaction from the ITO to the oxidized catalyst showcases a significant kinetic advantage for driving solar water oxidation at high pH. Computational analysis revealed a larger inner-sphere reorganization energy contribution for PCET than for ET arising from a more significant change in the Ru-O bond length for the PCET reaction. Extending the Marcus-Gerischer theory to PCET by including the excited electron-proton vibronic states and the proton donor-acceptor motion provided an apparent reorganization energy of 1.01 eV. This study demonstrates that the Marcus-Gerischer theory initially developed for ET can be reliably extended to PCET for quantifying and interpreting reorganization energies observed experimentally.

Molecular Wires for Efficient Long-Distance Triplet Energy Transfer.

We propose design rules for building organic molecular bridges that enable coherent long-distance triplet-exciton transfer. Using these rules, we describe example polychromophoric structures with low inner-sphere exciton reorganization energies, low static and dynamic disorder, and enhanced π-stacking interactions between nearest-neighbor chromophores. These features lead to triplet-exciton eigenstates that are delocalized over several units at room temperature. The use of such bridges in donor–bridge–acceptor assemblies enables fast triplet-exciton transport over very long distances that is rate-limited by the donor–bridge injection and bridge–acceptor trapping rates.

Exploring different equatorial donors in a series of five-coordinate Cu(II) complexes supported by rigid tetradentate ligands

A series of tetradentate mixed-donor ligands has been synthesized containing an amine, thioether, or phosphine donor at the 8-position of a 2-(1,1-di(pyridin-2-yl)ethyl)quinoline backbone. Upon metalation with CuCl2, the preorganized N4, N3P, and N3S donor ligands enforce distorted trigonal bipyramidal coordination environments around the copper metal center, in which a chlorido donor occupies the remaining axial coordination site. The complexes were characterized by elemental analysis, high-resolution mass spectrometry, and X-ray crystallography. The non-pyridyl equatorial donor was the sole difference from among the tetradentate ligands, and is responsible for the structural and electronic variations across the series. Indeed, more intermediate geometries between the ideal trigonal bipyramidal and square pyramidal extremes are observed with the larger phosphorus and sulfur donors. Relative to the N4 derivative, the N3P and N3S systems have greater chemical stability upon redox cycling as observed in spectroelectrochemical experiments and lower inner-sphere reorganization energies for the CuII/I redox couples based on density functional theory calculations.

Proton-Coupled Defects Impact O-H Bond Dissociation Free Energies on Metal Oxide Surfaces.

Proton-coupled electron transfer (PCET) reactions on metal oxides require coupling between proton transfer at the solid-liquid interface and electron transfer involving defects at or near the band edge. Herein, hybrid functional periodic density functional theory is used to elucidate the impact of proton-coupled defects on the bond dissociation free energies (BDFEs) of O-H bonds on anatase TiO2 surfaces. These O-H BDFEs are directly related to interfacial PCET thermochemistry. Comparison between geometrically similar O-H bonds associated with different defect types, namely conduction d-band electrons or valence p-band holes, reveals that the BDFEs differ by ∼81 kcal/mol (3.50 eV), comparable to the wide TiO2 band gap. These differences are shown to be determined primarily by differences in electron transfer driving forces, which are analyzed by using band energies and inner-sphere reorganization energies within a Marcus theory framework. These fundamental insights about the impact of proton-coupled defects on PCET thermochemistry at semiconductor surfaces have broad implications for electrocatalysis.

Oxygen Reduction by Iron Porphyrins with Covalently Attached Pendent Phenol and Quinol.

Phenols and quinols participate in both proton transfer and electron transfer processes in nature either in distinct elementary steps or in a concerted fashion. Recent investigations using synthetic heme/Cu models and iron porphyrins have indicated that phenols/quinols can react with both ferric superoxide and ferric peroxide intermediates formed during O2 reduction through a proton coupled electron transfer (PCET) process as well as via hydrogen atom transfer (HAT). Oxygen reduction by iron porphyrins bearing covalently attached pendant phenol and quinol groups is investigated. The data show that both of these can electrochemically reduce O2 selectively by 4e-/4H+ to H2O with very similar rates. However, the mechanism of the reaction, investigated both using heterogeneous electrochemistry and by trapping intermediates in organic solutions, can be either PCET or HAT and is governed by the thermodynamics of these intermediates involved. The results suggest that, while the reduction of the FeIII-O2̇- species to FeIII-OOH proceeds via PCET when a pendant phenol is present, it follows a HAT pathway with a pendant quinol. In the absence of the hydroxyl group the O2 reduction proceeds via an electron transfer followed by proton transfer to the FeIII-O2̇- species. The hydrogen bonding from the pendant phenol group to FeIII-O2̇- and FeIII-OOH species provides a unique advantage to the PCET process by lowering the inner-sphere reorganization energy by limiting the elongation of the O-O bond upon reduction.

The effect of inner-sphere reorganization on charge separated state lifetimes at sensitized TiO2 interfaces.

Improving the efficiency of photo-electrocatalytic cells depends on controlling the rates of interfacial electron transfer to promote the formation of long-lived charge separated states. Ultimately, for efficient catalytic assemblies to see widespread implementation, repeated electron transfer in the absence of charge recombination needs to be realized. In this study, a series of manganese-based transition metal complexes known to undergo charge transfer-induced spin crossover are employed to study how significant increases in inner-sphere reorganization energy affect the rates of interfacial electron transfer. Each complex is characterized by transient spectroscopic and electrochemical methods to calculate the rate of electron transfer to a model chromophore anchored to the surface of a TiO2 film. Likewise, open-circuit voltage decay measurements were used to determine the voltage-dependent lifetime of injected electrons in TiO2 in the presence of each complex. To further characterize the rates of electronic recombination, density functional theory was used to calculate the inner-sphere and outer-sphere reorganization energy for each complex. These calculations were then combined with classical Marcus theory to determine the theoretical rate of back-electron transfer from the TiO2 conduction band. These results show that, in model complexes, a significant reduction in the recombination rate constant is achieved for complexes possessing a significant inner-sphere reorganization energy.

Heterogeneous Rate Constants of the Electron-Transfer of Iron- and Ruthenium-bipyridine Complexes in Imidazolium-Based Ionic Liquids

The heterogeneous rate constants (ks) for the oxidation of iron- and ruthenium-bipyridine complexes, [Fe(bpy)3]²⁺/³⁺ and [Ru(bpy)3]²⁺/³⁺ have been determined using Nicholson's method in imidazolium-based ionic liquids with five different types of cation/anion over a range of temperature from 298–318 K. The heterogeneous rate constants of these redox reactions range from 10⁻⁴ to 10⁻³ cm s⁻¹, depending on the dynamic viscosity and type of cation/anion of the ILs. Marcus-Hush theory is used to explain the activation energies, Ea. Similar activation energies are found for the Fe-bipyridine and Ru-bipyridine complexes indicating that inner-sphere reorganization energy has only a small influence. For the calculation of the solvent-dependent outer sphere reorganization energy a dipole-free expression is used, adopted to the different dielectric properties of ionic liquids compared to organic solvents. i-Ru drops have been compensated using the corresponding experimental uncompensated Ru-values obtained from temperature dependent Bode-plots.

Theoretical Insights into Proton-Coupled Electron Transfer from a Photoreduced ZnO Nanocrystal to an Organic Radical.

Proton-coupled electron transfer (PCET) at metal-oxide nanoparticle interfaces plays a critical role in many photocatalytic reactions and energy conversion processes. Recent experimental studies have shown that photoreduced ZnO nanocrystals react by PCET with organic hydrogen atom acceptors such as the nitroxyl radical TEMPO. Herein, the interfacial PCET rate constant is calculated in the framework of vibronically nonadiabatic PCET theory, which treats the electrons and transferring proton quantum mechanically. The input quantities to the PCET rate constant, including the electronic couplings, are calculated with density functional theory. The computed interfacial PCET rate constant is consistent with the experimentally measured value for this system, providing validation for this PCET theory. In this model, the electron transfers from the conduction band of the ZnO nanocrystal to TEMPO concertedly with proton transfer from a surface oxygen of the ZnO nanocrystal to the oxygen of TEMPO. Moreover, the proton tunneling at the interface is gated by the relatively low-frequency proton donor-acceptor motion between the TEMPO radical and the ZnO nanocrystal. The ZnO nanocrystal and TEMPO are found to contribute similar amounts to the inner-sphere reorganization energy, implicating structural reorganization at the nanocrystal surface. These fundamental mechanistic insights may guide the design of metal-oxide nanocatalysts for a wide range of energy conversion processes.

Rylene and Rylene Diimides: Comparison of Theoretical and Experimental Results and Prediction for High-Rylene Derivatives.

Low rylene (R) and rylene diimides (RD) are important organic semiconductors and dyes. High R and RD with larger conjugated cores show different properties compared with their low counterparts. Herein, absorption spectra, frontier molecular orbitals, band gaps, inner-sphere reorganization energy (λi), ionization potential, electron affinity, and atomic charge population of 20 rylene compounds were calculated by the density functional theory method. The theoretical results agree well with experimental ones. We predict some unusual properties of some high rylene derivatives that are unknown compounds due to synthetic difficulties. The lowest unoccupied molecular orbital energy levels of RD compounds change slightly, from -3.61 to -3.79 eV, which makes them strong electron acceptors. The band gaps narrow with the size increase of conjugated cores, which makes high rylene derivatives near-infrared dyes. The rising highest occupied molecular orbital energy levels of high rylene derivatives makes them unstable in the air. The λi falls with the size increase of the conjugated core, and the size of RD-4 or R-4 is big enough for the small λi to favor charge transport. The charge population analysis indicates R and RD have different charge distribution under the effect of electron-withdrawing imide groups, which contributes to distinct properties.

Ultrafast Photoinduced Electron Transfer from Peroxide Dianion.

The encapsulation of peroxide dianion by hexacarboxamide cryptand provides a platform for the study of electron transfer of isolated peroxide anion. Photoinitiated electron transfer (ET) between freely diffusing Ru(bpy)3(2+) and the peroxide dianion occurs with a rate constant of 2.0 × 10(10) M(-1) s(-1). A competing electron transfer quenching pathway is observed within an ion pair. Picosecond transient spectroscopy furnishes a rate constant of 1.1 × 10(10) s(-1) for this first-order process. A driving force dependence for the ET rate within the ion pair using a series of Ru(bpy)3(2+) derivatives allows for the electronic coupling and reorganization energies to be assessed. The ET reaction is nonadiabatic and dominated by a large inner-sphere reorganization energy, in accordance with that expected for the change in bond distance accompanying the conversion of peroxide dianion to superoxide anion.

Effect of axial ligand, spin state, and hydrogen bonding on the inner-sphere reorganization energies of functional models of cytochrome P450.

Using a combination of self-assembly and synthesis, bioinspired electrodes having dilute iron porphyrin active sites bound to axial thiolate and imidazole axial ligands are created atop self-assembled monolayers (SAMs). Resonance Raman data indicate that a picket fence architecture results in a high-spin (HS) ground state (GS) in these complexes and a hydrogen-bonding triazole architecture results in a low-spin (LS) ground state. The reorganization energies (λ) of these thiolate- and imidazole-bound iron porphyrin sites for both HS and LS states are experimentally determined. The λ of 5C HS imidazole and thiolate-bound iron porphyrin active sites are 10-16 kJ/mol, which are lower than their 6C LS counterparts. Density functional theory (DFT) calculations reproduce these data and indicate that the presence of significant electronic relaxation from the ligand system lowers the geometric relaxation and results in very low λ in these 5C HS active sites. These calculations indicate that loss of one-half a π bond during redox in a LS thiolate bound active site is responsible for its higher λ relative to a σ-donor ligand-like imidazole. Hydrogen bonding to the axial ligand leads to a significant increase in λ irrespective of the spin state of the iron center. The results suggest that while the hydrogen bonding to the thiolate in the 5C HS thiolate bound active site of cytochrome P450 (cyp450) shifts the potential up, resulting in a negative ΔG, it also increases λ resulting in an overall low barrier for the electron transfer process.

Axial interactions in the mixed-valent Cu A active site and role of the axial methionine in electron transfer

Within Cu-containing electron transfer active sites, the role of the axial ligand in type 1 sites is well defined, yet its role in the binuclear mixed-valent CuA sites is less clear. Recently, the mutation of the axial Met to Leu in a CuA site engineered into azurin (CuA Az) was found to have a limited effect on E(0) relative to this mutation in blue copper (BC). Detailed low-temperature absorption and magnetic circular dichroism, resonance Raman, and electron paramagnetic resonance studies on CuA Az (WT) and its M123X (X = Q, L, H) axial ligand variants indicated stronger axial ligation in M123L/H. Spectroscopically validated density functional theory calculations show that the smaller ΔE(0) is attributed to H2O coordination to the Cu center in the M123L mutant in CuA but not in the equivalent BC variant. The comparable stabilization energy of the oxidized over the reduced state in CuA and BC (CuA ∼ 180 mV; BC ∼ 250 mV) indicates that the S(Met) influences E(0) similarly in both. Electron delocalization over two Cu centers in CuA was found to minimize the Jahn-Teller distortion induced by the axial Met ligand and lower the inner-sphere reorganization energy. The Cu-S(Met) bond in oxidized CuA is weak (5.2 kcal/mol) but energetically similar to that of BC, which demonstrates that the protein matrix also serves an entatic role in keeping the Met bound to the active site to tune down E(0) while maintaining a low reorganization energy required for rapid electron transfer under physiological conditions.

Oxidation-Potential Tuning of Tungsten–Alkylidyne Complexes over a 2 V Range

The electrochemistry and electronic structures of over 30 tungsten-alkylidyne compounds of the form W(CR)L(n)L'(4-n)X (R = H, Bu(t), Ph, p-C6H4CCH, p-C6H4CCSiPr(i)3; X = F, Cl, Br, I, OTf, Bu(n), CN, OSiMe3, OPh; L/L' = PMe3, 1/2 dmpe, 1/2 depe, 1/2 dppe, 1/2 tmeda, P(OMe)3, CO, CNBu(t), py), in which the alkylidyne R group and L and X ligands are systematically varied, have been investigated using cyclic voltammetry and density functional theory calculations in order to determine the extent to which the oxidation potential may be tuned and its dependence on the nature of the metal-ligand interactions. The first oxidation potentials are found to span a range of ∼2 V. Symmetry considerations and the electronic-structure calculations indicate that the highest occupied molecular orbital (and redox orbital) is of principal d(xy) orbital parentage for most of the compounds in this series. The dependence of the oxidation potential on ligand is a strong function of the symmetry relationship between the substituent and the d(xy) orbital, being much more sensitive to the nature of the equatorial L ligands (π symmetry, with respect to d(xy), ΔE1/2 ≅ 0.5 V/L) than to the axial CR and X ligands (nonbonding with respect to d(xy), ΔE(1/2) < 0.3 V/L). The oxidation potential is linearly correlated with the calculated d(xy) orbital energy (slope ≅ 1, R(2) = 0.97), which thus provides a convenient computational descriptor for the potential. The strength of the correlation and slope of unity are proposed to be manifestations of the small inner-sphere reorganization energy associated with one-electron oxidation.

Structure-Property Relationships of Fe4 S4 Clusters.

In this theoretical study, the sensitivity of Fe4 S4 cluster properties, such as potential energy, spin coupling, adiabatic detachment energy, inner-sphere reorganization energy, and reactivity, to structural distortions is investigated. [Fe4 S4 (SH)4 ]3-/2-/1- model clusters anchored by fixed hydrogen atoms are compared with Fe4 S4 clusters coordinated by ethyl thiolates with fixations according to cysteine residues in crystal structures. For the model system, a dependence of the ground-state spin-coupling scheme on the hydrogen-hydrogen distances is observed. The minima of the potential energy surface of [Fe4 S4 (SH)4 ]2-/1- clusters are located at slightly smaller hydrogen-hydrogen distances than those of the [Fe4 S4 (SH)4 ]3- cluster. For inner-sphere reorganization energies the spin-coupling scheme adopted by the broken-symmetry wave function plays an important role, since it can change the reorganization energies by up to 13 kcal mol-1 . For most structures, [Fe4 S4 (SR)4 ]2- and [Fe4 S4 (SR)4 ]1- (R=H or ethyl, derived from cysteine) favor the same coupling scheme. Therefore, the reorganization energies for this redox couple are relatively low (6-12 kcal mol-1 ) compared with the 2-/3- redox couple favoring different spin-coupling schemes before and after electron transfer (14-18 kcal mol-1 ). However, one may argue that more reliable reorganization energies are obtained if always the same spin-coupling pattern is enforced. All theoretical observations and insights are discussed in the light of experimental results distilled from the literature.

Influence of polar medium on the reorganization energy of charge transfer between dyes in a dye sensitized film

We study the kinetics of the lateral hole transfer occurring between dye molecules anchored at the surface of the metal oxide in Dye Sensitized Solar Cells (DSSC). We use Marcus' charge transfer rate equation for which we need the electronic coupling between two molecules (J) and the reorganization energy (λtot). In DSSC the medium surrounding the dyes is highly polar. This means that the contribution of the solvent to the reorganization energy cannot be neglected. Here we elaborate a method to calculate, from first principles, the total (i.e., inner- and outer-sphere) reorganization energy of hole exchange between ruthenium dyes. The influence of the solvent and of the ions in the solvent is incorporated. The inner-sphere reorganization energy depends on the nature of the dye, 0.1 eV for ruthenium dyes with CN ligands, 0.2 eV for ruthenium dyes with NCS ligands. In acetonitrile, the solvent reorganization energy contributes for at least 80% of the total giving a total reorganization energy of around 0.86 eV for ruthenium dyes with CN ligands and 0.95 eV for ruthenium dyes with NCS ligands. We use these results to estimate the rate of hole transfer within Marcus theory. We suggest that low diffusion coefficients observed experimentally may arise from the high polarity of the medium rather than by the chemical structure of the dye.

Arene Trifluoromethylation: An Effective Strategy to Obtain Air-Stable n-Type Organic Semiconductors with Tunable Optoelectronic and Electron Transfer Properties

Modulation of organic semiconductor band gap, electron affinities (EA), ionization potentials (IP), and reorganization energies (λ) associated with charge transfer is critical for its applications. We report here that trifluoromethylation not only increases both IP and EA significantly as expected but also narrows the HOMO-LUMO band gaps and increases considerably the air-stability of arene-based n-type organic semiconductors. The increased air-stability results from relatively high EA energies and a change in oxidation mechanism. Calculated EAs and IPs show that trifluoromethylated arenes are excellent candidates for n-type semiconductor materials; though a moderate increase of inner-sphere reorganization energy (λi) associated with charge transfer is the penalty for the improved performance of the trifluoromethylated compounds. However, since λi decreases as the π conjugation increases, a rational design to produce air-stable n-type semiconductor materials with reasonably small λi is simply to prepare trifluoromethylated arenes with extended π conjugation. Furthermore, we found that structural isomerization can fine-tune the optoelectronic and electronic transfer properties of the corresponding aromatics.

Ground-State and Excited-State Structures of Tungsten–Benzylidyne Complexes

The molecular structure of the tungsten-benzylidyne complex trans-W(≡CPh)(dppe)(2)Cl (1; dppe = 1,2-bis(diphenylphosphino)ethane) in the singlet (d(xy))(2) ground state and luminescent triplet (d(xy))(1)(π*(WCPh))(1) excited state (1*) has been studied using X-ray transient absorption spectroscopy, X-ray crystallography, and density functional theory (DFT) calculations. Molecular-orbital considerations suggest that the W-C and W-P bond lengths should increase in the excited state because of the reduction of the formal W-C bond order and decrease in W→P π-backbonding, respectively, between 1 and 1*. This latter conclusion is supported by comparisons among the W-P bond lengths obtained from the X-ray crystal structures of 1, (d(xy))(1)-configured 1(+), and (d(xy))(2) [W(CPh)(dppe)(2)(NCMe)](+) (2(+)). X-ray transient absorption spectroscopic measurements of the excited-state structure of 1* reveal that the W-C bond length is the same (within experimental error) as that determined by X-ray crystallography for the ground state 1, while the average W-P/W-Cl distance increases by 0.04 Å in the excited state. The small excited-state elongation of the W-C bond relative to the M-E distortions found for M(≡E)L(n) (E = O, N) compounds with analogous (d(xy))(1)(π*(ME))(1) excited states is due to the π conjugation within the WCPh unit, which lessens the local W-C π-antibonding character of the π*(WCPh) lowest unoccupied molecular orbital (LUMO). These conclusions are supported by DFT calculations on 1 and 1*. The similar core bond distances of 1, 1(+), and 1* indicates that the inner-sphere reorganization energy associated with ground- and excited-state electron-transfer reactions is small.

Theoretical Analysis of Mechanistic Pathways for Hydrogen Evolution Catalyzed by Cobaloximes

The mechanistic pathways for hydrogen evolution catalyzed by cobalt complexes with supporting diglyoxime ligands are analyzed with computational methods. The cobaloximes studied are Co(dmgBF(2))(2) (dmg = dimethylglyoxime) and Co(dpgBF(2))(2) (dpg = diphenylglyoxime) in acetonitrile. The reduction potentials and pK(a) values are calculated with density functional theory in conjunction with isodesmic reactions, incorporating the possibility of axial solvent ligand loss during the reduction process. The solvent reorganization energies for electron transfer between the cobalt complex and a metal electrode and the inner-sphere reorganization energies accounting for intramolecular rearrangements and the possibility of ligand loss are also calculated. The relative reduction potentials agree quantitatively with the available experimental values. The pK(a)s and reorganization energies agree qualitatively with estimates based on experimental data. The calculations suggest that a peak measured at ca. -1.0 V vs SCE in cyclic voltammetry experiments for Co(dmgBF(2))(2) is more likely to correspond to the Co(II)H/Co(I)H reduction potential than the Co(III)H/Co(II)H reduction potential. The calculations also predict pK(a) values of Co-hydride complexes and reduction potentials for both cobaloximes that have not been determined experimentally. The results are consistent with a mechanism in which the Co(III) and Co(II) complexes have two axial solvent ligands and the Co(I) complex has a single axial ligand along the reaction pathway. Analysis of the free energy diagrams generated for six different monometallic and bimetallic hydrogen production pathways identified the most favorable pathways for Co(dmgBF(2))(2) and tosic acid. The thermodynamically favored monometallic pathway passes through a Co(III)H intermediate, and Co(II)H reacts with the acid to produce H(2). The thermodynamically favored bimetallic pathways also pass through the Co(III)H intermediate, but the pathways in which two Co(III)H or two Co(II)H complexes react to produce H(2) are not thermodynamically distinguishable with these methods. On the basis of the electrostatic work term associated with bringing the two cobalt complexes together in solution, the preferred bimetallic pathway involves the reaction of two Co(III)H complexes to produce H(2). This mechanistic insight is important for designing more effective catalysts for solar energy conversion.

NMR Study of Ligand Exchange and Electron Self-Exchange between Oxo-Centered Trinuclear Clusters [Fe3(μ3-O)(μ-O2CR)6(4-R′py)3]+/0

The syntheses, single crystal X-ray structures, and magnetic properties of the homometallic μ₃-oxo trinuclear clusters [Fe₃(μ₃-O)(μ-O₂CCH₃)₆(4-Phpy)₃](ClO₄) (1) and [Fe₃(μ₃-O)(μ-O₂CAd)₆(4-Mepy)₃](NO₃) (2) are reported (Ad = adamantane). The persistence of the trinuclear structure within 1 and 2 in CD₂Cl₂ and C₂D₂Cl₄ solutions in the temperature range 190-390 K is demonstrated by ¹H NMR. An equilibrium between the mixed pyridine clusters [Fe₃(μ₃-O)(μ-O₂CAd)₆(4-Mepy)(3-x)(4-Phpy)(x)](NO₃) (x = 0, 1, 2, 3) with a close to statistical distribution of these species is observed in CD₂Cl₂ solutions. Variable-temperature NMR line-broadening made it possible to quantify the coordinated/free 4-Rpy exchanges at the iron centers of 1 and 2: k(ex)²⁹⁸ = 6.5 ± 1.3 × 10⁻¹ s⁻¹, ΔH(‡) = 89.47 ± 2 kJ mol⁻¹, and ΔS(‡) = +51.8 ± 6 J K⁻¹ mol⁻¹ for 1 and k(ex)²⁹⁸ = 3.4 ± 0.5 × 10⁻¹ s⁻¹, ΔH(‡) = 91.13 ± 2 kJ mol⁻¹, and ΔS(‡) = +51.9 ± 5 J K⁻¹ mol⁻¹ for 2. A limiting D mechanism is assigned for these ligand exchange reactions on the basis of first-order rate laws and positive and large entropies of activation. The exchange rates are 4 orders of magnitude slower than those observed for the ligand exchange on the reduced heterovalent cluster [Fe(III)₂Fe(II)(μ₃-O)(μ-O₂CCH₃)₆(4-Phpy)₃] (3). In 3, the intramolecular Fe(III)/Fe(II) electron exchange is too fast to be observed. At low temperatures, the 1/3 intermolecular second-order electron self-exchange reaction is faster than the 4-Phpy ligand exchange reactions on these two clusters, suggesting an outer-sphere mechanism: k₂²⁹⁸ = 72.4 ± 1.0 × 103 M⁻¹ s⁻¹, ΔH(‡) = 18.18 ± 0.3 kJ mol⁻¹, and ΔS(‡) = -90.88 ± 1.0 J K⁻¹ mol⁻¹. The [Fe₃(μ₃-O)(μ-O₂CCH₃)₆(4-Phpy)₃](+/0) electron self-exchange reaction is compared with the more than 3 orders of magnitude faster [Ru₃(μ₃-O)(μ-O₂CCH₃)₆(py)₃](+/0) self-exchange reaction (ΔΔG(exptl)(‡298) = 18.2 kJ mol⁻¹). The theoretical estimated self-exchange rate constants for both processes compare reasonably well with the experimental values. The equilibrium constant for the formation of the precursor to the electron-transfer and the free energy of activation contribution for the solvent reorganization to reach the electron transfer step are taken to be the same for both redox couples. The larger ΔG(exptl)(‡298) for the 1/3 iron self-exchange is attributed to the larger (11.1 kJ mol⁻¹) inner-sphere reorganization energy of the 1 and 3 iron clusters in addition to a supplementary energy (6.1 kJ mol⁻¹) which arises as a result of the fact that each encounter is not electron-transfer spin-allowed for the iron redox couple.