The Importance of Precursor and Successor Complex Formation in a Bimolecular Proton-Electron Transfer Reaction

Abstract

The transfer of a proton and an electron from the hydroxylamine TEMPOH (1-hydroxyl-2,2,6,6-tetramethylpiperidine) to [Co^III(Hbim)(H₂bim)₂]²⁺ (H₂bim = 2,2′-bi-imidazoline) has an overall driving force ΔG° = −3.0 ± 0.4 kcal mol⁻¹ and an activation barrier of ΔG^‡ = 21.9 ± 0.2 kcal mol⁻¹. Kinetic studies implicate a hydrogen-bonded ‘precursor complex’ at high [TEMPOH], prior to proton-electron (hydrogen atom) transfer. In the reverse direction, [Co^II(H₂bim)₃]²⁺ + TEMPO, a similar ‘successor complex’ was not observed, but upper and lower limits on its formation have been estimated. The energetics of formation of these encounter complexes are the dominant contributors to the overall energetics in this system: the ΔG°’ for the proton-electron transfer step is only −0.3 ± 0.9 kcal mol⁻¹. Thus formation of precursor and successor complexes can be a significant component of the thermochemistry for intermolecular proton-electron transfers, particularly in the low driving force regime, and should be included in quantitative analyses.

Proton-coupled electron transfer (PCET) reactions are critical steps in a variety of biologically and industrially important processes.¹ Reactions in which one electron and one proton transfer in a single kinetic step can be called hydrogen atom transfer (HAT) or, more generally, concerted proton-electron transfer (CPET).² Most current theoretical models for proton-electron transfer have their roots in electron transfer (ET) theories such as Marcus Theory.³ In applying Marcus Theory to bimolecular ET reactions, the reactants A⁺ + D are considered to proceed by initial formation of a precursor or encounter complex, A⁺|D. This undergoes ET to form a successor complex, A|D⁺, which then dissociates to products.⁴ It has long been recognized that the energetics of the ET step must be corrected for the energetics of formation of these precursor and successor complexes, as indicated by the use of ΔG°’ in Marcus treatments.⁴ Precursor and successor complexes are likely to be more important for PCET reactions, because the proton transfer component must occur over very short range,¹ yet they have not been included in most analyses to date. Described here, for the first time, are the energetics of a bimolecular PCET reaction including the precursor and successor complexes (Scheme 1), showing that the formation of these complexes can be energetically significant.⁵

Scheme 1.

Mechanism of HAT involving precursor and successor complexes; k_HAT is the rate limiting step and K₁ is the overall K_eq.

The deprotonated cobalt(III)-tris(2,2′-bi-imidazoline) complex Co^III(Hbim) reacts reversibly with the hydroxylamine TEMPOH to slowly form the reduced protonated Co^II(H₂bim) and the stable nitroxyl radical TEMPO (eq 1, N-N = 2,2′-bi-imidazoline = H₂bim). This is a net hydrogen atom transfer reaction. Equilibrium measurements, as previously described, gave K₁ = 169 ± 23 at 298 K and the ΔH°₁ and ΔS°₁ values in Table 1.⁶

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Table 1.

Activation and Ground State Thermodynamics for Co^III(Hbim) + TEMPOH in MeCN

	Value at 298 K a	ΔG° b	ΔH° b	ΔS° c
K1 d	169 ± 23	−3.0 ± 0.4	9.3 ± 0.4	41 ± 2
KP e	61.3 ± 0.8	−2.44 ± 0.05	−4 ± 2	−9 ± 4
K S	0.16 < KS < 2.6	0.27 ± 0.83

		Δ G ‡	Δ H ‡	Δ S ‡
k−1 = k−HATKS	(1.8 ± 0.5)×−4	22.5 ± 0.3	9.0 ± 0.8	−47 ± 3
k HAT	(5.25 ± 0.08)×10−4	21.9 ± 0.2	23 ± 2	3.3± 0.6

^aUnits: K₁: unitless; K_P, K_S: M⁻¹; k₋₁: M⁻¹ s⁻¹; k_HAT: s⁻¹.

^bkcal mol⁻¹ at 298 K.

^ccal mol⁻¹ K⁻¹.

^dData from ref. 6.

^eΔH°_P and ΔS°_P from Hess’ Law⁹.

The kinetics of Co^III(Hbim) + TEMPOH have been measured by observing the conversion of Co^III(Hbim) to Co^II(H₂bim) using UV-Vis spectroscopy.⁷ Under conditions of excess TEMPOH, the reactions proceed to completion and are first-order in cobalt based on studies with varying [Co^III(Hbim)] and global analysis of spectra from 350 - 800 nm over the course of 4-5 half-lives.⁷ The pseudo-first order rate constants k_obs vary linearly with [TEMPOH] at low concentrations, but level off above 40 mM (Figure 1). The kinetics are well fit by a saturation rate law⁸ (eq 2), k_HAT = (5.25 ± 0.08) × 10⁻⁴ s⁻¹, and K_P = 61.3 ± 0.8 M⁻¹ (ΔG°_P = −2.44 kcal mol⁻¹) at 298 K. The temperature dependence (278 - 313 K) of the rates from

$$k_{\mathit{obs}}=\frac{K_p{k}_{\mathrm{HAT}}\left[\mathrm{TEMPOH}\right]}{1+K_p\left[\mathrm{TEMPOH}\right]}$$ (2)

both the linear and saturated regions, yield the activation parameters and the ground state thermodynamics given in Table 1. The values for ΔH°_P and ΔS°_P are in agreement with those independently (and more precisely) determined from the overall thermochemistry and activation parameters using a thermochemical cycle (Hess’ Law).⁹

Figure 1.

0.3 mM Co^III(Hbim) + TEMPOH in MeCN at 298 K: (A) UV-vis spectra vs. time (45.5 mM TEMPOH), inset: 1^st-order fit of absorbance at 586 nm. (B) Plot of pseudo-first-order rate constants vs. [TEMPOH].

The simplest kinetic saturation model is the pre-equilibrium formation of an intermediate prior to the rate limiting step. Optical spectra of reactions at short times and TEMPOH concentrations up to 0.2 M, conditions where the intermediate is the dominant species present in solution, are within error of the λ_max and ε predicted for the sum of separated starting reagents. This indicates that the intermediate is a hydrogen bonded Co^III(Hbim)|TEMPOH precursor complex, only slightly perturbed from the starting materials, rather than a charge transfer complex or a species with a different coordination about cobalt.

Alternative formulations of the intermediate involving pre-equilibrium electron transfer (ET) or proton transfer (PT) are ruled out by the optical spectra and thermodynamic arguments.⁷ In these cases, reactions with high [TEMPO] at short times would predominantly contain Co^II(Hbim) or Co^III(H₂bim), but these have distinct optical spectra from what is observed.^13a In addition, ET from TEMPOH to Co^III(H₂bim) would be endoergic by 30 kcal mol⁻¹, based on the known E_1/2 values for Co^III(Hbim)¹⁰ and TEMPOH.⁶ Proton transfer (PT) from TEMPOH to Co^III(Hbim) is even more endoergic, 44 kcal mol⁻¹ based on the known pK_a values.^6,10

To probe the properties of the successor complex, the kinetics of the reverse reaction were measured both by ¹H NMR, [5-10 mM Co^II(H₂bim) and 3-15 equiv TEMPO], and by UV-vis [1-2 mM Co^II(H₂bim) and up to 0.38 M TEMPO].⁷ The ¹H NMR spectra indicate good mass balance and that equilibrium is reached with ~10% conversion of Co^II(H₂bim). The data are well fit by an opposing second-order approach-to-equilibrium kinetic model (eq 3),¹¹ with k₋₁ = (1.8 ± 0.5) × 10⁻⁴ M⁻¹ s⁻¹ at 298 K. Eyring analysis of the rate constants from 273 - 313 K is shown in Table 1. No saturation was observed up to 0.38 M TEMPO.

$$-\frac{d\left[{\mathrm{Co}}^{\mathrm{III}}\right]}{dt}=\frac{k_{\mathrm{HAT}}{K}_p\left[{\mathrm{Co}}^{\mathrm{III}}\right]\left[\mathrm{TEMPOH}\right]-k_{-\mathrm{HAT}}{K}_S\left[{\mathrm{Co}}^{\mathrm{II}}\right]\left[\mathrm{TEMPO}\right]}{1+K_p(\left[{\mathrm{Co}}^{\mathrm{III}}\right]+\left[\mathrm{TEMPOH}\right])}$$ (3)

The first-order kinetic behavior in [TEMPO] indicates that under these conditions, the successor complex Co^II(H₂bim)|TEMPO is formed only to a small extent. Analysis with a full kinetic model based on Scheme 1 (see Supporting Information) indicates that K_S must be less than 2.6 M⁻¹. The successor complex, although not observed, likely involves a hydrogen-bond from Co^II(H₂bim) to the nitroxyl radical. This analysis assumes that the formation of the precursor and successor complexes is fast on the timescale of the HAT reaction, which is reasonable given that formation of hydrogen bonded adducts is usually fast and that k_HAT is small, < 10⁻³ s⁻¹. A standard collisional model¹² can be used to estimate a lower limit for formation of the successor complex, K_S ≈ 0.16 M⁻¹, using molecular radii roughly estimated from crystallographic data.¹³ The range 2.6 M⁻¹ > K_S > 0.16 M⁻¹ indicates that the free energy of formation of the successor complex is 1.1 > ΔG°_S > −0.56 kcal mol⁻¹, or ΔG°_S = 0.27 ± 0.83 kcal mol⁻¹.

The free energies of activation and complex formation for reaction 1 are illustrated in Figure 2. The free energy for unimolecular HAT, ΔG°’_HAT, is given by the overall free energy ΔG°₁ minus the difference between the energies of forming the precursor (P) and successor (S) complexes, ΔG°_S and ΔG°_P (eq 4).⁴ ΔG°’_HAT is clearly very different from the overall free energy change, ΔG°₁. Quantitatively, ΔG°’_HAT = −0.3 ± 0.9 kcal mol⁻¹, roughly isoergic. In contrast, the overall ΔG°₁ is significantly downhill, −3.0 ± 0.4 kcal mol⁻¹ (K₁ = 169). The 2.7 ± 0.9 kcal mol⁻¹ difference between ΔG°’_HAT and ΔG°₁ is due to the much higher equilibrium constant for the precursor complex than for the successor complex. This is likely due to the TEMPOH→Co^III(Hbim) hydrogen bond being stronger than the Co^II(H₂bim)→TEMPO H-bond.

$$\Delta {G^{{°}^{\prime }}}_{\mathrm{HAT}}=\Delta {G^{°}}_1+\Delta {G^{°}}_{\mathrm{S}}-\Delta {G^{°}}_{\mathrm{P}}$$ (4)

Figure 2.

Free energy surface for reaction of Co^III(Hbim) + TEMPOH in MeCN (eq 1). The uncertainty in ΔG°_S for formation of Co^II(H₂bim)|TEMPO is indicated by the error bar. The top half of the Figure is not to scale, as indicated by the breaks in the lines.

The precursor and successor (P and S) complexes for proton-coupled electron transfer (PCET) are quite different than those for ET. Electrons can tunnel over multiple Ångstrom distances so there are usually no orientation requirements for the P and S complexes. These are typically treated as weak ‘encounter’ complexes whose energies of formation can be estimated by electrostatic models.¹² In PCET, however, the transfer of the proton occurs over tenths of Å, typically along a specific axis and often within a hydrogen bond. Therefore the simple electrostatic models used for ET are not appropriate for PCET. For instance, they predict that ΔG°_P = ΔG°_S because no net charge is transferred (for reaction 1, there is no electrostatic work because TEMPO and TEMPOH are neutral reactants).

P and S complexes for PCET (and PT) likely have specific orientation requirements where both steric interactions and hydrogen bonding are energetically significant. The Co^III(Hbim)|TEMPOH complex implicated here is likely to be structurally very similar to the precursor complex, though that may not always be the case. The energetics of PCET P and S complexes could in some cases be estimated using empirical models for hydrogen bond energies,^7,14 although the parameters needed are often not available for metal complexes or organic radicals. Hydrogen bonds are also important in organic hydrogen atom transfer reactions, but for a somewhat different reason: an H-atom donor such as phenol must shed its hydrogen-bonded solvent prior to reaction with an organic radical.^5b

In conclusion, precursor and successor complexes are an important part of PCET reactions. These complexes have specific orientations which are important to the PCET process. The energetics of their formation, as indicated by the Co^III(Hbim) + TEMPOH reaction analyzed here, can be a substantial component of the overall energy change. This is particularly the case in the low driving force regime that is important in biological and energy-conversion PCET processes.¹ Since the precursor and successor complexes have both steric interactions and hydrogen bonds, their energies of formation cannot be estimated with the electrostatic models common for ET reactions. These conclusions have important implications for analyses of PCET systems, from mechanistic arguments^1,15 to application of the Marcus cross relation^10,16 to sophisticated quantum theories.^1a,3a