Spin-forbidden hydrogen atom transfer reactions in a cobalt biimidazoline system

Abstract

Described here are hydrogen atom transfer (HAT) reactions from high-spin cobalt(II) tris(2,2′-bi-2-imidazoline) (Co^IIIIH₂2bim) to the hydrogen atom acceptors, 2,2,6,6-tetramethyl-1-piperidinyl-oxyl (TEMPO), 2,4,6-tri-tert-butylphenoxyl radical (^tBu₃ArO˙), and benzoquinone (BQ). The cobalt product is the oxidized and deprotonated, low-spin cobalt(III) complex (Co^IIIIIIHbim), and the organic products are TEMPOH, ^tBu₃ArOH, or hydroquinone, respectively. These reactions are formally spin forbidden because the spin state of the reactants is different from that of the products. For instance, quartet Co^IIIIH₂2bim plus doublet RO˙ can have a triplet or quintet ground state, while the Co^IIIIIIHbim + ROH product state is a singlet. Kinetics measured in the forward and reverse directions and thermochemical measurements provide a detailed picture of the reactions. The reactions are quite slow: the reaction of 10 mM Co^IIIIH₂2bim with excess TEMPO requires roughly a day at ambient temperatures to reach equilibrium. This is 3400 times slower than the related reaction of the iron analogue Fe^IIIIH₂2bim, which is 2 kcal mol⁻¹ more uphill. Mechanistic analyses show that the TEMPO reaction occurs by hydrogen atom transfer (HAT), and this is likely for the ^tBu₃ArO˙ and BQ reactions as well. This is an unusually well defined spin-forbidden HAT system, which serves as a model for more complex multi-spin state HAT processes such as those suggested to occur in cytochrome P450 and metal-oxo model systems. In principle, HAT could occur before, after, or concerted with spin change. Computational studies indicate a reaction mechanism involving pre-equilibrium spin state interconversion of quartet ⁴4Co^IIIIH₂2bim to its doublet excited state ²2Co^IIIIH₂2bim, followed by spin-allowed HAT to the organic acceptor. This mechanism is consistent with the available kinetic, thermochemical and spectroscopic measurements. It indicates that the slow rates are due to the large change in geometry between Co^IIIIH₂2bim and Co^IIIIIIHbim, rather than any inherent difficulty in changing spin state. The implications of these results for other spin-forbidden or ‘two-state’ HAT processes are discussed.

---

Introduction

The influence of spin changes on the reactivity of transition-metal complexes is a topic of increasing importance and debate.¹ Spin issues are more complicated in transition-metal chemistry than in organic reactions because the stronger spin–orbit coupling makes spin a less “good” quantum number. A number of studies have suggested that formal spin changes can have a substantial effect on transition-metal reactions,¹ while others indicate the opposite.² Perhaps the greatest attention has been paid to the role of spin states in hydrogen atom transfer (HAT) reactions of transition-metal oxo species, especially the ferryl (Fe=O) active site in cytochrome P450, other enzymes and model systems.³

HAT reactions involve the concerted transfer of a proton and an electron from one reagent to another (eqn (1)). HAT is a fundamental chemical reaction step⁴ that has long been recognized as an important part of organic reactivity such as halogenation and combustion.⁵ It has more recently been recognized as an important type of transition-metal reactivity,^1,3,4,6 including industrial processes, enzymatic reactions and organic transformations.^7,8 In metal complexes, net H˙ transfer typically occurs with the redox-active metal accepting/donating the electron and the proton moving to/from a basic site on a ligand (eqn (2)).⁶ In reactions of cytochrome P450 compound I, the proton adds to the oxo group and the electron primarily reduces the porphyrin radical cation.³ Since these reactions have a formal separation of the e⁻ and H⁺, they can be viewed as a subset of a larger class of concerted proton-electron transfer (CPET) or proton-coupled electron transfer (PCET) reactions.^6,9,10

A–H + B˙ → A˙ + H–B (1)

L_nM–X–H + B˙ → L_nM–X + H–B (2)

Computational studies by Shaik and co-workers, and others, have led the way in showing that the involvement of multiple spin states can significantly affect transition-metal HAT reactivity.^3h For instance, such ‘two-state reactivity’ has been suggested to account for some of the unusual experimental observations in P450 and other systems.^3,11 Recent experimental studies from Que and co-workers have indicated that their high-spin (S = 2) iron(IV)-oxo species cleave C–H bonds significantly faster than the related intermediate-spin (S = 1) complexes, providing experimental evidence that the high-spin form is more reactive.¹² It has often been suggested that unpaired spins at the abstracting atom are critical to this reactivity.¹³ However, d⁰permanganate and chromium(VI) compounds have long been known to be reactive H-atom abstractors.^6,14 More recently, Prokop, de Visser and Goldberg have reported an S = 0 manganese(V)-oxo complex that is highly reactive for HAT.¹⁵ Simple organic compounds, including alkenes, ketones and quinones, can also abstract H-atoms even though they have no unpaired spins.¹⁶ We have argued that spin states are not a primary determinant of HAT reactivity.⁶ We and others have found that in most cases, HAT rate constants can be quantitatively predicted based on the free energy of H-atom transfer (the driving force) and Marcus-type intrinsic barriers.^6,17 Steric effects can also be important.¹⁸ Resolving this issue has been complicated because most of the proposed ‘two-state reactivity' systems are complex, with multiple intermediates and spin states.

Described here are, to our knowledge, the first fully characterized examples of spin-forbidden HAT reactions, in which the reactants and products are well-characterized species.¹⁹ These reactions are relatively simple models for the more complex processes occurring in heme and non-heme enzymes and model systems. The reactions involve hydrogen atom transfer from cobalt(II) tris(2,2′-bi-2-imidazoline), Co(H₂bim)₃²⁺, abbreviated Co^IIIIH₂2bim (H₂bim = 2,2′-bi-2-imidazoline), forming the oxidized and deprotonated analogue Co(H₂bim)₂(Hbim)²⁺ (Co^IIIIIIHbim, Scheme 1; ancillary H₂bim ligands that do not change protonation state during the reaction are indicated just by N–N). The H-atom is transferred to the stable organic radicals TEMPO (2,2,6,6-tetramethyl-1-piperidinyloxyl), 2,4,6-tri-tert-butylphenoxyl (^tBu₃ArO˙),²⁰ or benzoquinone (BQ, which accepts two hydrogen atoms to form hydroquinone, H₂2Q). These reactions are overall spin-forbidden because they interconvert high-spin (HS) Co(II) complexes (⁴T_1g, t_2g⁵e_g² in idealized O_h symmetry, S = ³/₂) and low-spin (LS) octahedral Co(III) complexes (¹A_1g, t_2g⁶, S = 0).²¹ For instance, in the reaction of Co^IIIIH₂2bim (S = ³/₂) with ^tBu₃ArO˙ (S = ¹/₂) (Scheme 1), the reactant state can be S = 1 or S = 2, but the products Co^IIIIIIHbim and ^tBu₃ArOH are all S = 0.

Scheme 1 Reactivity of Co^IIIIH₂2bim with hydrogen atom acceptors X.

The cobalt HAT reactions are much slower than similar reactions of the isostructural iron–2,2′-biimidazoline compounds or other related iron and ruthenium complexes.^19,22–26 The Co^IIIIH₂2bim/Co^IIIIIIHbim HAT self-exchange reaction²⁷ is also much slower than for its Fe and Ru counterparts.^22,25a The slowness of the cobalt HAT reactions parallel related electron transfer (ET) reactions that interconvert HS Co(II) and LS Co(III), which are the textbook examples of slow ET.^28,29 This report presents experimental and computational studies that probe the detailed mechanism of the reactions, including whether spin-state change precedes the HAT step, follows HAT, or is concerted with HAT. It is concluded that the spin-state change occurs in a rapid pre-equilibrium step prior to HAT, and that the origin of the low reactivity of the cobalt complexes is not due to any inherent difficulty in changing the spin state.

Results

I. Thermochemistry

Cyclic voltammetry of [Co^II(H₂bim)₃][Cl]₂^27,30 in MeCN with 0.1 M [ⁿBu₄N][PF₆] shows a broad, quasi-reversible wave with E_1/2 = −0.60 ± 0.10 V vs. Cp₂Fe^+/0.^19,31 The broadness of the wave is presumably due to slow electrochemical kinetics.²⁷ In order to obtain a more reliable potential, an equilibrium constant was measured for the oxidation of Co^IIIIH₂2bim to Co^IIIIIIH₂2bim by decamethylferrocenium hexafluorophosphate ([Cp₂^*Fe][PF₆]) in MeCN (eqn (3)). Addition of aliquots of Co^IIIIH₂2bim to [Cp₂^*Fe]⁺ caused a drop in the optical absorbance of [Cp₂^*Fe]⁺ (λ_max = 780 nm) and growth of Co^IIIIIIH₂2bim absorbance (Fig. 1). These reactions proceed slowly to equilibrium over about 4000 s. Analyses of the spectra showed good mass balance, with a reasonable isosbestic point at 593 ± 1 nm and yielded K₃ = 0.090 ± 0.032 (E₃ = −0.062 ± 0.011 V). With E_1/2([Cp₂^*Fe][PF₆]) = −0.59 V,³² this gives E_1/2(Co^IIIIIIH₂2bim) = −0.53 ± 0.02 V vs. Cp₂Fe^+/0 in MeCN.

Fig. 1 UV-Visible spectra for the reaction of Co^IIIIH₂2bim + [Cp₂^*Fe]PF₆ (1.32 mM) ⇋ Co^IIIIIIH₂2bim + Cp₂^*Fe upon reaching equilibrium. Initial [Co^IIIIH₂2bim]: 0 mM, solid red line; 1.12 mM, solid blue line; 1.93 mM, dashed green line; and 3.35 mM, dotted black line.

The pK_a of Co^IIIIIIH₂2bim was determined to be 20.3 ± 0.6 in MeCN based on a spectrophotometric titrationvs. the iron complex, Fe^IIIIIIHbim {pK_a(Fe^IIIIIIH₂2bim) = 17.5 ± 0.55²²} or vs.piperidine (the latter obtained in the presence of 0.1 M [ⁿBu₄N][PF₆]).^19,31 The pK_a and E_1/2 values together give the bond dissociation free energy (BDFE) of an N–H bond in Co^IIIIH₂2bim of 70 ± 1 kcal mol⁻¹.^33–35 This is in agreement with previous equilibrium measurements which give BDFE = 69.5 ± 0.9 kcal mol⁻¹, the bond dissociation enthalpy (BDE) = 62 ± 1 kcal mol⁻¹ and an unusually large negative entropy for H-atom loss, −41 cal mol⁻¹ K⁻¹.^19b

II. Reactivity

A. Co^IIIIH₂2bim + TEMPO ⇄ Co^IIIIIIHbim + TEMPOH. Co^IIIIH₂2bim (10 mM) reacts with 3–15 equiv. TEMPO to give an equilibrium mixture of Co^IIIIH₂2bim, TEMPO, Co^IIIIIIHbim and TEMPOH over 48 h at 298 K (eqn (4)), as previously reported.^19b,c1H NMR spectra indicate excellent mass balance and ∼10% conversion of Co^IIIIH₂2bim. In the opposite direction, Co^IIIIIIHbim (0.3–0.6 mM) + 10–1000 equiv. of the hydroxylamine TEMPOH gives Co^IIIIH₂2bim and TEMPO in >90% yield over the course of 3–5 h. The derived equilibrium constant and thermodynamic parameters from a Van't Hoff analysis are given in Table 1.

Table 1 Kinetic and thermodynamic values for HAT reactions of Co^IIIIH₂2bim with hydrogen acceptors, X: Co^IIIIH₂2bim + X → Co^IIIIIIHbim + H-X.^a

Substrate X	K eq, k	ΔG	ΔH	ΔS
a Values at 298 K. Units: K4, K5, K5: unitless; K4P, K4S: M^−1; k4, k5, k6: M^−1 s^−1; k–4HAT: s^−1; ΔG and ΔH: kcal mol^−1; ΔS: cal mol^−1 K^−1. b Results from refs. 19b,c. Based on data from 273–313 K for ΔH4^‡, ΔS4^‡; 278–313 K for ΔH–4HAT^‡, ΔS–4HAT^‡. k4 = K4Pk4HAT. c Thermochemical data from ref. 19b. Eyring parameters based on rate constants from 297–341 K. d Reaction of Co^IIIIH22bim + ½ BQ (benzoquinone) to make Co^IIIIIIHbim + ½ H22Q (hydroquinone). e Co^IIIIIIHbim + H22Q → Co^IIIIIIHbim|H22Q, See experimental section, ESI and Fig. S1†.
TEMPO ^b	K 4 = (5.9 ± 0.8) × 10^−3	ΔG4° = +3.0 ± 0.4	ΔH4° = −9.3 ± 0.4	ΔS4° = −41 ± 2
	K 4S = 61.3 ± 0.8	ΔG4S° = −2.44 ± 0.05	ΔH4S° = −4 ± 2	ΔS4S° = −9 ± 4
	0.16 < K4P < 2.6	ΔG4P° = 0.27 ± 0.83
	k 4 = (1.8 ± 0.5) × 10^−4	ΔG4^‡ = 22.5 ± 0.3	ΔH4^‡ = 9.0 ± 0.8	ΔS4^‡ = −47 ± 3
	k –4HAT = (5.25 ± 0.08) × 10^−4	ΔG–4HAT^‡ = 21.9 ± 0.2	ΔH–4HAT^‡ = 23 ± 2	ΔS–4HAT^‡ = 3 ± 6
^t Bu3ArO˙ ^c	K 5 = 3 × 10^5	ΔG5° = −7.5 ± 1.3	ΔH5° = −21 ± 1.4	ΔS5° = −45 ± 6
	k 5 = 167 ± 22	ΔG5^‡ = 14.4 ± 0.5	ΔH5^‡ = 3.3 ± 0.9	ΔS5^‡ = −37 ± 3
	k 5H/k5D = 1.30 ± 0.06
½BQ ⇌ ½H22Q^d	K 6 = 2.4 ± 0.8	ΔG6° = −0.52 ± 0.11
	K 6S = 14 ± 7^e	ΔG6S° = −1.6 ± 0.3^e
	k −6H/k−6Dca. 1.5

---

The kinetics of reaction (4) have been monitored in both directions using UV-Visible spectroscopy.^19c In the forward direction, the kinetic data are well fit by an opposing second-order approach-to-equilibrium kinetic model over the available range of [TEMPO], with k₄ = (1.8 ± 0.5) × 10⁻⁴ M⁻¹ s⁻¹ at 298 K. Eyring parameters derived from rate constants from 273–313 K are given in Table 1. In the reverse direction, optical measurements show second-order kinetics at [TEMPOH] < 40 mM, and saturation behaviour above this concentration.^19c The kinetics implicate a reversibly formed intermediate, most likely a hydrogen bonded complex on the pathway to HAT, shown as Co^IIIIIIHbim|TEMPOH in eqn (4). In the terminology of Marcus Theory, this is the ‘successor complex’, and the observed bimolecular k₄ is equal to k_4HATK_4P. Analysis of the saturation kinetics at 298 K gives K_4S = 61.3 ± 0.8 M⁻¹ and the first-order rate constant for the hydrogen atom transfer step k_–4HAT = (5.25 ± 0.08) × 10⁻⁴ s⁻¹ (Van't Hoff and Eyring parameters in Table 1). No saturation is observed in the forward direction at all experimentally accessible concentrations of TEMPO; K_4P was be estimated to be 0.16 < K_4P < 2.6 M⁻¹.^19c

B. Co^IIIIH₂2bim + ^tBu₃ArO˙ → Co^IIIIIIHbim + ^tBu₃ArOH. Co^IIIIH₂2bim (11.5 mM) is oxidized by 0.8 equiv. of ^tBu₃ArO˙ (9.6 mM) in ∼1 min to form Co^IIIIIIHbim and ^tBu₃ArOH in MeCN (eqn (5)). Clean conversion to products is observed by ¹H NMR spectroscopy in reactions with ≤1 equiv. of ^tBu₃ArO˙ (100 ± 10% yield based on stoichiometry). When excess ^tBu₃ArO˙ is used, other products are observed on the timescale of the NMR experiment, but excess ^tBu₃ArO˙ can be used without decomposition on shorter (stopped-flow) timescales. This reaction is faster than the TEMPO analogue in part because it is much more favourable, ΔG₅° = −7.5 ± 1.3 kcal mol⁻¹vs. ΔG₄° = +3 ± 0.4 kcal mol⁻¹ (Table 1). Both reactions have remarkably unfavourable entropies of reaction (ΔS₅°∼ –45 ± 6 cal mol⁻¹ K⁻¹).^19b This is likely due to the fact that HS Co^II has more low frequency vibrational modes than Co^III, as has recently been discussed for these and related iron complexes.^19b,24

The reaction of Co^IIIIH₂2bim (0.58–1.36 mM) and ^tBu₃ArO˙ (0.65–2.10 mM) has been studied using stopped-flow rapid-scanning UV-visible spectrophotometry under second-order conditions, monitoring the appearance of Co^IIIIIIHbim (λ_max = 586 nm) and the disappearance of ^tBu₃ArO˙ (λ_max = 640 nm) (Fig. 2). Global fitting of the spectra using Specfit™ software³⁶ indicated simple bimolecular kinetics with a rate constant k₅ = 167 ± 22 M⁻¹ s⁻¹ (Eyring parameters in Table 1).

Fig. 2 (A) Stack plot showing the UV-Visible spectra of the reaction of 1.36 mM Co^IIIIH₂2bim + 2.10 mM ^tBu₃ArO˙, showing the appearance of Co^IIIIIIHbim (and the remaining ^tBu₃ArO˙). (B) Absorbance at 586 nm over 30 s (in red), superimposed with the second-order fit (in green).

The H/D kinetic isotope effect (KIE) for reaction (5) was measured by using 1.6% CD₃OD in CH₃CN for kinetic studies of Co^IIIIH₂2bim (0.58–0.66 mM) plus ^tBu₃ArO˙ (0.82–4.7 mM). This is at least 600 equivalents of CD₃OD per Co^IIIIH₂2bim (or 100 CD₃OD per exchangeable H) and thus should achieve high deuterium enrichment of the exchangeable NH protons. Control reactions performed in the presence of CH₃OH yielded a rate constant of 156 ± 4 M⁻¹ s⁻¹, within error of k_5H, indicating that any solvent effect is negligible. The second-order rate constant k_5D = 120 ± 5 M⁻¹ s⁻¹, which gives a small kinetic isotope effect of k_5H/k_5D = 1.30 ± 0.06 (Fig. 3).

Fig. 3 Plot of second-order rate constants (k_5H, red circles; k_5D, blue diamonds) measured as a function of [^tBu₃ArO˙], where the lines show the average rate constant for each reaction.

C. Co^IIIIH₂2bim + ½ Benzoquinone (BQ) ⇄ Co^IIIIIIHbim + ½ Hydroquinone (H₂2Q). The reaction between Co^IIIIH₂2bim and benzoquinone (BQ), like the TEMPO reaction above, proceeds to an equilibrium with Co^IIIIIIHbim and hydroquinone (H₂2Q) (eqn (6)). For instance, starting with products for experimental convenience, Co^IIIIIIHbim (3.8 mM) reacts with 50.9–105.3 mM 0.5 equivalents of H₂2Q over approximately one day to form Co^IIIIH₂2bim and 0.5 equiv. BQ. Under similar conditions, the analogous iron reaction is complete in less than a second. ¹H NMR spectroscopy shows some decomposition over the timescale of the experiment, with the total Co concentration decreasing by 24 ± 14%. Despite this decay, a reasonable estimate of K₆ = 2.4 ± 0.8 could be determined (see Experimental section). This yields ΔG₆° = −0.52 ± 0.11 kcal mol⁻¹, which is in excellent agreement with ΔG₆° predicted from the BDFEs of Co^IIIIH₂2bim and H₂2Q (BDFE_avg = 70 ± 1 kcal mol⁻¹).^35,37

Optical monitoring of the reaction of Co^IIIIIIHbim and H₂2Q showed a rapid decrease in optical absorbance, occurring within the time it takes to mix solutions in a cuvette, followed by slow conversion to Co^IIIIH₂2bim over the course of hours. The initial drop in absorbance is likely due to formation of a hydrogen-bonded complex between Co^IIIIIIHbim and H₂2Q, analogous to the complex formed with TEMPOH (eqn (4)). Analysis of data over a range of concentrations gave K_6S = 14 ± 7 M⁻¹ (See Experimental section, ESI and Fig. S1†). Attempts to analyze the subsequent slow spectral changes using single wavelength data, Specfit™ global analysis software, or the method of initial rates were not successful, even using a variety of reasonable kinetic models (see ESI†). In one typical example, 0.64 mM Co^IIIIIIHbim + 71.7 mM H₂2Q, gave an approximate initial rate of d[Co^III]_total/dt ≈ 7 × 10⁻⁸ M s⁻¹ ([Co^III]_total = [Co^IIIIIIHbim] + [Co^IIIIIIHbim|H₂2Q]), which could translate to a bimolecular rate constant of k₋₆ ∼10⁻³ M⁻¹ s⁻¹, although some data suggested that under some conditions the rates might be second order in [Co^III]_total. The difficulties in analyzing the kinetic data likely result from the complexity of the mechanism (as well as the competing decomposition). The reaction likely occurs via formation of the semiquinone radical, Co^IIIIIIHbim|H₂2Q → Co^IIIIH₂2bim + HQ˙, and the HQ˙ likely reacts competitively with another Co^IIIIIIHbim to form Q or with Co^IIIIH₂2bim to reform starting materials (both pathways have ΔG° ∼ +8 kcal mol⁻¹).³⁷ This detailed examination of reaction (6) corrects the preliminary estimate of a second-order rate constant reported earlier.^19a The reaction of Co^IIIIIIDbim + D₂2Q, with the same concentrations as the example above, showed slower changes in the optical spectra and suggested a small KIE of ca. 1.5.

III. Calculations

Density functional theory calculations were performed on the cobalt-species relevant to HAT (Co^IIIIIIHbim and Co^IIIIH₂2bim) in order to gain deeper insight into the factors that govern HAT reactions in this system. Geometry optimizations (using the OPBE functional and a polarized double zeta basis, BSI) were straightforward, showing no unusual features. Several conformers exist for each structure because the protonated non-coordinated nitrogen atoms of the H₂bim and Hbim ligands adopt slightly pyramidal structures and the nitrogen lone pairs on each H₂bim ligand can be either syn or anti to one another. Test calculations show that different conformers are very close in energy to one another (1 kcal mol⁻¹ or less). The calculated energies, summarized in Table 2, all refer to the ‘same’ overall conformer for each species. The larger basis set BSII is expanded to triple-zeta for the nitrogen atoms.

Table 2 Calculated quartet/doublet splittings for Co^IIIIH₂2bim, singlet/triplet splittings for Co^IIIIIIHbim and energies of reaction (4), as well as the experimental value of ΔG₄°.^a

Method	ΔE/ΔG (^4,24,2Co^IIIIH22bim)	ΔE/ΔG (^1,31,3Co^IIIIIIHbim)	ΔE/ΔG (reaction 4)
a In kcal mol^−1. For reaction (4), overall energetics are calculated for the transformation ^44Co^IIIIH22bim + TEMPO → ^1Co^IIIIIIHbim + TEMPOH. ΔE values are zero-point energy corrected electronic energies, ΔG values are at 298 K and values labelled ‘PCM’ include a correction for acetonitrile solvent effects calculated using PCM at the OPBE/BSI level.
OPBE/BSI	9.01/10.83	−0.66/−3.22	26.66/32.00
OPBE/BSII	8.79/10.62	−0.21/−2.78	27.37/32.71
B3LYP/BSII	14.44/16.26	0.88/−1.68	35.88/41.21
B3LYP*/BSII	10.24/12.07	2.63/0.06	28.00/33.33
B3LYP**/BSII	5.83/7.65	4.36/1.79	19.99/25.32
B3LYP**-D3/BSII	2.50/4.32	7.42/4.85	12.82/18.16
OPBE(PCM)/BSI	(−)/7.93	(−)/4.56	(−)/17.70
B3LYP**(PCM)/BSII	(−)/4.75	(−)/9.58	(−)/11.02
B3LYP**-D3(PCM)/BSII	(−)/1.42	(−)/12.64	(−)/3.85
Experiment	(−)	(−)	(−)/3.0

---

The OPBE functional³⁸ was used for geometry optimization partly due to suggestions that it provides accurate relative energies for different spin states of metal complexes.³⁹ Accurate DFT calculation of spin-state splittings is known to be challenging, with results often being very sensitive to small changes in the nature of the functional.^40,41 Gas phase calculations at the OPBE/BSI level predict a quartet ground state for Co^IIIIH₂2bim, but surprisingly, the Co(III) species Co^IIIIIIHbim is predicted to have a triplet ground state, slightly lower in electronic energy and free energy than the singlet state found experimentally. As can be seen in Table 2, the calculated energies are not very basis-set sensitive, with very small changes in energy resulting from expanding the nitrogen atom basis set to 6-311G* in BSII. The spin-state splittings are however strongly sensitive to the functional used. B3LYP predicts relative spin state energetics for the Co(III) species similar to those found with OPBE, but for Co(II), B3LYP favours the high-spin ground state. Decreasing the proportion of exact exchange (in B3LYP* and B3LYP**) favours the low-spin states in both compounds, as commonly observed.^40,41 Including a single-point -D3 correction for dispersion⁴² at the OPBE structures further favours the slightly more compact low-spin states. Note that the computed splitting for Co^IIIIIIHbim may be partly affected by what is likely to be an incorrect description of the triplet state. The latter involves significantly less than two unpaired electrons on Co, with significant spin density on the deprotonated Hbim ligand, corresponding to a mixture of the expected electronic structure with a resonance form with low-spin Co(II) and an Hbim radical. This type of unpaired electron delocalization with ligand oxidation is not supported by the experimental spectroscopy but was noted in a previous computational study of Fe^IIIIIIHbim complexes,²⁴ and may be due to problems with the electron self-interaction error in DFT. None of the other species show this problem.

To provide some insight into the contribution of solute entropy to the reaction energy, it is interesting also to note the calculated gas-phase entropy changes at 298 K, based on the OPBE/BSI frequency calculations, which are not shown in Table 2. For quartet to doublet excitation of Co^IIIIH₂2bim, and singlet to triplet excitation of Co^IIIIIIHbim, these are −8.0 cal mol⁻¹ K⁻¹ and 10.8 cal mol⁻¹ K⁻¹, respectively, consistent with significantly stiffer vibrational behaviour for the low-spin states. This leads to calculated free energies for spin-state exchange (at 298 K) of 10.83 and −3.22 kcal mol⁻¹, respectively.

Inclusion of approximate acetonitrile solvent effects with a polarized continuum model changes the relative energetics significantly, as the low-spin complexes involve tighter metal–ligand binding, hence greater polarization of the ligands, and stronger interactions with solvent.⁴³ The calculated energies in the presence of the continuum solvent model include both enthalpic and entropic effects corresponding to the solute–solvent interaction. This leads to a decreased quartet to doublet excitation free energy for Co^IIIIH₂2bim and an increased singlet to triplet excitation free energy for Co^IIIIIIHbim. At the B3LYP**-D3(PCM)/BSII level, these values are 1.42 and 12.64 kcal mol⁻¹, respectively.

The calculated reaction energy for reaction (4), HAT from Co^IIIIH₂2bim to TEMPO, is also shown at various levels of theory in Table 2.⁴⁴ In the gas phase, this reaction is predicted to be very unfavourable, both in energy and free energy terms. The entropy of reaction (not shown in Table 2) is computed to be −22.6 cal mol⁻¹ K⁻¹, showing that the increase in vibrational frequencies upon oxidation plays a significant role in the reaction thermodynamics. Including the effect of the continuum solvent stabilizes the Co(III) product more strongly than the reactant, leading to a much smaller reaction free energy, with the B3LYP**-D3(PCM) method yielding a value very close to the experimental ΔG₄° = +3 kcal mol⁻¹. This is probably in part due to cancellation of errors, but we nevertheless use values based on this method henceforth in the paper.

The solvation calculations do not provide a separate estimate for entropy and enthalpy, but it is reasonable to assume that Co^IIIIIIHbim is strongly stabilized in enthalpic terms by solvent, but that this has an entropic cost. This is consistent with the experimental measurement of a highly negative entropy of reaction. Based on the calculations, the negative ΔS° is due partly to the vibrational entropy of the system (calculated gas phase entropy change of −22.6 cal K⁻¹ mol⁻¹) but also to the greater solvent organization around Co^IIIIIIHbim.

Many attempts were made to locate an adiabatic transition state for HAT from Co^IIIIH₂2bim to TEMPO, without success.⁴⁵ This is due to the narrowly avoided nature of the potential energy surface crossing associated with the proton-coupled electron-transfer. Perhaps this indicates that reactions of this type, in which proton and electron transfers are concerted but ‘separate’ in some way, may require different computational approaches such as Hammes–Schiffer's multistate continuum theory.⁴⁶

Discussion

The cobalt reactions described here are very slow in comparison to similar metal-mediated hydrogen atom transfer (HAT) reactions. HAT from Co^IIIIH₂2bim to TEMPO has k₄ = (1.8 ± 0.5) × 10⁻⁴ M⁻¹ s⁻¹, while the same reaction with the equivalent iron complex Fe^IIIIH₂2bim is 3400 times faster (k_Fe = 0.62 ± 0.8 M⁻¹ s⁻¹).²⁴ In this comparison, the iron reaction is slightly less favourable, as ΔG₄° and ΔG_Fe° are +3.0 ± 0.4 and +5.0 ± 0.1 kcal mol⁻¹,²⁴ so at the same driving force the iron would likely be another factor of 5 faster.⁴⁷ The Co^IIIIH₂2bimreduction of benzoquinone takes roughly a day at typical concentrations, while the analogous iron reaction is done in less than a second. In general, the rates of the iron reactions are typical of isoergic or downhill transfers of H˙ between electronegative elements (N or O), while the cobalt examples are unusually slow.⁴⁸ From another perspective, we have previously estimated H-atom transfer self-exchange rate constants for metal complexes using the Marcus cross relation (an improved version of that analysis is given in ESI†), with the conclusion that the cobalt value is at least a million times smaller than that for iron.²⁷

The sections below examine the mechanism of the cobalt reactions at two levels of detail in order to understand both why they are so slow and the role of the spin change. First, we discuss whether the reactions occur by HAT or whether they could occur by stepwise transfer of the electron and the proton. Then, computations are used to examine the TEMPO reaction, which clearly occurs by HAT, to ask whether the H˙ transfer occurs prior to the spin change, after the spin change, or concurrent with spin change. Finally, we discuss how the analysis of this well-characterized system has broader implications for other, more complex spin-forbidden processes.

I. Reaction mechanisms, Part 1: HAT vs. initial PT or ET

Any reaction involving transfer of one electron and one proton can occur by (i) initial proton transfer (PT) followed by electron transfer (ET); (ii) ET followed by PT; or (iii) transfer of e⁻ and H⁺ in the same kinetic step (HAT/CPET).^6,9,35 For the reaction of ⁴4Co^IIIIH₂2bim with ²TEMPO, ΔG° for initial PT to form ⁴4Co^IIIIHbim and ²TEMPOH⁺ is indicated by the pK_as of each reactant (the superscripts indicate the spin states; Scheme 2). The pK_a of TEMPOH⁺˙ is ∼ −4³⁵ and a lower limit for the pK_a of Co^IIIIH₂2bim is given by the known pK_a(Co^IIIIIIH₂2bim) = 20.3 ± 0.6.³¹ Thus ΔpK_a > 24 for an initial PT step, and ΔG_PT4° > +33 kcal mol⁻¹. Since this is much higher than the observed barrier for the reaction, ΔG₄^‡ = 22.5 ± 0.3 kcal mol⁻¹, initial PT is not possible. Initial ET from ⁴4Co^IIIIH₂2bim to ²TEMPO forms ¹1Co^IIIIIIH₂2bim + ¹TEMPO⁻, which is roughly as unfavourable, with ΔE_1/2 = −1.42 V (ΔG_ET4° = +32.7 kcal mol⁻¹), based on E_1/2(Co^IIIIIIH₂2bim) = −0.53 ± 0.02 V and E_1/2(TEMPO˙^/−) = −1.95 V³⁵ (all potentials here vs. Cp₂Fe^+/0 in MeCN). Thus, the Co^IIIIH₂2bim + TEMPO reaction cannot occur by initial ET or PT; the proton and electron are indicated to transfer in the same kinetic step (HAT).

Scheme 2 Possible pathways for reaction (4). HAT is thermodynamically favoured over initial PT or ET.

This conclusion is not affected by spin issues. Both in this specific case and in general, forming alternative spin states of the products would be less favourable. For instance, the pK_a of Co^IIIIH₂2bim used in the analysis above refers to proton dissociation to give the most stable form of the conjugate base Co^IIIIHbim, in this case with the same quartet spin state. Therefore, proton transfer from Co^IIIIH₂2bim to TEMPO to give the doublet Co^IIIIHbim would have a more positive ΔG°_PT, and therefore is also not a possible mechanism. For electron transfer, the redox potential used in the analysis is for the most thermodynamically favourable spin-forbidden ⁴4Co^IIIIH₂2bim → ¹1Co^IIIIIIH₂2bim couple (this is why the chemical equilibration in eqn (3) and Fig. 1 requires an hour to go to completion). Electron transfer to form the triplet Co(III) product would only make ΔG°_ET more positive. Pre-equilibrium conversion of ⁴4Co^IIIIH₂2bim to ²2Co^IIIIH₂2bim would also have no effect on the ΔG°_ET. Thus the Co^IIIIH₂2bim + TEMPO reaction cannot occur by initial ET or PT, regardless of spin state.

For the reactions of Co^IIIIH₂2bim with ^tBu₃ArO˙ and Co^IIIIIIHbim with H₂2Q, such thermochemical arguments are not definitive. For Co^IIIIH₂2bim + ^tBu₃ArO˙, PT is ruled out but initial ET is possible (ΔG_PT5° > 32 kcal mol⁻¹ is larger than ΔG₅^‡ = 14.4 ± 0.1 kcal mol⁻¹, but ΔG_ET5° = 3.9 ± 0.7 kcal mol⁻¹ is smaller).⁴⁹ A rough estimate of this initial ET rate constant from the Marcus cross relation, k_ET5 ≤ 1 M⁻¹ s⁻¹, is slower than the observed rate of k₅ = 167 ± 22 M⁻¹ s⁻¹, but perhaps within the uncertainty of the cross relation.^28,50–52 Another possible pathway could involve initial uphill conversion of ⁴4Co^IIIIH₂2bim to ²2Co^IIIIH₂2bim followed by ET to ^tBu₃ArO˙.⁵³ For Co^IIIIIIHbim + H₂2Q, initial ET can be ruled out based on its very high ΔG_ET° (>36 kcal mol⁻¹), but initial PT is possible based on ΔG_PT° = +13 ± 1 kcal mol⁻¹.⁵⁴ Still, for both the ^tBu₃ArO˙ and BQ/H₂2Q reactions, other arguments suggest that HAT mechanisms are likely. In both cases, HAT is significantly more favourable than initial ET or PT and primary kinetic isotope effects are observed, k_5H/k_5D = 1.3 ± 0.1 and k_−6H/k_−6D = ca. 1.5, indicating that the proton is transferring in the rate determining step.^55,56

II. Reaction mechanism, Part 2: The role of the spin-state change

The Co^IIIIH₂2bim + TEMPOH reaction is, to our knowledge, the first spin-forbidden hydrogen atom transfer (HAT) reaction where the reactants and products have all been isolated and characterized. The ^tBu₃ArO˙ and BQ reactions likely also involve spin-forbidden HAT, but we focus on the TEMPOH reaction because its HAT mechanism is better established. The precursor complex containing high-spin (HS) ⁴4Co^IIIIH₂2bim (S = ³/₂, ⁴T_1g, t_2g⁵e_g², in octahedral symmetry) and TEMPO (S = ¹/₂) has a total spin quantum number S = 1 or 2, depending on how the spins couple. The products, however, have S = 0 (no unpaired electrons): low-spin (LS) Co^IIIIIIHbim (¹A_1g, t_2g⁶) and TEMPOH. The reactions are formally spin-forbidden because they start on one spin-state surface and finish on a different one.

A. Concerted vs. stepwise HAT and spin-state change. With the mechanism of HAT established, computations were used to determine whether the spin state change occurs before, during or after HAT. Computations have explored the energy surfaces for Co^IIIIH₂2bim + TEMPO. The cobalt species is a quartet with three unpaired electrons, TEMPO is a doublet with one unpaired electron. This means that the encounter complex between them should have near-degenerate quintet and triplet states; we discuss reactivity of the latter, from which only one spin flip is required to yield product. The triplet surface of the Co^IIIIH₂2bim|TEMPO precursor complex intersects the surface of the singlet Co^IIIIIIHbim|TEMPOH successor complex along a multidimensional seam. The minimum energy crossing point (MECP) could be the high point along the reaction coordinate (equivalent to a saddle point connecting the reactants and products), or it could occur before or after the transition structure (TS). In the first case, HAT and spin-state change are concerted, while the other two mechanisms involve stepwise spin-state change and HAT. The MECP being prior to the TS, for instance, would indicate that spin change occurs prior to hydrogen transfer. Such pre-equilibrium spin change has been suggested for cobalt ET reactions⁵⁷ and it has been implicated in other chemical reactions.¹ Rapid equilibration among spin states has been discussed as one possible scenario in two-state reactivity, for instance in a study on alkane hydroxylation by synthetic iron(IV) oxo complexes.^3u These three possible pathways are illustrated in Scheme 3, and free energy surfaces corresponding to the three cases are drawn in Fig. 4. It should be emphasized that the one-dimensional surfaces in Fig. 4 are very crude simplifications of the actual multidimensional surfaces. For instance, the structural change that accompanies spin change is not along the minimum energy pathway for the direct spin-allowed reaction, as suggested by this picture. Related pictures have been used to show the relationship between stepwise and concerted paths for dissociative electron transfer as a function of differing energetics.⁵⁸

Scheme 3 Three possible mechanisms for spin-forbidden HAT.

Fig. 4 Schematic free energy surfaces for the conversion of the triplet reactant state of ⁴4Co^IIIIH₂2bim|²TEMPO (blue) to the singlet state for ²2Co^IIIIH₂2bim|²TEMPO (green) in the three possible cases. (A) Pre-equilibrium spin change prior to HAT; (B) HAT prior to spin change; and (C) HAT concerted with spin change because the minimum energy crossing point (MECP) is below the HAT transition structures on the two surfaces.

The possibility of concerted HAT and spin change (Fig. 4C) has not been probed computationally, both because these calculations are very challenging and because one of the stepwise paths is energetically very reasonable, as described below. This favouring of a stepwise path fits with the suggested general argument^1b,66 that except in special circumstances, bimolecular spin-forbidden processes are expected to occur preferentially through stepwise mechanisms, involving a unimolecular spin-state change and a spin-allowed bimolecular step. Since both spin-state changes and bimolecular reactions have unfavourable entropies of activation,^1b a spin-forbidden HAT step would be doubly unfavourable for entropic reasons, whereas this is not true for the individual steps of the stepwise mechanism. Some cases where bond-making and breaking occurs concertedly with spin-state change are known.^1b This tends to be only in cases where spin-state change in both reactants and products is very unfavourable (e.g., in decomposition of gas phase ³CH₃O⁺ to yield ¹HCO⁺ and H₂, the singlet state of the reactant is high in energy, and likewise for the triplet states of products).⁵⁹ In the present reactions, this is not the case, as the different spin states of the Co^III and especially Co^II species are quite close in energy.

One stepwise mechanism involves initial spin-allowed HAT from the quartet state of Co^IIIIH₂2bim to give triplet Co^IIIIIIHbim (⁴4Co^IIIIH₂2bim|²TEMPO → ³3Co^IIIIIIHbim|¹TEMPOH), followed by spin relaxation through spin-orbit coupling⁶⁰ to the experimentally observed singlet state (Fig. 4B). The latter step is assumed to be rapid, for reasons discussed below for the analogous spin-state change of Co^IIIIH₂2bim. The key step here is therefore the first one. Combining the overall calculated reaction energy and the spin-state splitting of Table 1, it can be seen that the initial product in this mechanism, ³3Co^IIIIIIHbim + TEMPOH, lies much higher in free energy than reactants, by ca. 16 kcal mol⁻¹ according to the B3LYP**-D3 calculations. Though there will inevitably be some error in this calculated value, we note that the different calculations in the Table all tend to give either a large singlet/triplet splitting or a high reaction free energy, so that the total free energy of high-spin products relative to reactants is never lower than 15 kcal mol⁻¹. Hence the large reaction free energy is probably a fairly reliable computational prediction. In addition, octahedral Co(III) complexes are almost always LS. Co^III complexes with nitrogen ligands are far from the spin-crossover point⁶¹ (CoF₆³⁻,⁶² and a more recent nitrogen coordinated Co complex⁶³ are some of the rare notable HS Co^III complexes). This indicates that the HS Co(III) state is not likely to be accessible as an intermediate. The transition state for HAT would lie still higher in free energy, due to the unfavourable entropic contribution from bringing two separate molecules together (ca. 10 kcal mol⁻¹) as well as any contribution from the intrinsic barrier to transfer. Indeed, in the related iron reaction,²⁴ the activation free energy for the similar HAT step is 14 kcal mol⁻¹. Hence the free energy of activation of the ⁴4Co^IIIIH₂2bim + TEMPO → ³3Co^IIIIH₂2bim + TEMPOH step would probably be well above 25 kcal mol⁻¹. Notwithstanding the computational uncertainties mentioned above, this value is higher than the experimentally observed activation free energy ΔG₄^‡ = 22.5 kcal mol⁻¹, and therefore initial HAT followed by spin-change is unlikely to be the preferred mechanism.

The second possibility is initial spin crossover of quartet Co^IIIIH₂2bim to its doublet state, followed by spin-allowed HAT to yield singlet Co^IIIIIIHbim (Fig. 4A). Experiments^64,65 and theory⁶⁶ both show that spin crossover in transition-metal complexes occurs rapidly when it is thermodynamically favoured, with k > 10⁶ s⁻¹ in almost all cases at room temperature, and often significantly larger. For instance, conversion of LS [Co^II(trpy)₂]²⁺ in methanol solution to the HS spin state (ΔH° = +2 kcal mol⁻¹) occurs faster than 2 ns (k > 3 × 10⁸ s⁻¹; trpy = 2-2′;6′,2′′-terpyridine).^67,68b For the pathway discussed here, the downhill direction is the reverse process, relaxation of doublet Co^IIIIH₂2bim to quartet. Reaction in the thermodynamically favoured direction is fast especially when the potential energy surfaces of the two states intersect at a point that lies close in energy to the equilibrium structure of the higher-energy spin state. Accordingly, we have optimized the structure of the minimum energy crossing point (MECP) between doublet and quartet potential energy surfaces. These calculations were performed at the OPBE/BSI level of theory in vacuum. As often in such cases, the MECP is indeed found to lie very close in energy to the doublet minimum, just 1.2 kcal mol⁻¹ higher. This value would certainly change somewhat if one included the effect of solvent and switched to a more accurate functional, but it would be expected to remain very low. Hence the process ²2Co^IIIIH₂2bim → ⁴4Co^IIIIH₂2bim should be very fast, with a rate constant at least 10⁶ s⁻¹. The calculations therefore support a mechanism of initial spin change followed by HAT (Scheme 4).

Scheme 4 Changes in the occupation of the cobalt d orbitals for the pathway of spin change followed by hydrogen atom transfer.

The free energy at room temperature for the forward spin-state change, ⁴4Co^IIIIH₂2bim → ²2Co^IIIIH₂2bim, is calculated to be ∼1.4 kcal mol⁻¹ [B3LYP**-D3/BSII(PCM)] so the predicted spin-crossover equilibrium constant K_sc is ∼0.1. The B3LYP**-D3 level of theory may slightly underestimate the quartet–doublet splitting, but it should be noted that a fairly small splitting is consistent with the spectroscopic analysis in the next section. With this value, and k(²Co → ⁴Co) > 10⁶ s⁻¹, we estimate that ⁴4Co^IIIIH₂2bim → ²2Co^IIIIH₂2bim should have a rate constant of at least 10⁵ s⁻¹. This is nine orders of magnitude faster than the observed rate of reaction, so this step should be in rapid pre-equilibrium. The overall reaction is therefore expected to occur under ‘Curtin–Hammett conditions’, where a rapid pre-equilibrium allows the system to proceed via the more reactive state - in this case via the doublet excited spin state.

A rough estimate of the rate constant for spin-allowed HAT from ²2Co^IIIIH₂2bim to TEMPO can be obtained by comparison with the spin-allowed reaction of the iron analogue, iron(II) tris(bis-tetrahydropyrimidine) Fe^II(H₂bip)₃²⁺ with TEMPO, which occurs with a rate constant of 2.6 × 10² M⁻¹ s⁻¹ (ΔG^‡ = 14 kcal mol⁻¹).²⁴ The reaction of excited-state ²2Co^IIIIH₂2bim is a little less favourable in free energy terms than this iron analogue (ca. + 2.4 vs. −0.3 kcal mol⁻¹), which should make the ²2Co^IIIIH₂2bim rate constant about a factor of 10 smaller (∼1.3 kcal mol⁻¹ higher barrier). Also, the intrinsic barrier for the cobalt reaction is likely to be higher than the iron case, because the ²2Co^IIIIH₂2bim → ¹1Co^IIIIIIH₂2bim conversion involves significant bond length changes due to the transfer of a σ antibonding (e_g) electron (low-spin Co(II) complexes are typically Jahn–Teller distorted⁶⁸). Thus we estimate an activation free energy for the forward reaction from ²2Co^IIIIH₂2bim ≥ 17 kcal mol⁻¹. If one adds the calculated free energy difference between ²2Co^IIIIH₂2bim and ⁴4Co^IIIIH₂2bim, this would give an overall activation free energy of ca. ≥ 18 kcal mol⁻¹,⁶⁹ in reasonable agreement with the experimental value of 22.5 kcal mol⁻¹, especially considering the significant uncertainty in the calculated spin-state splitting. A similar pathway of initial spin crossover has been suggested for electron-transfer self exchange reaction between ⁴T_1g Co(NH₃)₆²⁺ and ¹A_1g Co(NH₃)₆³⁺ on the basis of computations.⁷⁰

C. Experimental support for low-energy spin crossover for Co^IIIIH₂2bim. HS/LS equilibria have been observed for a number of nitrogen-ligated Co(II) complexes⁶⁸ and a few octahedral LS Co(II) complexes are known (although they are rare and tend to form five-coordinate species). For example, [Co^II(trpy)₂]²⁺ compounds are mixtures of HS and LS forms in solution at room temperature.⁶⁸ Thus it is reasonable to propose that initial conversion of Co^IIIIH₂2bim to its low-spin state has only a modest energy cost.

Experimentally, the optical spectrum of Co^IIIIH₂2bim (Fig. 5) provides an estimate of the vertical excitation energy from the ⁴T_1g ground state to the ²E_g excited state (in this analysis we assume idealized octahedral symmetry). Following other analyses of HS Co(II) spectra,⁶⁸ the two ligand field bands are assigned as [λ_max (ε)]: 1035 nm (11 M⁻¹ cm⁻¹), ⁴T_1g(F) → ⁴T_2g, and 485 nm (46 M⁻¹ cm⁻¹): ⁴T_1g(F) → ⁴T_1g(P). Using the d⁷ Tanabe–Sugano diagram, the ratio of these transition energies (2.13) indicates that Δ_o ≈ 10 000 cm⁻¹ and B ≈ 690 cm⁻¹ (Δ_o/B ≈ 15; see ESI†). For comparison, the high-spin [Co(bpy)₃]²⁺ ion in [Co(bpy)₃][NaRh(ox)₃] has λ_max = 870 nm and Δ_o ≈ 12 700 cm⁻¹.^68a The parameters for Co^IIIIH₂2bim indicate that the ²E_g state is 4600 cm⁻¹ (13 kcal mol⁻¹) above the ground state at the geometry of the ⁴T_1g ground state.

Fig. 5 Optical and near-IR spectrum of Co^IIIIH₂2bim in MeCN.

This vertical²E_g − ⁴T_1g excitation energy is of course larger than the energy difference between the minima of the ⁴T_1g and ²E_g states. Computationally, at the OPBE/BSI level, the electronic energy of the doublet at the quartet geometry is 14 kcal mol⁻¹ higher than at the doublet minimum. This deformation energy, plus the best estimate that the doublet minimum is 1.4 kcal mol⁻¹ above the quartet minimum, gives a rough computational estimate of ca. 15 kcal mol⁻¹ for the vertical ²E_g − ⁴T_1g energy. Given the uncertainties in the calculations as well as in the experimental analysis, this is nicely consistent with the spectroscopy. For comparison, the [Co^II(trpy)₂]²⁺ ion in solid [Co(trpy)₂](PF₆)₂ has a split transition (λ_max = 960 and 1090 nm) close to that of Co^IIIIH₂2bim, and is HS with a small thermal population of the LS state.⁶⁷ In methanol solution, the order of the spin states is reversed and Co^II(trpy)₂²⁺ is LS with rapid conversion to the HS spin state. In sum, the experimental and computational results, the spectroscopy, and the literature precedents are all consistent with the conclusion that quartet Co^IIIIH₂2bim has a low-lying doublet-spin state. These data therefore support a mechanism of spin-change prior to HAT, as shown in Fig. 4A and Scheme 4.

Conclusions and implications

TEMPO, ^tBu₃ArO˙ and benzoquinone (BQ) oxidize high-spin (HS, quartet) Co^IIIIH₂2bim to low-spin (LS) Co^IIIIIIHbim and TEMPOH, ^tBu₃ArOH and hydroquinone, respectively. The TEMPOH reaction has been shown to proceed by hydrogen atom transfer (concerted transfer of e⁻ and H⁺) and the ^tBu₃ArO˙ and BQ reactions likely follow the same pathway. The TEMPO reaction has been examined in the most detail, experimentally and computationally. It is, to our knowledge, the first experimentally fully characterized spin-forbidden HAT reaction, converting triplet or quintet ⁴4Co^IIIIH₂2bim + ²TEMPO to singlet products, ¹1Co^IIIIIIHbim + ¹TEMPOH.

Computational and experimental studies indicate that the ⁴4Co^IIIIH₂2bim + ²TEMPO reaction likely involves a spin change prior to HAT reactivity. Spin-change of the reactant ⁴4Co^IIIIH₂2bim to the excited doublet state is estimated to be about 1.4 kcal mol⁻¹ uphill, after consideration of different functionals and with inclusion of solvent effects. This value is consistent with an estimate of the excitation energy from the optical spectrum. The proposed pathway is illustrated in Fig. 6. The triplet precursor complex [⁴4Co^IIIIH₂2bim|²TEMPO] on the blue surface is in rapid pre-equilibrium with its spin excited state [²2Co^IIIIH₂2bim|²TEMPO] on the (green) singlet surface. This singlet precursor complex then undergoes spin-allowed HAT to form the singlet products.

Fig. 6 Proposed schematic reaction pathway for the conversion of precursor complex ⁴Co^IIIIIIH₂2bim|²TEMPO on the blue triplet free-energy surface to the ¹Co^IIIIIIHbim|¹TEMPOH successor complex on the green singlet surface. The suggested reaction pathway is indicated by the red arrows. Initial pre-equilibrium formation of singlet ²Co^IIIIH₂2bim|²TEMPO is calculated to be 1.4 kcal mol⁻¹ uphill, and the experimental values are ΔG^‡ = 22 kcal mol⁻¹ and ΔG° = +0.3 kcal mol⁻¹.

The HAT reactions in this study are thus indicated to proceed under ‘Curtin–Hammett conditions’, in which a rapid pre-equilibrium allows access to a spin-allowed HAT step. This mechanism provides an understanding of why the cobalt HAT reactions are so much slower than related reactions. Most examples of roughly isoergic HAT between electronegative atoms occur within seconds at typical concentrations, while the Co^IIIIH₂2bimreduction of benzoquinone requires ca. a day. HAT from Co^IIIIH₂2bim to TEMPO occurs 3400 times slower than the related iron reaction, which is 2 kcal mol⁻¹ less favourable. Under Curtin–Hammett conditions, the overall rate is not affected by the energy of the intermediate, only by the difference between the reactants and the transition state. In other words, the measured rate constant for each reaction takes the form k_obs ∼ K_sc*k_HAT and the slowness of the reactions has two origins. First of all, the equilibrium constant of the initial spin conversion process, K_sc, is shown from spectroscopy and computations to be <1.⁷¹ Secondly, while k_HAT is for a spin-allowed process, it is small because of the expected large inner-sphere reorganization on interconversion of LS Co^II and LS Co^III, mostly due to the large change in Co–N bond lengths. While experimental structures are not available for LS Co^II, the six Co–N bond lengths in high-spin Co^IIIIH₂2bim (∼2.14 Å) are an average of 0.21 Å longer than in low-spin Co^IIIIIIH₂2bim (∼1.92 Å).²⁷ Although the LS Co^II complex likely has somewhat shorter distances than the HS form, with only one electron in e_g-type σ* orbitals, substantial reorganization is still expected.

This analysis is related to the discussions some time ago of the very slow electron transfer reactions that involve the HS Co(II)/LSCo(III) redox couple.⁵⁷ These reactions are the classic examples of large inner-sphere reorganization energies λ, due to the large change in cobalt–ligand bond lengths between HS Co(II) and LS Co(III). There have also been proposals that the reactions occur by direct spin-forbidden ET with a small electron coupling, while others have suggested that spin interconversions play a key role.⁵⁷

These cobalt reactions, complicated as they are, can serve as relatively simple model systems for spin-forbidden HAT processes in heme and non-heme iron-oxo enzymes and related model systems with various metal centres. As noted above, these reactions are of much current interest and have been described as having two-state reactivity.³ This term is increasingly widely used and seems to have taken on a number of meanings. At one level, it simply refers to reactions that involve more than one spin state, and therefore likely involve a formal spin crossing somewhere along the reaction coordinate. The cobalt reactions discussed here clearly fall in this category. ‘Two-state reactivity’ also appears to have been used to indicate that a reaction proceeds concurrently on two different spin states, or that blended spin surfaces are involved.^3h,l,o However, the arguments presented above suggest that these solution HAT reactions with multiple accessible spin states will more likely be under Curtin–Hammett conditions, in which rapid initial pre-equilibrium between the spin states allows the reaction to proceed via the lowest energy transition structure (TS) (Fig. 6). This could be the mechanism for many solution and enzymatic HAT reactions, and in fact is one of the pathways discussed for a non-heme iron(IV) oxo system on the basis of DFT calculations.^3u Spin interconversion is typically fast, occurring on sub-microsecond timescales for downhill processes.

In summary, the effects of spin-state changes from reactant to product should be pronounced primarily when the excited spin states are high in energy (as in Fig. 4C), or when the reaction chemistry occurs faster than spin conversion. For reactions of first-row transition-metal species with low lying excited spin states, we suggest that the most common mechanism involves rapid spin pre-equilibrium that allows the system to access the lowest energy transition state (Curtin–Hammett conditions). Under these conditions, the spin change should not be a bottleneck for the reaction. The reactions analyzed here are not slow because of any difficulty in changing spin state. They are slow because of their need to convert to a higher energy spin state, and especially because of their large intrinsic barriers resulting from the substantial change in structure between the cobalt(II) and cobalt(III) complexes.

Experimental section

General considerations

All manipulations were carried out under nitrogen using glove-box/vacuum line techniques. ¹H NMR spectra were obtained on Bruker Avance spectrometers (Avance-500, DRX-499 and Avance-300), and are reported as (chemical shift δ, assignment, number of protons). All NMR integration errors are estimated as ±10%. UV-visible spectra were obtained with a Hewlett-Packard 8453 diode-array spectrophotometer. Air-sensitive samples were prepared in a glovebox in quartz cuvettes attached to Teflon-stoppered valves and topped with 14/20 ground glass joints. Rapid kinetic measurements were taken using an OLIS RSM-1000 stopped flow instrument which has a rapid scanning monochromator and a UV-Vis detector. More detailed descriptions of the experimental methods are given in ESI†.

Materials

Unless otherwise noted, all solvents were purchased from Fisher Scientific or EMD Chemicals. Anhydrous acetonitrile (MeCN; <10 ppm H₂O) was purchased from Honeywell Burdick & Jackson, sparged with argon and plumbed from a steel keg directly into a glovebox. Deuterated CD₃CN was purchased from Cambridge Isotope Laboratories, dried over CaH₂, vacuum transferred to P₂O₅, then vacuum transferred to fresh CaH₂ and finally into an empty vessel. All reagents were purchased by Aldrich and used as received except for H₂2Q and BQ. H₂2Q was recrystallized 2–3 times in acetone or ethanol and dried under vacuum. D₂2Q was prepared by recrystallizing H₂2Q from D₂O–CD₃OD. BQ was recrystallized once in ethanol and then sublimed 1–2 times at room temperature under static vacuum. [Cp₂^*Fe]PF₆⁷² and ^tBu₃ArO˙²⁰ were prepared according to literature procedures. Cobalt(II) tris[2,2′-bi-2-imidazoline][perchlorate] ([Co^II(H₂bim)₃][ClO₄]₂, Co^IIIIH₂2bim) and [Co^III(H₂bim)₃][ClO₄]₃ (Co^IIIIIIH₂2bim); and [Co^III(H₂bim)₂(Hbim)][ClO₄]₂ (Co^IIIIIIHbim) were synthesized and characterized following literature procedures.²⁷

CAUTION: perchlorate salts are explosive and should be handled with care and in small quantities. They should not be heated when dry or subjected to friction or shock, such as scratching with a non-Teflon-coated spatula.

K _eq measurements

In a typical experiment (reaction of Co^IIIIH₂2bim with [Cp₂^*Fe]PF₆), four Kontes cuvettes were each charged with 2 mL of a 1.32 mM MeCN solution of [Cp₂^*Fe]PF₆ (6.2 mg in 10 mL). Co^IIIIH₂2bim was added as a solid to three of the four cuvettes to form 1.12, 1.93 and 3.35 mM solutions. Spectra of the three reaction cuvettes showed a slow drop in absorbance at 780 nm (λ_max for Cp₂^*Fe⁺), over ca. 4000 s. Good mass balance was observed, with a reasonable isosbestic point at λ = 593 ± 1 nm. The final, constant absorbance gave the concentration of [Cp₂^*Fe]PF₆ at equilibrium, using ε₇₈₀ = 600 M⁻¹ cm⁻¹ (no other species absorb at 780 nm). Assuming mass balance, [Cp₂^*Fe]_eq = [Cp₂^*FePF₆]_initial − [Cp₂^*FePF₆]_eq, [Co^IIIIIIH₂2bim]_eq = [Cp₂^*Fe]_eq and [Co^IIIIH₂2bim]_eq = [Co^IIIIH₂2bim]_initial − [Cp₂^*Fe]_eq. The derived concentrations give the constant K₃ = [Co^IIIIIIH₂2bim][Cp₂^*Fe]/[Co^IIIIH₂2bim][Cp₂^*Fe⁺] = 0.090 ± 0.032 and E = (RT/F)ln(K₃) = −0.062 ± 0.011 V. Since E_1/2([Cp₂^*Fe]PF₆) = −0.59 V vs. Cp₂Fe^+/0 in MeCN,³²E_1/2(Co^IIIIIIH₂2bim) = −0.53 ± 0.02 V vs. Cp₂Fe^+/0 in MeCN. The K_eq for Co^IIIIIIHbim + H₂2Q ⇄ Co^IIIIIIHbim--H₂2Q was measured using a similar method.

For the reaction of Co^IIIIIIHbim+ ½H₂2Q ⇄ Co^IIIIH₂2bim+ ½BQ, four J. Young NMR tubes were charged with 500 μL of 4 mM Co^IIIIIIHbim solution containing HMDS, and solid H₂2Q was added to four of the five tubes to give 50.9, 74.5 and 105.3 mM solutions. ¹H NMR spectra were obtained at intervals from 40 min–44 h, monitoring the integrals of Co^IIIIH₂2bim (δ 21–22 ppm), Co^IIIIIIHbim (δ 2.5–5 ppm) and {H₂2Q + BQ} (δ 6–7 ppm) until the spectra stopped changing (20 h). Mass balance was assumed to obtain estimates of the equilibrium constant K₆.

Co^IIIIH₂2bim + ^tBu₃ArO˙ by ¹H NMR spectroscopy. Two J. Young NMR tubes were charged with 400 μL of a solution of Co^IIIIH₂2bim (11.5 mM, 11.6 mg in 1.5 mL CD₃CN) and solid ^tBu₃ArO˙ (0.8 equiv, 9.6 mM, 1.0 mg) was added to one of the tubes. ¹H NMR spectra were recorded within 1 h, and integrations relative to HMDS were determined using Mestre-C^TM for Co^IIIIH₂2bim (δ 21–22 ppm), Co^IIIIIIHbim (δ 2.5–5 ppm) and ^tBu₃ArOH (δ 7–7.5 ppm, δ1.2–1.6 ppm). Relative to the integration of Co^IIIIH₂2bim in the control solution, the yield of Co^IIIIIIHbim was 83% and ^tBu₃ArOH was 80%, as expected for 0.8 equiv. ^tBu₃ArO˙, with 17% Co^IIIIH₂2bim remaining.

Co^IIIIH₂2bim + ^tBu₃ArO˙: Stopped-flow kinetics. In the glovebox, two syringes were loaded with MeCN solutions of Co^IIIIH₂2bim (2.72 mM) and ^tBu₃ArO˙ (1.64–4.21 mM), respectively. At least six kinetic runs were performed per set (all concentrations become diluted by half in the stopped-flow). The data were fit to mixed second-order kinetics using the OLIS SVD global fitting software. The average rate constant for each set of runs was plotted vs. [^tBu₃ArO˙] using KaleidaGraph software, weighting each rate constant with 2× its standard deviation and fitting to a line of zero slope, to determine an overall rate constant. The kinetic isotope effect was determined following a version of the procedure above.

Computational details. Structures were optimized for the full Co(H₂2bim)₃²⁺ system (as well as the related Co(H₂2bim)₂(Hbim)²⁺ and Co(H₂2bim)₃³⁺) in vacuum using the OPBE functional³⁸ and the Gaussian 03 package.⁷³ The standard SDD core potential⁷⁴ with its associated basis set was used to describe the cobalt atom, with the standard 6-31G* basis used to describe all other atoms (BSI). Vibrational frequencies were computed at the same level of theory at the optimized geometry and used to estimate zero-point energy and free energy corrections (at 298K). Single-point energy calculations were carried out using the OPBE functional³⁸ and BSI including a polarized continuum model using the integral equation formalism⁷⁵ with parameters for acetonitrile. Additional vacuum single-point energy calculations were carried out using BSII, identical to BSI except that the 6-311G* basis was used on all nitrogen and oxygen atoms. A range of density functionals were used, including OPBE, B3LYP⁷⁶ as implemented in Gaussian and modified versions of the B3LYP functional in which the proportion of exact exchange was reduced from 20 to 15% (B3LYP*) or to 10% (denoted here B3LYP**). Single point corrections for dispersion were computed using the -D3 method of Grimme⁴² at the OPBE structures. The MECP optimization was performed using the code written by one of us,⁷⁷ in conjunction with Gaussian. Briefly, this code generates Gaussian input for both spin states, runs single point energy and gradient calculations, extracts output, generates an effective gradient pointing towards the MECP and uses this to update the geometry until convergence.

Acknowledgements

We gratefully acknowledge financial support from the U.S. National Institutes of Health (GM50422) and the University of Washington. We thank Dr. J. J. Warren for the preparation of the D₂Q and for helpful comments on the manuscript.

Notes and references

1. (a) cf. R. Poli, Acc. Chem. Res., 1997, 30, 494–501; (b) J. N. Harvey, Phys. Chem. Chem. Phys., 2007, 9, 331–343; (c) R. Poli and J. N. Harvey, Chem. Soc. Rev., 2003, 32, 1–8; (d) P. Gütlich, Y. Garcia and H. A. Goodwin, Chem. Soc. Rev., 2000, 29, 419–427; (e) J. W. Turner and F. A. Schultz, Coord. Chem. Rev., 2001, 219–221, 81–97; (f) H. A. Goodwin, Top. Curr. Chem., 2004, 234, 23–47 (in the volume Spin Crossover in Transition Metal Compounds, Vol. II, ed. P. Gütlich, Springer-Verlag, Berlin); (g) P. Gütlich, P. J. van Koningsbruggen and F. Renz, Struct. Bonding, 2004, 107, 27–75; (h) A. B. Gaspar, V. Ksenofontov, M. Seredyuk and P. Gütlich, Coord. Chem. Rev., 2005, 249, 2661–2676; (i) I. Krivokapic, M. Zerara, M. L. Daku, A. Vargas, C. Enachescu, C. Ambrus, P. Tregenna-Piggott, N. Amstutz, E. Krausz and A. Hauser, Coord. Chem. Rev., 2007, 251, 364–378 , and references therein; (j) A. S. Veige, L. M. Slaughter, E. B. Lobkovsky, P. T. Wolczanski, N. Matsunaga, S. A. Decker and T. R. Cundari, Inorg. Chem., 2003, 42, 6204–6224; (k) J. L. Detrich, O. M. Reinaud, A. L. Rheingold and K. H. Theopold, J. Am. Chem. Soc., 1995, 117, 11745–11748; (l) C. R. Landis, C. M. Morales and S. S. Stahl, J. Am. Chem. Soc., 2004, 126, 16302–16303.
2. One clear example is in ref. 1k. As discussed below, spin-interconversion reactions typically occur very rapidly, on the nanosecond timescale. See ref. 1d,f.
3. (a) cf., Cytochrome P450: Structure, Mechanism, and Biochemistry, P. R. Ortiz de Montellano, New York, Kluwer/Plenum, 2005; (b) J. T. Groves, J. Inorg. Biochem., 2006, 100, 434–447; (c) I. G. Denisov, T. M. Makris, S. G. Sligar and I. Schlichting, Chem. Rev., 2005, 105, 2253–2278; (d) S. Shaik, D. Kumar, S. P. de Visser, A. Altun and W. Thiel, Chem. Rev., 2005, 105, 2279–2328; (e) M. T. Green, J. H. Dawson and H. B. Gray, Science, 2004, 304, 1653–1656; (f) K. L. Stone, R. K. Behan and M. T. Green, Proc. Natl. Acad. Sci. U. S. A., 2006, 103, 12307–12310; (g) J. Rittle and M. T. Green, Science, 2010, 330, 933–937; (h) D. Schröder, S. Shaik and H. Schwarz, Acc. Chem. Res., 2000, 33, 139–145; (i) B. Meunier, S. P. de Visser and S. Shaik, Chem. Rev., 2004, 104, 3947–3980; (j) S. Shaik, D. Kumar, S. P. de Visser, A. Altun and W. Thiel, Chem. Rev., 2005, 105, 2279–2328; (k) C. V. Sastri, J. Lee, K. Oh, Y. J. Lee, J. Lee, T. A. Jackson, K. Ray, H. Hirao, W. Shin, J. A. Halfen, J. Kim, L. Que Jr, S. Shaik and W. Nam, Proc. Natl. Acad. Sci. USA, 2007, 104, 19181–19186; (l) S. Shaik, H. Hirao and D. Kumar, Acc. Chem. Res., 2007, 40, 532–542; (m) D. A. Plattner, Angew. Chem., Int. Ed., 1999, 38, 82–86; (n) J. N. Harvey, R. Poli and K. M. Smith, Coord. Chem. Rev., 2003, 238–239, 347–361; (o) H. Hirao, L. Que, Jr, W. Nam and S. Shaik, Chem.–Eur. J., 2008, 14, 1740–1756; (p) P. Comba and G. Rajaraman, Inorg. Chem., 2008, 47, 78–93; (q) D. Balcells, E. Clot and O. Eisenstein, Chem. Rev., 2010, 110, 749–823; (r) F. Ogliaro, N. Harris, S. Cohen, M. Filatov, S. P. de Visser and S. Shaik, J. Am. Chem. Soc., 2000, 122, 8977–8989; (s) S. Shaik, M. Filatov, D. Schröder and H. Schwarz, Chem.–Eur. J., 1998, 4, 193–199; (t) S. P. de Visser, J. Am. Chem. Soc., 2006, 128, 15809–15818; (u) H. Hirao, D. Kumar, L. Que, Jr and S. Shaik, J. Am. Chem. Soc., 2006, 128, 8590–8606.
4. Hydrogen-Transfer Reactions, ed. J. T. Hynes, J. P. Klinman, H.-H. Limbach and R. L. Schowen, Wiley-VCH, Weinheim, 2007.
5. (a) Free Radicals, ed. J. K. Kochi, Wiley, New York, 1973, especially K. U. Ingold, ch. 2, vol. 1, pp. 67ff; G. A. Russell, ch. 7, vol. 1, pp. 275–331; and H. O'Neal and S. W. Benson, ch. 17, vol. 2, pp. 275–359; (b) J. Fossey, D. Lefort and J. Sorba, Free Radicals in Organic Chemistry, Wiley, New York, 1995; (c) J. E. Leffler, An Introduction to Free Radicals, Wiley, New York, 1993, ch. 7–8; (d) B. Halliwell and J. M. C. Gutteridge, Free Radicals in Biology and Medicine, Oxford University Press, New York, 1999; (e) Oxidative Stress: Oxidants and Antioxidants, ed. H. Sies, Academic, New York, NY, 1991; (f) Active Oxygen in Chemistry, ed. C. S. Foote, J. S. Valentine, J. Liebman and A. Greenberg, Blackie, Chapman and Hall, Glasgow, 1995.
6. J. M. Mayer, Acc. Chem. Res., 2011, 44, 36–46.
7. (a) R. A. Sheldon and J. K. Kochi, Metal-Catalyzed Oxidation of Organic Compounds, Academic Press, New York, 1981; (b) G. W. Parshall and S. D. Ittel, Homogeneous Catalysis: The Applications and Chemistry of Catalysis by Soluble Transition Metal Complexes, Wiley-Interscience, New York, 2nd edn, 1992; (c) G. W. Parshall and W. A. Nugent, CHEMTECH, 1988, 18, 184–190; G. W. Parshall and W. A. Nugent, CHEMTECH, 1988, 18, 314–320; G. W. Parshall and W. A. Nugent, CHEMTECH, 1988, 18, 376–384; (d) Comprehensive Organic Synthesis Vol. 7 (Oxidation), ed. B. M. Trost, Pergamon, New York, 1991; (e) Organic Syntheses by Oxidation with Metal Compounds, ed. W. J. Mijs and C. R. H. I. de Jonge, Plenum, New York, 1986; (f) R. A. Sheldon and H. van Bekkum, Fine Chemicals Through Heterogeneous Catalysis, Wiley-VCH, New York, 2001; (g) C. Limberg, Angew. Chem., Int. Ed., 2003, 42, 5932–5954; (h) A. A. Gridnev and S. D. Ittel, Chem. Rev., 2001, 101, 3611–3659.
8. (a) J. Stubbe and W. A. van der Donk, Chem. Rev., 1998, 98, 705–762; (b) R. P. Pesavento and W. A. van der Donk, Adv. Protein Chem., 2001, 58, 317–385; (c) E. N. G. Marsh, BioEssays, 1995, 17, 431–441; (d) J. L. Pierre and F. Thomas, C. R. Chim., 2005, 8, 65–74; (e) M. Fontecave and J. L. Pierre, C. R. Acad. Sci. Ser. II C, 2001, 4, 531–538; (f) A. Decker, M. S. Chow, J. N. Kemsley, N. Lehnert and E. I. Solomon, J. Am. Chem. Soc., 2006, 128, 4719–4733; (g) S. W. Ragsdale, Chem. Rev., 2006, 106, 3317–3337; (h) M.-H. Baik, M. Newcomb, R. A. Friesner and S. J. Lippard, Chem. Rev., 2003, 103, 2385–2419; (i) B. J. Brazeau, R. N. Austin, C. Tarr, J. T. Groves and J. D. Lipscomb, J. Am. Chem. Soc., 2001, 123, 11831–11837.
9. (a) Chem. Rev., 2010, 110, issue 12, 6937–7100: Introduction: Proton-Coupled Electron Transfer: S. Hammes-Schiffer, Chem. Rev., 2010, 110, 6937–6938; (b) M. H. V. Huynh and T. J. Meyer, Chem. Rev., 2007, 107, 5004–5064; (c) C. Costentin, Chem. Rev., 2008, 108, 2145–2179.
10. (a) In this report we use the term ‘hydrogen atom transfer’ or HAT only to imply the net transfer of H˙ from one reagent to another, as in eqn (1) and (2). It should be noted, however, that the meaning of this term is being re-examined in light of the formal separation of the e⁻ and H⁺ that occurs in many transition-metal reactions and some organic processes. See: C. R. Waidmann, X. Zhou, E. A. Tsai, W. Kaminsky, D. A. Hrovat, W. T. Borden and J. M. Mayer, J. Am. Chem. Soc., 2009, 131, 4729–4743; (b) J. M. Mayer, D. A. Hrovat, J. L. Thomas and W. T. Borden, J. Am. Chem. Soc., 2002, 124, 11142–11147; (c) O. Tishchenko, D. G. Truhlar, A. Ceulemans and M. T. Nguyen, J. Am. Chem. Soc., 2008, 130, 7000–7010; (d) G. A. DiLabio and K. U. Ingold, J. Am. Chem. Soc., 2005, 127, 6693–6699.
11. S. Shaik, H. Chen and D. Janardanan, Nat. Chem., 2010, 3, 19–27.
12. G. Xue, R. De Hont, E. Münck and L. Que, Jr., Nat. Chem., 2010, 2, 400–405.
13. cf. D. Balcells, C. Raynaud, R. H. Crabtree and O. Eisenstein, Inorg. Chem., 2008, 47, 10090–10099.
14. (a) Oxidation in Organic Chemistry, ed. K. B. Wiberg, Academic Press, New York, 1965; Part A; (b) R. Stewart, Oxidation Mechanisms, Benjamin, New York, 1964; (c) J. M. Mayer, Acc. Chem. Res., 1998, 31, 441–450; (d) J. M. Mayer, Annu. Rev. Phys. Chem., 2004, 55, 363–390.
15. K. A. Prokop, S. P. de Visser and D. P. Goldberg, Angew. Chem., Int. Ed., 2010, 49, 5091–5095.
16. (a) cf. C. Rüchardt, M. Gerst and J. Ebenhoch, Angew. Chem., Int. Ed. Engl., 1997, 36, 1406–1430; (b) P. J. Wagner, Y. Zhang and A. E. Puchalski, J. Phys. Chem., 1993, 97, 13368–13374; (c) C. Biondi, R. Galeazzi, G. Littarru and L. Greci, Free Radical Res., 2002, 36, 399–404.
17. (a) Correlations of HAT reactivity with driving force have been found in a number of systems, see, for instance, ref. 6,14c,d; (b) A. Gunay and K. H. Theopold, Chem. Rev., 2010, 110, 1060–1081; (c) S. P. de Visser, J. Am. Chem. Soc., 2010, 132, 1087–1097.
18. (a) cf., ref. 17b; (b) N. A. Eckert, S. Vaddadi, S. Stoian, R. J. Lachicotte, T. R. Cundari and P. L. Holland, Angew. Chem., Int. Ed., 2009, 48, 3622–3626; (c) J. England, M. Martinho, E. R. Farquhar, J. R. Frisch, E. L. Bominaar, E. Munck and L. QueJr., Angew. Chem., Int. Ed., 2009, 48, 3622–3626; (d) B. Karamzadeh, D. Kumar, G. N. Sastry and S. P. de Visser, J. Phys. Chem. A, 2010, 114, 13234–13243; (e) R. Breslow, X. J. Zhang and Y. Huang, J. Am. Chem. Soc., 1997, 119, 4535–4536; (f) M. S. Chen and M. C. White, Science, 2007, 318, 783–787; (g) S. Das, G. W. Brudvig and R. H. Crabtree, J. Am. Chem. Soc., 2008, 130, 1628–1637 , and references therein.
19. (a) Some aspects of these reactions have been discussed in other contexts: J. P. Roth, J. C. Yoder, T.-J. Won and J. M. Mayer, Science, 2001, 294, 2524–2526; (b) E. A. Mader, V. W. Manner, T. F. Markle, A. Wu, J. A. Franz and J. M. Mayer, J. Am. Chem. Soc., 2009, 131, 4335–4345; (c) E. A. Mader and J. M. Mayer, Inorg. Chem., 2010, 49, 3685–3687 . This report defines reaction (4) in the opposite direction (from Co^IIIIIIHbim + TEMPOH) so the thermochemical values are of opposite sign.
20. V. W. Manner, T. F. Markle, J. H. Freudenthal, J. P. Roth and J. M. Mayer, Chem. Commun., 2008, 256–258.
21. The spin-states of Co^IIIIH₂2bim and Co^IIIIIIHbim have been experimentally determined; see ref. 27.
22. J. P. Roth, S. Lovell and J. M. Mayer, J. Am. Chem. Soc., 2000, 122, 5486–5498.
23. E. A. Mader, A. S. Larsen and J. M. Mayer, J. Am. Chem. Soc., 2004, 126, 8066–8067.
24. E. A. Mader, E. R. Davidson and J. M. Mayer, J. Am. Chem. Soc., 2007, 129, 5153–5166.
25. (a) A. Wu and J. M. Mayer, J. Am. Chem. Soc., 2008, 130, 14745–14754; (b) A. Wu, J. Maslan, R. D. Swartz, W. Kaminsky and J. M. Mayer, Inorg. Chem., 2007, 46, 11190–11201.
26. (a) J. J. Warren and J. M. Mayer, J. Am. Chem. Soc., 2008, 130, 2774–2776; (b) V. W. Manner, A. G. DiPasquale and J. M. Mayer, J. Am. Chem. Soc., 2008, 130, 7210–7211; (c) S. Miyazaki, T. Kojima, J. M. Mayer and S. Fukuzumi, J. Am. Chem. Soc., 2009, 131, 11615–11624.
27. J. C. Yoder, J. P. Roth, E. M. Gussenhoven, A. S. Larson and J. M. Mayer, J. Am. Chem. Soc., 2003, 125, 2629–2640.
28. T. J. Meyer and H. Taube, in Electron Transfer Reactions, in Comprehensive Coordination Chemistry, ed. G. Wilkinson, Pergamon, New York, 1987, vol. 1, ch. 7.2.
29. S. Wherland, Coord. Chem. Rev., 1993, 123, 169–199.
30. J. C. Wang and J. E. Bauman, Jr, Inorg. Chem., 1965, 4, 1613.
31. J. P. Roth, Intrinsic and Thermodynamic Influences on Hydrogen Atom Transfer Reactions Involving Transition Metal Complexes, PhD Thesis, University of Washington, Seattle, WA, 2000, pp. 128–129.
32. N. G. Connelly and W. E. Geiger, Chem. Rev., 1996, 96, 877–910.
33. BDFE = 23.1E_1/2 + 1.37pK_a + C_G and C_G = 54.9 kcal mol⁻¹ in MeCN for potentials referenced to Cp₂Fe+/0.^19b,34,35.
34. M. Tilset, in Electron Transfer in Chemistry, ed. V. Balzani, Wiley-VCH, Weinheim, Germany, 2001, vol. 2, pp.677–713.
35. J. J. Warren, T. A. Tronic and J. M. Mayer, Chem. Rev., 2010, 110, 6961–7001.
36. Specfit™/32, versions v3.0.26 and v3.0.36, Spectrum Software Associates, Marlborough, MA, 2000.
37. (a) The overall reaction has ΔG₆° = −0.52 ± 0.11 kcal mol⁻¹. The BDFEs of the two O–H bonds in H₂2Q are 78 ± 1 and 62 ± 1 kcal mol⁻¹,^37b roughly evenly spaced around the BDFE of Co^IIIIH₂2bim (69.5 ± 0.9 kcal mol⁻¹).^19b; (b) BDFEs from ref. 35. Alternatively, starting from the gas phase data in: R. M. Borges dos Santos and J. A. Martinho Simoes, J. Phys. Chem. Ref. Data, 1998, 27, 707–739 and converting to MeCN using the method described in ref. 19b gives BDFE(H₂2Q) = 79 ± 2 kcal mol⁻¹, and therefore BDFE(HQ˙) = 61 ± 3 kcal mol⁻¹, using the average BDFE of both H-atoms in H₂2Q³⁵; (c) the likely HQ˙ intermediate can react with Co^IIIIH₂2bim to make Co^IIIIIIHbim + H₂2Q; it can react with Co^IIIIIIHbim either by HAT to make Co^IIIIH₂2bim + BQ or by PT to make Co^IIIIIIH₂2bim + Q˙⁻; and it can disproportionate to BQ + H₂2Q. It is not evident that any of these processes is much slower than the others, making the kinetic treatment complex. It is therefore not surprising that the optical data cannot be well fit to a simple rate law, especially with competing decomposition.
38. N. C. Handy and A. J. Cohen, Mol. Phys., 2001, 99, 403–412; J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
39. See e.g. M. Swart, J. Chem. Theory Comput., 2008, 4, 2057–2066.
40. O. Salomon, M. Reiher and B. A. Hess, J. Chem. Phys., 2002, 117, 4729–4737.
41. J. N. Harvey, Struct. Bonding, 2004, 112, 151–183.
42. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 154104.
43. A. M. Schmiedekamp, M. D. Ryan and R. J. Deeth, Inorg. Chem., 2002, 41, 5733–5743.
44. Calculations are performed from the separated reactants to the separated products. It is unlikely that the hydrogen-bonding affects the change in spin state (calculations performed to confirm did not properly converge).
45. Test calculations at the B3LYP** level in the presence of continuum solvent were able to locate the pre- and post-reactive complexes ²2Co^IIIIH₂2bim|²TEMPO and ¹1Co^IIIIIIHbim|¹TEMPOH on the singlet potential energy surface (in the former case, using an unrestricted ansatz). These complexes lie as expected slightly lower in energy than the corresponding separated species, and were used as the starting and ending points in the search for a transition state.
46. S. Hammes-Schiffer and A. A. Stuchebrukhov, Chem. Rev., 2010, 110, 6939.
47. The iron reactions closely follow the cross relation (with f ≅ 1)¹⁹ which implies that rate constants vary with K_eq^1/2. The 2 kcal mol⁻¹ difference in ΔG° then corresponds to a factor of 5.3 difference in HAT rate constants.
48. See ref. 6 and 10a; the vanadium-oxo/hydroxo system presented in ref. 6 is another exception to this generalization.
49. (a) ΔG_PT5° >32 kcal mol⁻¹ from pK_a(^tBu₃ArOH⁺˙) = −3³⁵ and pK_a(Co^IIIIH₂2bim) >20.3 (see above); (b) ΔG_ET5° = 3.9 ± 0.7 kcal mol⁻¹ from E_1/2(Co^IIIIIIH₂2bim) = −0.53 ± 0.02 V and E_1/2(^tBu₃ArO˙^/−) = −0.70 V. See ref. 35.
50. (a) The Marcus cross relation, k_AB = (k_AAk_BBK_ABf)^½, is applied using ΔG_ET5° = 3.9 ± 0.7 kcal mol⁻¹, ≤10⁻⁶ M⁻¹ s⁻¹ for the Co^IIIIH₂2bim + Co^IIIIIIH₂2bim self-exchange rate constant,²⁷ and <10⁹ M⁻¹ s⁻¹ for the ^tBu₃ArO˙ + ^tBu₃ArO⁻ self exchange (this is the value measured for phenoxyl + 4-methylphenoxide and related electron transfers in water, and is close to the diffusion limit in MeCN); (b) P. Neta and J. Grodowski, J. Phys. Chem. Ref. Data, 2005, 34, 109–199; (c) J. Lind, X. Shen, T. E. Eriksen and G. Merenyi, J. Am. Chem. Soc., 1990, 112, 479–482.
51. (a) Some comparisons of measured vs. calculated rate constants using the Marcus Cross Relation: M. Chou, C. Creutz and N. Sutin, J. Am. Chem. Soc., 1977, 99, 5615–5623; (b) J. Gribble and S. Wherland, Inorg. Chem., 1989, 28, 2859–2863.
52. (a) Marcus Theory has also been applied to electron transfer with cobalt complexes in terms of volumes of activation: H. Doine and T. W. Swaddle, Inorg. Chem., 1991, 30, 1858–1862; (b) M. R. Grace, H. Takagi and T. W. Swaddle, Inorg. Chem., 1994, 33, 1915–1920; (c) R. D. Shalders and T. W. Swaddle, Inorg. Chem., 1995, 34, 4815–4820; (d) ref. 29, and references therein.
53. If initial spin-change to the low-spin ²2Co^IIIIH₂2bim is uphill by ΔG^°4,2_Co, then ET from ²2Co^IIIIH₂2bim to ^tBu₃ArO˙ is more favorable than ET from by ⁴4Co^IIIIH₂2bim by exactly that amount (by Hess' law). Following Marcus theory, roughly half of that increased driving force should appear in a lower barrier. Thus, all other things being equal, the spin-change-then-ET pathway should be less favorable than direct ET from ⁴4Co^IIIIH₂2bim, by ΔG^°4,2_Co − ½ΔG^°4,2_Co = ½ΔG^°4,2_Co. This could potentially be balanced by a smaller intrinsic barrier for ²2Co^IIIIH₂2bim/¹1Co^IIIIIIH₂2bim, but this is difficult to estimate. ⁴4Co^IIIIH₂2bim has two electrons in the e_g antibonding orbitals while ²2Co^IIIIH₂2bim has one (t_2g⁶ e_g¹, low-spin d⁷) and should be Jahn-Teller distorted. See ref. 68.
54. (a) ΔG_ET° > 36 kcal mol⁻¹ is estimated from E_1/2(para-methoxyphenol) = 1.03 ± 0.02 V^54c and taking as an upper limit for E_1/2(Co^IIIIIIHbim) the E_1/2 of the protonated Co^IIIIIIH₂2bim, −0.53 V; (b) ΔG_PT° = +13 ± 1 kcal mol⁻¹ is determined from pK_a(H₂Q) = 30 ± 0.3^54d and the pK_a(Co^IIIIIIH₂2bim) given above; (c) T. Osako, K. Ohkubo, M. Taki, Y. Tachi, S. Fukuzumi and S. Itoh, J. Am. Chem. Soc., 2003, 125, 11027–11033; (d) The pK_a of H₂Q is 19.76 in DMSO,^54e which was converted to a value in MeCN following ref. 54f; (e) F. G. Bordwell and J.-P. Cheng, J. Am. Chem. Soc., 1991, 113, 1736–1743; (f) I. M. Kolthoff and M. K. Chantooni, Jr, J. Phys. Chem., 1976, 80, 1306–1310.
55. B. K. Carpenter, Determination of Organic Reaction Mechanisms, John Wiley & Sons, Inc., New York, 1984, pp. 97–100.
56. A mechanism of rapid pre-equilibrium ET followed by a rate-limiting PT step is quite unlikely given the slow ET reactions of the cobalt complexes and the quite exoergic PT step that would be involved (ΔG_5ET° = 3.9 ± 0.7 kcal mol⁻¹ and the overall ΔG₅° of = −7.5 kcal mol⁻¹ imply ΔG_5PT° for the second step of an ET/PT path of −11.4 kcal mol⁻¹.
57. (a) Ref. 28, 29, 51 and 52 ; (b) M. D. Newton and N. Sutin, Annu. Rev. Phys. Chem., 1984, 35, 437; (c) M. D. Newton, J. Phys. Chem., 1991, 95, 30–38; (d) ref. 52c ; (e) J. F. Endicott, B. Durham, M. D. Glick, T. J. Anderson, J. M. Kuszaj, W. G. Schmonsees and K. P. Balakrishnan, J. Am. Chem. Soc., 1981, 103, 1431–1440; (f) E. Buhks, M. Bixon, J. Jortner and G. Navon, Inorg. Chem., 1979, 18, 2014; (g) J. F. Endicott, K. Kumar, T. Ramasami and F. P. Rotzinger, Prog. Inorg. Chem., 1983, 30, 141–187.
58. C. Costentin, M. Robert and J.-M. Savéant, J. Am. Chem. Soc., 2004, 126, 16834–16840.
59. J. N. Harvey and M. Aschi, Phys. Chem. Chem. Phys., 1999, 1, 5555–5563.
60. M. Y. M. Pau, J. D. Lipscomb and E. I. Solomon, Proc. Natl. Acad. Sci. U. S. A., 2007, 104, 18355–18362.
61. A. F. Cotton, G. Wilkinson, C. A. Murillo and M. Bochmann, Advanced Inorganic Chemistry, John Wiley & Sons, Inc., New York, 6th edn, 1999, pp. 816–824.
62. (a) F. A. Cotton and M. D. Meyers, J. Am. Chem. Soc., 1960, 82, 5023–5026; (b) F. A. Cotton and M. D. Meyers, J. Am. Chem. Soc., 1960, 82, 5027–5030.
63. P. Comba, M. Kerscher, G. A. Lawrance, B. Martin, H. Wadepohl and S. Wunderlich, Angew. Chem., Int. Ed., 2008, 47, 4740–4743.
64. See e.g. P. Gutlich, A. Hauser and H. Spiering, Angew. Chem., Int. Ed. Engl., 1994, 33, 2024–2054.
65. M. Besora, J.-L. Carreón-Macedo, A. J. Cowan, M. W. George, J. N. Harvey, P. Portius, K. L. Ronayne, X.-Z. Sun and M. Towrie, J. Am. Chem. Soc., 2009, 131, 3583–3592.
66. M. Besora, J.-L. Carreón-Macedo, Á. Cimas and J. N. Harvey, Adv. Inorg. Chem., 2009, 61, 573–623.
67. J. K. Beattie, R. A. Binstead, M. T. Kelso, P. Favero, T. G. Dewey and D. H. Turner, Inorg. Chim. Acta, 1995, 235, 245–251.
68. (a) I. Krivokapic, M. Zerara, M. L. Dakua, A. Vargas, C. Enachescu, C. Ambrusc, P. Tregenna-Piggott, N. Amstutz, E. Krausz and A. Hauser, Coord. Chem. Rev., 2007, 251, 364–378; (b) J. K. Beattie, Adv. Inorg. Chem., 1988, 32, 1–49; (c) H. A. Goodwin, Top. Curr. Chem., 2004, 234, 23–47; (d) ref. 67 .
69. This estimate is obtained by adding the increment of 1.3 kcal mol⁻¹ to the spin splitting of 1.4 kcal mol⁻¹, the Fe^II(H₂bip)₃²⁺ + TEMPO reaction barrier of 14 kcal mol⁻¹, and an estimated vibrational term of 1.5 kcal mol⁻¹.
70. S. Larsson, K. Stahl and M. C. Zerner, Inorg. Chem., 1986, 25, 3033–3037.
71. (a) J. I. Seeman, J. Chem. Educ., 1986, 63, 42–48; (b) J. I. Seeman, Chem. Rev., 1983, 83, 83–134 , eq. 25.
72. D. M. Duggan and D. N. Hendrickson, Inorg. Chem., 1975, 14, 955–970.
73. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople, Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford, CT, 2004.
74. M. Dolg, U. Wedig, H. Stoll and H. Preuss, J. Chem. Phys., 1987, 86, 866–872.
75. M. Cossi, G. Scalmani, N. Rega and V. Barone, J. Chem. Phys., 2002, 117, 43–54.
76. A. D. Becke, J. Chem. Phys., 1993, 98, 5648–5652.
77. J. N. Harvey, A. Aschi, H. Schwarz and K. Koch, Theor. Chem. Acc., 1998, 99, 95–99.

---

Footnotes

† Electronic supplementary information (ESI) available: Raw data and discussion of rate constants and complications with initial rate data for BQ, Marcus cross relation analysis, estimation of the energy of the ²E_g state for Co(H₂2bim), detailed experimental methods, and computational details (Cartesian coordinates and energies). See DOI: 10.1039/c1sc00387a

‡ Current address: Explosives Applications and Special Projects, Los Alamos National Laboratory, MS C920, Los Alamos, NM, 87545, USA; vwmanner@lanl.gov.

§ Current address: Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Ave, CSE/200, Argonne, IL, 60439-4837, USA; mader@anl.gov.

---