Nitroxyl Radical plus Hydroxylamine Pseudo Self-Exchange Reactions: Tunneling in Hydrogen Atom Transfer

Abstract

Bimolecular rate constants have been measured for reactions that involve hydrogen atom transfer (HAT) from hydroxylamines to nitroxyl radicals, using the stable radicals TEMPO^• (2,2,6,6-tetramethylpiperidine-1-oxyl radical), 4-oxo-TEMPO^• (2,2,6,6-tetramethyl-4-oxo-piperidine-1-oxyl radical), di-tert-butylnitroxyl (^tBu₂NO^•), and the hydroxylamines TEMPO-H, 4-oxo-TEMPO-H, 4-MeO-TEMPO-H (2,2,6,6-tetramethyl-N-hydroxy-4-methoxy-piperidine), and ^tBu₂NOH. The reactions have been monitored by UV-vis stopped-flow methods, using the different optical spectra of nitroxyl radicals. The HAT reactions all have |ΔG^o| ≤ 1.4 kcal mol⁻¹ and therefore are close to self-exchange reactions. The reaction of 4-oxo-TEMPO^• + TEMPO-H → 4-oxo-TEMPO-H + TEMPO^• occurs with k_2H,MeCN = 10 ± 1 M⁻¹ s⁻¹ in MeCN at 298 K (K_2H,MeCN = 4.5 ± 1.8). Surprisingly, the rate constant for the analogous deuterium atom transfer reaction is much slower: k_2D,MeCN = 0.44 ± 0.05 M⁻¹ s⁻¹ with k_2H,MeCN/k_2D,MeCN = 23 ± 3 at 298 K. The same large kinetic isotope effect (KIE) is found in CH₂Cl₂, 23 ± 4, suggesting that the large KIE is not caused by solvent dynamics or hydrogen bonding to solvent. The related reaction of 4-oxo-TEMPO^• with 4-MeO-TEMPO-H(D) also has a large KIE, k_3H/k_3D = 21 ± 3 in MeCN. For these three reactions, the E_aD – E_aH values, between 0.3 ± 0.6 and 1.3 ± 0.6 kcal mol⁻¹, and the log(A_H/A_D) values, between 0.5 ± 0.7 and 1.1 ± 0.6, indicate that hydrogen tunneling plays an important role. The related reaction of ^tBu₂NO^• + TEMPO-H(D) in MeCN has a large KIE, 16 ± 3 in MeCN, and very unusual isotopic activation parameters, E_aD – E_aH = −2.6 ± 0.4 and log(A_H/A_D) = 3.1 ± 0.6. Computational studies, using POLYRATE, also indicate substantial tunneling in the (CH₃)₂NO^• + (CH₃)₂NOH model reaction for the experimental self-exchange processes. Additional calculations on TEMPO(^•/H), ^tBu₂NO(^•/H), and Ph₂NO(^•/H) self-exchange reactions reveal why the phenyl groups make the last of these reactions several orders of magnitude faster than the first two. By inference, the calculations also suggest why tunneling appears to be more important in the self-exchange reactions of dialkylhydroxylamines than of arylhydroxylamines.

Introduction

Hydrogen transfer reactions are among the most fundamental of chemical reactions.¹ Tunneling of the proton is emphasized in many treatments of hydrogen transfer,^{1 2 3-4} and an increasing number of these reactions are being found to have large hydrogen/deuterium kinetic isotope effects (KIEs) and activation parameters that indicate the importance of tunneling.⁵ While a number of these reactions are understood in detail, there is limited intuition about why some hydrogen-transfer reactions display the hallmarks of tunneling and others do not. Described here are experimental and computational studies of hydrogen-atom transfer (HAT) pseudo self-exchange reactions between dialkylnitroxyl radicals and dialkylhydroxylamines (eq 1) that indicate the occurrence of substantial hydrogen tunneling. These are simple and unusual cases of tunneling in oxygen-to-oxygen HAT. The contrast between these reactions and the closely related reactions of arylnitroxyl radicals which do not show the experimental markers of tunneling is also examined.

$${\mathrm{R}}_2{\mathrm{NO}}^{•}+{\mathrm{R}}_2\mathrm{NOH}\to {\mathrm{R}}_2\mathrm{NOH}+{\mathrm{R}}_2{\mathrm{NO}}^{•}$$ (1)

Hydrogen atom transfer (HAT) has been studied for over a century⁶ and is the simplest chemical reaction that involves the transfer of two particles, a proton and an electron. It can therefore be considered to be a type of ‘proton-coupled electron transfer’ (PCET).^7,8 HAT is important in combustion and selective oxidation of alkanes, in the formation and reactivity of protein-based radicals and reactive oxygen species (ROS), and many other processes.⁹ For example, HAT from the double allylic C–H bond in linoleic acid to the iron(III)-hydroxide active site in lipoxygenases has received particular attention because its H/D KIE of up to ∼80 indicates the importance of tunneling.^5a,10 HAT involving of nitroxyl radicals and hydroxylamines is important in much of the chemistry of nitroxyl radicals,¹¹ such as their role as catalysts and co-catalysts in oxidation of organic substrates.^{12-13 14 15} N-hydroxyphthalimide (NHPI) has been widely explored as a co-catalyst in Co/Mn-catalyzed autoxidations of alkylaromatics, with the active species being the corresponding phthalimide N-oxyl radical (PINO^•).¹⁶ HAT reactions from benzylic C-H bonds to PINO^• in acetic acid have large deuterium KIEs (17−28 at 298 K)¹⁷ and the pseudo self-exchange reaction between PINO^• and 4-Me-NHPI in acetic acid has k_H/k_D = 11.0 (k_H = 677 ± 24 M⁻¹ s⁻¹).¹⁸ Reactions of nitroxyl radicals with arylhydroxylamines, however, exhibit much smaller KIEs, with k_H/k_D = 1.5−1.9 at ambient temperatures (see Table 2 below).^13,14

Table 2.

Driving Forces, Rate Constants, and Kinetic Isotope Effects for Nitroxyl plus Hydroxylamine Reactions.^a

Reaction	Solvent	ΔG°b	kH (M−1 s−1)a	kD (M−1 s−1)a,c	kH/kDa,c	Ref.
4-oxo-TEMPO• + TEMPO-Hd	MeCN	−0.9 ± 0.2	10 ± 1	0.44 ± 0.05	23 ± 3	e
4-oxo-TEMPO• + TEMPO-H	CH2Cl2	−1.2 ± 0.2	48 ± 4	2.1 ± 0.3	23 ± 4	e
4-oxo-TEMPO• + TEMPO-H	CCl4	–	300 ± 30	17 ± 4	18 ± 5	e
4-oxo-TEMPO• + 4-MeO-TEMPO-H	MeCN	−0.6 ± 0.2	7.8 ± 0.7	0.37 ± 0.05	21 ± 3	e
tBu2NO• + TEMPO-H	MeCN	1.3 ± 0.2	1.9 ± 0.2	0.12 ± 0.02	16 ± 3	e
tBu2NO• + TEMPO-H	CH2Cl2	1.4 ± 0.2	4.6 ± 0.4	0.35 ± 0.04	13 ± 2	e
PINO• + 4Me-NHPIf	AcOH(D)	−0.4 ± 0.1	677 ± 24	61.3 ± 2.1	11.0 ± 0.5	18
4-Me-PINO• + NHPIf	AcOH(D)	0.4 ± 0.1	354 ± 23	31.8 ± 2.0	11.1 ± 1.0	18
tBu2NO• + tBu2NOH	CCl4	0	320 ± 40	–	–	13
tBu2NO• + tBu2NOH	C6H5Cl	0	240 ± 60	–	–	13
tBu(Ar)NO• + tBu(Ar)NOHg	CCl4	0	(2.0 ± 0.4) × 103	(1.3 ± 0.2) × 103	1.5 ± 0.4	13
tBu(Ar)NO• + tBu(Ar)NOHg	C6H5Cl	0	(5.2 ± 0.4) × 102	–	–	13
tBu(Ar)NO• + tBu(Ar)NOHg	CH2Cl2	0	< 20	–	–	13
Ph2NO• + Ph2NOH	CCl4	0	> 107	–	–	13
	hexane	−0.2 ± 0.1	(4.3 ± 0.2) × 104	(2.5 ± 0.1) × 104	1.7 ± 0.1	14
	hexane	2.0 ± 0.1	(4.5 ± 0.2) × 103	(2.9 ± 0.2) × 103	1.6 ± 0.1	14
B + A (R = CPh3)	hexane	0.9 ± 0.1	(1.4 ± 0.1) × 104	(7.3 ± 0.4) × 103	1.9 ± 0.2	14
B (R = Ph) + A	hexane	1.6 ± 0.1	(8.6 ± 0.4) × 103	(5.7 ± 0.3) × 103	1.5 ± 0.1	14
TEMPO• + A	hexane	−0.6 ± 0.1	(7.6 ± 0.4) × 104	–	–	14
TEMPO• + A (R = CPh3)	hexane	−1.4 ± 0.1	(1.5 ± 0.1) × 105	–	–	14
4-oxo-TEMPO• + A	hexane	−1.3 ± 0.1	(6.4 ± 0.3) × 104	–	–	14

^aT = 298 (this work and ref.18), 300 (ref. ¹³), and 293 K (ref. ¹⁴); – means not determined.

^bkcal mol⁻¹.

^cNot corrected for the incomplete (98±1%) deuterium enrichment; the true k_H/k_D values are roughly a factor of two higher; see text.

^dRef. ²⁰.

^eThis work.

^fPINO^• = phthalimide N-oxyl radical, NHPI = N-hydroxyphthalimide.

^gAr = 2,6-dimethoxyphenyl.

We have focused on HAT self-exchange reactions, such as the nitroxyl/hydroxylamine reactions examined here (eq 1), both because of their relative simplicity and because of our finding that the Marcus cross relation usually predicts HAT rate constants within an order of magnitude or two.^{19 20-21} This treatment is a new approach to understanding HAT rate constants²² and has been found to hold for both organic reactions and examples involving transition metal complexes. For instance, the cross relation predicts and explains the inverse temperature dependence of the rate of HAT from [Fe^II(H₂bip)₃]²⁺ to the stable nitroxyl radical TEMPO^• (2,2,6,6-tetramethylpiperidine-1-oxyl radical).²⁰ Of the various HAT reactions involving TEMPO^• / TEMPO-H and transition metal complexes that we have examined,^19,20,23,24 the Marcus approach appears to be least accurate for Ru^II(acac)₂(py-imH) + TEMPO^• → TEMPO-H and Ru^III(acac)₂(py-im), which has a large KIE.^24b These results prompted our examination of nitroxyl/hydroxylamine self-exchange reactions; the kinetics of 4-oxo-TEMPO^• plus TEMPO-H were briefly mentioned in a preliminary communication about the [Fe^II(H₂bip)₃]²⁺ reaction.²⁰

Results

I. Equilibrium Constants

The reaction of 4-oxo-TEMPO^• and TEMPO-H in CD₃CN forms an equilibrium mixture with 4-oxo-TEMPO-H and TEMPO^• (eq 2), with all four species observed by ¹H NMR spectroscopy. All of the resonances have been assigned for the

(2)

paramagnetic and diamagnetic species, even though 4-oxo-TEMPO-H has not been isolated. Equilibrium is rapidly established (see below) and integration of each species using Lorentzian line fitting gave K_2H,CD3CN = 4.5 ± 1.8 at 298 K.²⁵ In CD₂Cl₂, K_2H,CD2Cl2 = 7.6 ± 2.4 was measured similarly. As expected, the equilibrium constants for deuterium atom transfer in CD₃CN and CD₂Cl₂ (K_2D), measured using TEMPO-D, are within experimental error of being the same as the K_2H values (Table 1). The equilibrium constants are the averages of three independent measurements. All errors reported herein are ± 2σ.

Table 1.

Thermodynamic Parameters for Pseudo Self-Exchange Reactions of Nitroxyl Radicals and Hydroxylamines.^a

Reaction	Solvent	K (298 K)	ΔH°	ΔS°
(2) 4-oxo-TEMPO• + TEMPO-H	CD3CN	4.5 ± 1.8	−1.7 ± 0.7	−2.6 ± 2.1
4-oxo-TEMPO• + TEMPO-D	CD3CN	4.7 ± 1.8	−1.7 ± 0.7	−2.5 ± 2.4
4-oxo-TEMPO• + TEMPO-H	CD2Cl2	7.6 ± 2.4	−2.6 ± 0.8	−4.8 ± 2.6
4-oxo-TEMPO• + TEMPO-D	CD2Cl2	6.6 ± 2.2	−2.6 ± 0.8	−5.1 ± 2.8
(3) 4-oxo-TEMPO• + 4-MeO-TEMPO-H	CD3CN	2.8 ± 1.2	−2.2 ± 0.4	−5.8 ± 2.3
4-oxo-TEMPO• + 4-MeO-TEMPO-D	CD3CN	3.1 ± 1.2	−2.4 ± 0.7	−5.8 ± 2.3
(4) tBu2NO• + TEMPO-H	CD3CN	0.11 ± 0.02	2.7 ± 0.9	4.6 ± 2.8
tBu2NO• + TEMPO-D	CD3CN	0.11 ± 0.03	2.4 ± 0.9	3.7 ± 2.9
tBu2NO• + TEMPO-H	CD2Cl2	0.10 ± 0.02	3.1 ± 0.8	5.6 ± 2.6
tBu2NO• + TEMPO-D	CD2Cl2	0.10 ± 0.02	3.1 ± 0.8	5.8 ± 2.4

^aMeasurements at 278−318 K; ΔH° in kcal mol⁻¹, ΔS° in cal mol⁻¹ K⁻¹.

HAT equilibria are also rapidly established between 4-oxo-TEMPO^• and 4-MeOTEMPO-H (eq 3) and between ^tBu₂NO^• and TEMPO-H (eq 4; Table 1). The measured uphill free energy for reaction 4, ΔG^o_4H,CD3CN = 1.3 ± 0.1 kcal mol⁻¹, is very close to the 1.5 kcal mol⁻¹ difference in O–H bond dissociation enthalpies (ΔBDE) of TEMPO-H (69.7 kcal mol⁻¹) and ^tBu₂NOH (68.2 kcal mol⁻¹) reported by Bordwell in DMSO.²⁶

(3)

(4)

The equilibrium constants for H and D transfer were determined at temperatures from 278−318 K for reactions 2−4 in CD₃CN (Figure 1) and for reactions 2 and 4 in CD₂Cl₂ (Figure S1; Table 1). Van't Hoff analysis yields small ground state reaction enthalpies and entropies, |ΔH^o| ≤ 3.1 kcal mol⁻¹ and |ΔS^o| ≤ 5.8 cal mol⁻¹ K⁻¹. These values support the hypothesis that reactions 2−4 can be regarded as pseudo self-exchange reactions. Small values of ΔS^o are also typical of organic HAT reactions, even for those that are not self-exchange reactions.²³

Figure 1.

Van't Hoff plot for reactions 2−4 in CD₃CN at 278−318 K.

II. Kinetic Measurements

Attempts to directly measure the rate of HAT self-exchange between TEMPO^• and TEMPO-H by ¹H NMR line broadening were unsuccessful.²⁷ Therefore, we have studied the pseudo self-exchange reactions in eqs 2-4 using stopped-flow optical measurements. The reaction between 4-oxo-TEMPO^• and TEMPO-H (eq 2), for instance, is readily monitored by UV-vis spectroscopy because the spectrum of 4-oxo-TEMPO^• in MeCN (λ_max = 440 nm, ε = 5.5 M⁻¹ cm⁻¹) is different from that of TEMPO^• (λ_max = 460 nm, ε = 10.3 M⁻¹ cm⁻¹), particularly in ε.

The reaction kinetics have been measured by UV-vis stopped flow techniques under pseudo first order conditions, with an excess of TEMPO-H (59−292 mM, ≥10 equiv) over 4-oxo-TEMPO^• (5.9−12 mM) in MeCN (Figure 2a). Under these conditions the reaction proceeds essentially to completion (K_2H,MeCN = 4.5). The optical data were fitted across the whole spectral region (350−550 nm) using SPECFIT global analysis software.²⁸ The data fit well to a simple first-order A → B model (Figure 2b), and the pseudo first-order rate constants k_obs are independent of the initial concentration of 4-oxo-TEMPO^•. Plotting k_obs versus [TEMPO-H] yields a straight line (Figure 3), indicating a first order dependence on [TEMPO-H] and a bimolecular rate constant for the forward reaction in eq 2 of k_2H,MeCN = 10 ± 1 M⁻¹ s⁻¹ at 298 K. Reactions with less TEMPO-H, under second order approach-to-equilibrium conditions A + B ⇄ C + D, gave the same value of k_2H,MeCN within error.

Figure 2.

(a) Overlay of UV-vis spectra for the reaction of 8.8 mM 4-oxo-TEMPO^• with 88 mM TEMPO-H (eq 2) in MeCN over 5 s at 298 K. (b) Absorbance at 460 nm showing the raw data (○) and first order A → B fit using SPECFIT (—).

Figure 3.

Plot of pseudo first order k_obs versus [TEMPO-H(D)] for reaction 2 in MeCN (k_H/k_D = 23 ± 3) and in CH₂Cl₂ (k_H/k_D = 23 ± 4) at 298 K.

To investigate the role of solvent, the same kinetic experiments were performed in CH₂Cl₂ and CCl₄ solutions. Analysis as above gave k_2H,CH2Cl2 = 48 ± 4 M⁻¹ s⁻¹ (Figure 3) and k_2H,CCl4 = 300 ± 30 M⁻¹ s⁻¹ at 298 K. These rate constants are, respectively, 4.8 and 30 times larger than in MeCN.

The KIE for reaction 2 was examined using TEMPO-D prepared by TEMPO^• reduction with Na₂S₂O₄ in acetone-d₆/D₂O. This TEMPO-D, which was 98 ± 1% D by ¹H NMR integration, reacts with 4-oxo-TEMPO^• in MeCN with k_2D,MeCN = 0.44 ± 0.05 M⁻¹ s⁻¹ (Figure 3). This rate constant is 23 ± 3 times slower than that for the same reaction of TEMPO-H at 298 K. Within experimental error, essentially the same apparent isotope effects are found in CH₂Cl₂, 23 ± 4, and in CCl₄, 18 ± 5. Thus solvent polarity and hydrogen bonding to solvent do not significantly affect the KIEs. The ratio of the rate constants, however, is only a lower limit to the true KIE because the residual 2 ± 1% H in the TEMPO-D contributes significantly to the reactions. If the TEMPO-D was 99% D, the true KIE would be 30, and if it was 97% D, the true KIE would be 72.²⁹ These are the experimental bounds on the KIE.

The kinetics of 4-oxo-TEMPO^• plus excess 4-MeO-TEMPO-H (eq 3) in MeCN were measured and analyzed in a similar fashion, to give k_3H = 7.8 ± 0.7 M⁻¹ s⁻¹ at 298 K (Figure S2). This is about 20% lower than the rate constant for reaction 2 under the same conditions, which is consistent with the equilibrium constant for reaction 3, K_3H,MeCN = 2.8 ± 1.2, being a little smaller than K_2H,MeCN = 4.5 ± 1.8 for reaction 2.

Similar to the case for reaction 2, the rate constant for reaction of the deuterated hydroxylamine, 4-MeO-TEMPO-D, at 298 K is much slower, k_3D = 0.37 ± 0.05 M⁻¹ s⁻¹ (Figure S2), than that for the reaction of the undeuterated compound. Since the 4-MeO-TEMPO-D is also 98 ± 1% deuterated, the k_3H/k_3D = 21 ± 3 at 298 K is also a lower limit to the true KIE. Rate constants and k_H/k_D values at 298 K for the forward reactions 2−4 are given in Table 2, along with the rate constants for other nitroxyl plus hydroxylamine reactions.

The reaction of ^tBu₂NO^• and TEMPO-H (eq 4) in MeCN is uphill in free energy (K_4H,MeCN = 0.11), so the kinetics were measured by UV-vis stopped flow techniques under second order approach-to-equilibrium conditions. The optical spectra of ^tBu₂NO^• (λ_max = 454 nm, ε = 8.9 M⁻¹ cm⁻¹) and TEMPO^• (λ_max = 460 nm, ε = 10.3 M⁻¹ cm⁻¹) are similar, so the overall change of the absorbance is small (Figure S3). Under the experimental conditions ([^tBu₂NO^•] =12−139 mM, [TEMPO-H] = 118−237 mM), spectra of reaction mixtures at short times show absorbances ∼10% higher than equimolar solutions of ^tBu₂NO^•, suggesting partial formation of a complex between ^tBu₂NO^• and TEMPO-H. Consistent with this suggestion, adding 2,4,6-tri-tert-butylphenol to solutions of ^tBu₂NO^• caused similar changes in optical spectra, even though HAT does not occur (ΔBDE = +14 kcal mol⁻¹).³⁰ These changes in reaction 4 are subtle, however, and are too small to enable determination of a value for the equilibrium constant. There are also subtle differences between the final reaction spectrum and that of TEMPO^•, suggesting that the products could also be, in part, hydrogen-bonded.

The forward bimolecular rate constant for eq 4 under these conditions, k_4H,MeCN, is 1.9 ± 0.2 M⁻¹ s⁻¹ at 298 K, as determined by fitting the data to an opposing second order equilibrium model (A + B ⇄ C + D) with a fixed K_4H,MeCN = 0.11, using SPECFIT²⁸ (Figure S3). When TEMPO-D is used, the initial spectra of the reaction mixtures are much closer to those of solutions of pure ^tBu₂NO^•, suggesting that adduct formation is isotopically sensitive, and is less favorable for TEMPO-D than for TEMPO-H. The rate constant for D-atom transfer, k_4D,MeCN = 0.12 ± 0.02 M⁻¹ s⁻¹ indicates k_4H,MeCN/k_4D,MeCN = 16 ± 3 at 298 K. Reaction 4 behaves similarly in CH₂Cl₂ solvent, showing a similar isotope effect: k_4H,CH2Cl2/k_4D,CH2Cl2 = 13 ± 2.

Rate constants for reactions 2−4 have been measured as a function of temperature over 35−40 K temperature ranges. Selected Eyring plots are shown in Figure 4, and all Eyring and Arrhenius activation parameters are listed in Table 3. Table 4 shows the difference between the H versus D activation energies (E_aD – E_aH) and pre-exponential factors, log(A_H/A_D).

Figure 4.

Eyring plots for (a) 4-oxo-TEMPO^• + TEMPO-H (reaction 2) and (b) ^tBu₂NO^• + TEMPO-H (reaction 4), both in MeCN and CH₂Cl₂.

Table 3.

Eyring and Arrhenius Parameters for H- and D-Atom Transfer Reactions.^a

Reaction	Solvent	T (K)	ΔH‡	ΔS‡	Ea	log A
4-oxo-TEMPO• + TEMPO-Hb	MeCN	278−318	3.0 ± 0.5	−43 ± 3	3.6 ± 0.5	3.8 ± 0.6
4-oxo-TEMPO• + TEMPO-D	MeCN	278−318	4.3 ± 0.4	−46 ± 2	4.9 ± 0.4	3.3 ± 0.4
4-oxo-TEMPO• + TEMPO-H	CH2Cl2	273−308	3.0 ± 0.4	−41 ± 2	3.6 ± 0.4	4.3 ± 0.4
4-oxo-TEMPO• + TEMPO-D	CH2Cl2	273−308	3.3 ± 0.4	−46 ± 2	3.9 ± 0.4	3.2 ± 0.4
4-oxo-TEMPO• + 4-MeO-TEMPO-H	MeCN	278−318	4.8 ± 0.3	−38 ± 2	5.4 ± 0.3	4.9 ± 0.4
4-oxo-TEMPO• + 4-MeO-TEMPO-D	MeCN	288−328	5.4 ± 0.3	−42 ± 2	6.0 ± 0.3	4.0 ± 0.4
tBu2NO• + TEMPO-H	MeCN	278−318	7.7 ± 0.3	−31 ± 2	8.3 ± 0.3	6.4 ± 0.4
tBu2NO• + TEMPO-D	MeCN	278−318	5.1 ± 0.3	−45 ± 2	5.7 ± 0.3	3.3 ± 0.4
tBu2NO• + TEMPO-H	CH2Cl2	273−308	7.1 ± 0.3	−32 ± 2	7.6 ± 0.3	6.3 ± 0.4
tBu2NO• + TEMPO-D	CH2Cl2	273−308	4.0 ± 0.3	−47 ± 2	4.5 ± 0.3	2.9 ± 0.4
PINO• + 4Me-NHPIc	AcOH	290−309	9.8 ± 0.2	−13 ± 1	10.4 ± 0.2	10.4 ± 0.2
4-Me-PINO• + NHPIc	AcOH	290−309	10.0 ± 0.2	−13 ± 1	10.6 ± 0.2	10.4 ± 0.2

^aΔH^‡, E_a in kcal mol⁻¹; ΔS^‡ in cal mol⁻¹ K⁻¹.

^bOriginally reported in ref. 20.

^cRef. ¹⁸.

Table 4.

Kinetic Isotope Effects and Differences in Protio and Deutero Arrhenius Parameters.^a

Reaction	solvent	kH/kD	EaD – EaH	log(AH/AD)
4-oxo-TEMPO• + TEMPO-H	MeCN	23 ± 3	1.3 ± 0.6	0.5 ± 0.7
4-oxo-TEMPO• + TEMPO-H	CH2Cl2	23 ± 4	0.3 ± 0.6	1.1 ± 0.6
4-oxo-TEMPO• + 4-MeO-TEMPO-H	MeCN	21 ± 3	0.6 ± 0.4	0.9 ± 0.6
tBu2NO• + TEMPO-H	MeCN	16 ± 3	−2.6 ± 0.4	3.1 ± 0.6
tBu2NO• + TEMPO-H	CH2Cl2	13 ± 2	−3.1 ± 0.4	3.4 ± 0.6

^ak_H/k_D at 298 K, E_aD – E_aH in kcal mol⁻¹.

III. Computational Studies

In order to investigate the role of tunneling in self-exchange reactions between nitroxyl radicals and hydroxylamines, we performed multi-dimensional tunneling calculations, using Gaussrate³¹ as the interface between Gaussian 03³² and Polyrate.³³ Our computations were carried out using both the MPW1K³⁴ and the more recently developed MO5−2X³⁵ and MO6³⁶ functionals. The 6−31+G(d,p) basis set³⁷ was employed for all of these calculations. Tunneling rates were computed, using the small-curvature tunneling (SCT) approximation.³⁸

Because of the computational demands of the SCT tunneling calculations, calculations on the ^tBu₂NO^• + ^tBu₂NOH and TEMPO^• + TEMPO-H systems were too big to be practical. Therefore, we began by performing calculations on (CH₃)₂NO^• + (CH₃)₂NOH. The calculated rate constants, activation parameters, and H/D kinetic isotope effects for this reaction are given in Table 5.

Table 5.

Computed canonical variational transition state theory (CVT) and small curvature tunneling (SCT) rate constants and Arrhenius activation parameters for at the MPW1K/6−31+G(d,p) level of theory.

Reaction	Method	kH	kD	kH/kD	Ea,H	log(AH)	Ea,D	log(AD)
Me2NO• + HONMe2	CVT	5.65 × 10−4	8.67 × 10−5	6.5	14.8	7.6	15.8	7.6
Me2NO• + HONMe2	SCT	4.85 × 101	2.47 × 10−1	196	6.1	6.2	7.3	4.8
MeHNO• + HONHMe	SCT	1.83× 101	7.65 × 10−2	239	6.1	5.8	7.4	4.3

^a k_H, k_D, M⁻¹ s⁻¹; E_a,H, E_a,D, kcal mol⁻¹.

The transition structure (TS) for (CH₃)₂NO^• + (CH3)₂NOH, shown in Figure 5a, has C_2h symmetry. The SCT calculations start at this TS and descend down a minimum energy path toward the reactants/products. Unfortunately, starting from the TS and moving along this reaction coordinate, the C_s plane of symmetry was maintained throughout the reaction. Consequently, the SCT calculations did not lead to the hydrogen-bonded reactant complex (CH₃)₂NOH...^•ON(CH₃)₂, which has C₁ symmetry (Figure 5b). Instead, the calculations led to the C_s TS that connects the two enantiomeric geometries of the reactant complex. Destroying the C_s plane in the C_2h TS by substituting two CD₃ for two CH₃ groups failed to coax the hydrogen-bonded complex to depart from the ridge on the potential energy surface that connects the two enantiomers.

Figure 5.

(a) Transition structure for hydrogen transfer between (CH₃)₂NOH and (CH₃)₂NO^•. (b) H-bonded complex between (CH₃)₂NOH and (CH₃)₂NO^•. Bond lengths are in Ångstroms.

However, we were able to follow the reaction path back from the TS to the reactants for the self-exchange reaction between the monomethylnitroxyl radical and the monomethylhydroxylamine. The calculated values of k_H, E_a, A, and k_H/k_D for this reaction, (CH₃)HNO^• + HONH(CH₃), are also given in Table 5. The two reactions are close enough to lead us to believe that the computational results for the dimethyl reaction are reliable, despite our being unable to follow the reaction path all the way back to the reactant complex in this case. Most of the tunneling seems to originate from regions along the reaction path that are closer to the TS, where the reaction barrier is narrow, than from regions close to the reactants, where the barrier is much wider and the deviation from C_s symmetry is significant.

The formation of the (CH₃)₂NOH...^•ON(CH₃)₂ reactant complex (Figure 5B) from the separated reactants is enthalpically favorable: ΔH = −4.6 kcal mol⁻¹ [calculated with MPW1K/6−31+ G(d,p)]. However, the entropy of complex formation [ΔS = −26.7 cal K⁻¹ mol⁻¹] is so unfavorable that the calculated value of the gas phase equilibrium constant [K = 1.4 × 10⁻⁴ M⁻¹] at 298 K is small. Since at 298 K the reactants are lower in free energy than the reactant complex, the computed rate constants, A factors, and activation energies reported in Table 5 are for reactions starting from the separated reactants.

We used all three functionals -- MPW1K, MO5−2X, and MO6 -- to calculate the barrier height for the hydrogen self-exchange reaction, (CH₃)₂NO^• + (CH₃)₂NOH, starting from the C₁ reactant complex. All three functionals gave enthalpies of activation for passage over the reaction barrier that were the same to within 1.0 kcal mol⁻¹. Therefore, we elected to do the tunneling calculations with just one of them, MPW1K.

The MPW1K rate constants at 298 K for the hydrogen and deuterium self-exchange reactions were computed by canonical variational transition state theory (CVT) for passage over the barrier and by small curvature tunneling (SCT) calculations for passage through the barrier. The results are contained in Table 5. The Arrhenius activation parameters, obtained from the temperature dependences of the calculated rate constants around 298 K, are also given in Table 5.

The k_H values in Table 5 show that the SCT rate constant for hydrogen tunneling through the barrier is computed to be larger than the CVT rate constant for passage over it by a factor of about 10⁵. Tunneling reduces E_a by 8.7 kcal mol⁻¹ for hydrogen, with a decrease in log A of only 1.4. The large reduction in E_a and the small decrease in log A shows that our SCT calculations predict that tunneling is very efficient in (CH₃)₂NO^• + (CH₃₎₂NOH. The width of the barrier to this reaction is computed to be only 0.42 Å, which is presumably why tunneling is computed to be so effective at increasing the reaction rate.

Table 5 also contains the results of our calculations for deuterium self-exchange in (CH₃)₂NO^• + (CH₃)₂NOD. Comparison of the CVT and SCT rate constants for D shows that tunneling is also predicted to dominate the reaction involving deuterium. However, a very large H/D KIE of k_H/k_D = 196 is predicted for tunneling. Of this ratio, a factor of 7.4 is due to H tunneling with a 1.2 kcal mol⁻¹ lower E_a, than D. An even larger factor is due to log A_H being about 1.4 larger than log A_D. Even though H is calculated to tunnel through the barrier at an average energy of about 1.2 kcal mol⁻¹ lower than D, H is calculated to tunnel with a higher probability than D by a factor of 26.5.³⁹

Our SCT value of H/D KIE of 196 for (CH₃)₂NO^• + (CH3)₂NOH/D is about a factor of 5 larger than the experimental values for reaction of TEMPO-H with a variety of nitroxide radicals (Table 2). However, as already noted, the true H/D KIEs are substantially larger than the values given in Table 2, because of the incomplete D enrichment. For TEMPO-H/D + 4-oxo-TEMPO^•, the measured k_H/k_D of 23 at 98 ± 1% D corresponds to a true KIE of about 40 (the 98 ± 1% range gives values of 30−70).

The calculated bimolecular SCT rate constant of k = 48.5 M⁻¹ s⁻¹ is in excellent agreement with the rate constants in Table 2 for the TEMPO-H reactions. The closest experimental analogy to this gas phase rate constant is the k of 300 M⁻¹ s⁻¹ for 4-oxo-TEMPO^• + TEMPO-H in CCl₄, which has ΔG^o ≅ −1 kcal mol⁻¹. In contrast, the CVT rate constant of k = 5.65 × 10⁻⁴ M⁻¹s⁻¹ for (CH3)₂NO^• + (CH3)₂NOH underestimates the experimental rate constants (Table 2) by a factor of 10⁴ − 10⁶. Thus, our calculations on both the rate of and H/D KIE for this model reaction strongly support the conclusion that the dialkylnitroxyl radical reactions in Table 2 all occur by tunneling through the reaction barrier, rather than by passage over it.

Although we were unable to perform SCT calculations on larger systems, we did carry out CVT calculations on the ^tBu₂NO(^•/H), TEMPO(^•/H) and Ph₂NO(^•/H) self-exchange reactions. For each one, the TS was located and confirmed to have one imaginary frequency by a vibrational analysis. Key features of the geometries of the nitroxide reactants and the self-exchange TSs are given in Figure 6, along with the calculated E_a values from CVT for each reaction.

Figure 6.

Bond lengths (Å), atomic spin densities (in green), and activation energies (kcal mol⁻¹) for the nitroxyl radicals, (a) ^tBu₂NO^•, (b) TEMPO^•, and (c) Ph₂NO^•, and the transition structures and CVT activation energies for their hydrogen self-exchange reactions with the corresponding hydroxylamines.

As shown in Figure 6, the geometries of the TSs for all three reactions are very similar. In each TS the O-H bonds approximately bisect the C-N-C angles, strongly suggesting that the electron and the proton are transferred together between the same AO on each oxygen. This inference is confirmed by inspection of the SOMOs for the three TSs, which are shown in Figure 7. Thus, all three reactions proceed by a mechanism in which a hydrogen atom is transferred between a pair of oxygen AOs, rather than by a mechanism in which a proton is transferred between one pair of oxygen AOs and an electron is transferred between a different pair of oxygen AOs (which in some contexts has been called proton-coupled electron transfer, PCET).⁴⁰

Figure 7.

SOMOs of the transition structures for hydrogen exchange reactions: (a) ^tBu₂NO^• + ^tBu₂NOH, (b) TEMPO^• + TEMPO-H , and (c) Ph₂NO^• + Ph₂NOH.

The CVT activation energies for the dialkylnitroxyl reactions, E_a = 15.7 and 14.5 kcal mol⁻¹ for ^tBu₂NO^• + ^tBu₂NOH and TEMPO^• + TEMPO-H, respectively, are much larger than the corresponding energy for Ph₂NO^• + Ph₂NOH, 5.6 kcal mol⁻¹. This is in pleasing agreement with the experimental finding that the rate constant for Ph₂NO^• + Ph₂NOH¹³ is at least five orders of magnitude faster than those for ^tBu₂NO^• + ^tBu₂NOH¹³ and TEMPO^• + TEMPO-H. Comparisons of the geometries and spin densities of the nitroxide reactants and TSs in Figure 6 indicates that the phenyl groups lower the barrier to reaction by providing greater delocalization of the unpaired electron in the TS for Ph₂NO^• + Ph₂NOH reaction than in the Ph₂NO reactant.

In the nitroxyl radicals, the unpaired spin density of 0.88 in the N-O group of Ph₂NO^• is about 0.1 smaller than the unpaired spin densities of 0.98 and 1.00 in the NO groups of TEMPO^• and ^tBu₂NO^•, respectively. The C-N bond lengths in Ph₂NO^• are calculated to be 0.07 and 0.08 Å shorter than those in TEMPO and ^tBu₂NO^•, respectively. This is a larger difference than the ∼0.04 Å difference in covalent radii between sp² and sp³ carbon atoms. These results indicate that the phenyl groups in Ph₂NO^• delocalize the unpaired electron in the two-center, three-electron N-O π bond.

On going from the reactants to the TS, the four C-N bond lengths in Ph₂NO^• shorten by an average of 0.02 Å; whereas the C-N bond lengths in TEMPO^• and ^tBu₂NO^• shorten by less than 0.01 Å. In addition, the spin densities in the NO groups of the Ph₂NO^• + Ph₂NOH TS are 0.08 smaller than the spin density in the NO group of Ph₂NO^•; whereas, the corresponding decrease in the spin densities in the NO groups is only about 0.03 in both TEMPO^• + TEMPO-H and ^tBu₂NO^• + ^tBu₂NOH. The larger decreases in the C-N bond lengths and in the NO spin densities between the Ph₂NO^• reactants and the TS for Ph₂NO^• + Ph₂NOH are both consistent with the TS for this reaction being stabilized by electron delocalization into the phenyl groups. We believe that this is the reason why the hydrogen self-exchange reaction of this diarylnitroxyl radical is many orders of magnitude faster than those of the dialkylnitroxyl radicals in Table 2.

Discussion

Nitroxyl radical plus hydroxylamine reactions have been studied experimentally and computationally. The experimental reactions (eqs 2-4) are close to isoergic in both MeCN and CH₂Cl₂, with |ΔG^o| ≤ 1.4 kcal mol⁻¹ (Table 2), and involve reagents that are sterically quite similar. Thus these reactions are good approximations of self-exchange reactions. Self-exchange reactions are inherently simpler to analyze because of their symmetry, which requires that the transition structure, or more generally the seam on the potential energy surface, be symmetrically placed between the reactant and product.

Thermochemical data show that the reactions must occur by concerted rather than stepwise transfer of the proton and electron. For self-exchange reactions, the potential stepwise mechanisms with initial electron or proton transfer are the microscopic reverse of each other.⁴¹ For the TEMPO^• + TEMPO-H self-exchange reaction, both stepwise pathways proceed through a TEMPO⁻ + TEMPO-H^•+ intermediate state. Based on the known E_1/2 and pK_a values, this state is about 60 kcal mol⁻¹ higher than TEMPO^• + TEMPO-H (2.6 V or 44 pK_a units).⁴² For the pseudo self-exchange reactions in eqs 2-4, the data are not available to make a full analysis, but the E_1/2 and pK_a values are not very different for the various compounds,²⁶ so these reactions will also have potential intermediate states lying ca. 60 kcal mol⁻¹ uphill. This is dramatically higher than the Eyring barriers ΔG^‡ < 20 kcal mol⁻¹ found for reactions 2−4. Thus the stepwise pathways are not possible and the reaction must occur by concerted H⁺/e⁻ transfer.

I. Solvent Effects

The experimental rate constants are faster in less polar and less hydrogen-bonding solvents (Table 2). For 4-oxo-TEMPO^• + TEMPO-H, the rate constants are 10, 48, and 300 M⁻¹ s⁻¹ in MeCN, CH₂Cl₂, and CCl₄, respectively. Litwinienko, Ingold, et al. have shown that for HAT reactions of phenols, solvent effects on the rate constants are predominantly due to the formation of a hydrogen bond between the H-atom donor and the solvent.⁴³ Only the fraction of the phenol that is not hydrogen bonded is reactive, and the reactivity of the non-hydrogen bonded phenol is not significantly affected by solvent. Qualitatively, this explains why the TEMPO-H reactions are slower in MeCN, a good hydrogen bond acceptor, than in chlorinated solvents. The formation of TEMPO-H•••NCMe hydrogen bonds is indicated by the TEMPO-H O–H stretching frequency in CD₃CN (3495 cm⁻¹), being ∼100 cm⁻¹ lower than ν(TEMPO-H) in CD₂Cl₂ (3583 cm⁻¹) and CCl₄ (3597 cm⁻¹). A recent crystal structure of TEMPO-H shows hydrogen bonds between TEMPO-H molecules with O...O distances of 2.83 and 2.88 Å.²³

Quantitatively, the Litwinienko and Ingold model predicts that the solvent effect will be independent of the H-atom acceptor.^44,45 However, the experimental ratios of rate constants in CH₂Cl₂ vs. MeCN are 4.8 ± 0.6 for 4-oxo-TEMPO^• + TEMPO-H and 2.4 ± 0.3 for ^tBu₂NO^• + TEMPO-H.⁴⁴ The 4-oxo-TEMPO^• + TEMPO-H reaction (eq 2) appears to be affected by solvent polarity as well as hydrogen bonding, as it is 6 times faster in CCl₄ than in CH₂Cl₂ (Table 2). A more dramatic effect has been reported for the ^tBuArNO^•/^tBuArNOH self-exchange reaction (Ar = 2,6-dimethoxyphenyl), which is more than a hundred times faster in CCl₄ than in CHCl₃ and CH₂Cl₂: 2 × 10³ versus < 20 M⁻¹ s⁻.¹³ A reviewer has suggested that these anomalous kinetic solvent effects may be due to changes in the nitroxyl radical spin density with solvent,⁴⁶ which are known to affect their rate constant for reaction with alkyl radicals.⁴⁷

II. Kinetic Isotope Effects and Evidence for Tunneling

Hydrogen tunneling is suggested by the large k_H/k_D values of 23 ± 3, 21 ± 3, and 16 ± 3 at 298 K for reactions 2−4 in MeCN. A one-dimensional semi-classical transition state theory model, taking ΔG^‡_D – ΔG^‡_H to be at most the difference in zero-point energies, predicts a maximum k_H/k_D of 9 at 298 K using the measured OH and OD stretches.^3,4,48 A more complete semi-classical model including bending modes gives a maximum KIE of about 13 for cleavage of an O–H bond.³ The computed CVT H/D KIEs at 298 K, without tunneling, are 6.5, 4.9, 4.9, and 4.7 for the self-exchange reactions involving Me₂NO^•, ^tBu₂NO^•, TEMPO^•, and Ph₂NO^•. These computed H/D KIEs are all significantly lower than the measured values for reactions 2−4, but they are ca. three times larger than the KIEs in Table 2 for reactions involving monoarylhydroxylamines, including the ^tBu(Ar)NO^• + ^tBu(Ar)NOH self-exchange [Ar = 2,6-(MeO)₂C₆H₃].

The experimental activation energies also provide evidence for tunneling. According to Bell,³ tunneling is indicated when E_aD – E_aH is larger than the difference in zero-point energies, 1.3 kcal mol⁻¹ in this case,⁴⁸ and/or when there are significant differences in the pre-exponential terms, A_H/A_D < 0.7 or A_H/A_D > 1.4, or |log(A_H/A_D)| > 0.15. All of the reactions studied here have log(A_H/A_D) larger than this semi-classical limit, except perhaps for reaction 2 in MeCN which has log(A_H/A_D) = 0.5 ± 0.7 (Table 4). For reactions 2 and 3, the positive values of log(A_H/A_D), the low values of both A_H and A_D (<10⁵ M⁻¹ s⁻¹), and low E_a (<6 kcal mol⁻¹) values all suggest that there is significant tunneling in the reactions of both the H and D isotopomers.⁵

The small-curvature tunneling calculations on (CH₃)₂NO^• + (CH₃)₂NOH also show that tunneling is the dominant pathway in this model reaction for a self-exchange involving a dialkylnitroxyl radical reacting with a dialkylhydroxylamine. Tunneling through the barrier is computed to be about 10⁵ times faster than passage over the barrier for H, and more than 10³ times faster, even for D. The experimental KIEs vary little with solvent – between MeCN, CH₂Cl₂, and CCl₄ for reaction 2, and between MeCN and CH₂Cl₂ for reaction 4 – indicating that the solvent plays little role in the tunneling process.⁴⁹

The ^tBu₂NO^• + TEMPO-H reaction (eq 4) is found to have very unusual activation parameters. These data derive from quite small changes in absorbance (see above), but they are based on three separate measurements of rate constants at each temperature, with consistent multiple stopped-flow runs in each measurement. The resulting A_H is a thousand times larger than A_D both in MeCN and CH₂Cl₂, and E_aD is substantially smaller than E_aH: E_aD – E_aH = −2.5 ± 0.4 in MeCN and −3.1 ± 0.4 kcal mol⁻¹ in CH₂Cl₂. That E_aD < E_aH is indicated by the increase in k_4H/k_4D values with temperature, in MeCN from 11 ± 1 at 278 K to 17 ± 2 at 308 K and 21 ± 6 at 318 K. These values are surprising both because they are so different than those for the very similar reactions 2 and 3,⁵⁰ and because E_aD < E_aH is opposite to the predictions of both semi-classical and tunneling models.^3,5 While similar unusual activation parameters have been reported for two other HAT/PCET reactions,⁵¹ we are not sure of the origin in this case. It is interesting that the formation of the hydrogen-bonded precursor complex in this reaction, TEMPO-H/D...^•ON^tBu₂, also appears to be isotopically sensitive (see above).^17,52

In light of the importance of tunneling for the TEMPO^•/TEMPO-H self-exchange reaction, the success of the Marcus cross relation for reactions involving TEMPO^• is perhaps surprising. The cross relation is a semiclassical treatment that does not include hydrogen tunneling. Still, the cross relation is essentially interpretative, and will still hold if the self-exchange and cross reactions are accelerated a comparable amount by tunneling.

III. Comparison with related reactions

The rate constants for nitroxyl + hydroxylamine self-exchange and pseudo self-exchange reactions show a remarkable range, from 2 to >10⁷ M⁻¹ s⁻¹ (Table 2). Other XO^• + XOH reactions show similar variation: ^tBu₂C=NO^• + ^tBu₂C=NOH in benzene, 1.3 M⁻¹ s⁻¹;⁵³ 2,4,6-^tBu₃C₆H₂O^• + 2,4,6-^tBu₃C₆D₂OH in CCl₄, 220 M⁻¹ s⁻;^{13b t}BuOO^• + ^sBuOOH in isopentane, 490 M⁻¹ s⁻¹;^{54 t}BuO^• + ^tBu₃COH in ^tBuOO^tBu, ∼3 × 10⁴ M⁻¹ s⁻¹;⁵⁵ and PhO^• + 2-naphthol (ΔG^o ≈ −2 kcal mol⁻¹) in MeCN, 4.5 × 10⁶ M⁻¹ s⁻¹.^52,56 The most striking comparison is from the measurements of R₂NOH + R₂NO^• self-exchange reactions by Kreilick and Weissman in CCl₄: 320 M⁻¹ s⁻¹ for R = ^tBu vs. >10⁷ M⁻¹ s⁻¹ for R = Ph.¹³ The dichotomy between the dialkyl- and arylhydroxylamine reactions is also evident in the HAT kinetic isotope effects. The more rapid arylhydroxylamine reactions have k_H/k_D < 2, while the slower dialkylnitroxyl reactions have k_H/k_D > 10 (Table 2).

Reactions of the acylnitroxyl PINO^• display yet another pattern of reactivity.^17,18 The pseudo self-exchange reaction of PINO^• with the hydroxyphthalate Me-NHPI has values of E_a (10 kcal mol⁻¹) and A_H (10^10.4 M⁻¹ s⁻¹) that are significantly larger than those of the TEMPO^•/4-oxo-TEMPO^•/4-MeO-TEMPO^• reactions (eqs 2 and 3): E_a ≤ 6 kcal mol⁻¹ and A_H ≤ 10⁵ M⁻¹ s⁻¹ (Table 3). The reactions of PINO^• with p-xylene and toluene appear to involve tunneling, but in contrast to reactions 2−4, they show large values of E_aD – E_aH and negative values of log(A_H/A_D) (3.0 ± 0.3 kcal mol⁻¹, −0.8 ± 0.3 for p-xylene), suggesting that tunneling is more pronounced for H than for D.^17,18 The related HAT reaction of (CF₃)₂NO^• with toluene, with k_H/k_D = 13 and log(A_H/A_D) ≈ 0 (A_H ≈ A_D ≈ 10₄), was not suggested to involve significant tunneling.⁵⁷

The diversity of behavior is remarkable for such similar reactions. All of the nitroxyl/hydroxylamine reactions discussed here are close to isoergic (|ΔG^o| ≤ 2 kcal mol⁻¹, Table 2) so the driving forces are not the cause of these differences. The differences between the dialkyl- and the arylhydroxylamine reactions could conceivably be largely due to a steric effect. The bulkier tertiary alkyl groups might make assembly of the precursor complex more difficult and could keep the oxygen atoms farther apart. Such a difference in TS geometries would lead to higher barriers and longer H-transfer distances, enhancing the importance of tunneling in the dialkylnitroxyl reactions. However, the results of our calculations show that there is very little difference between the geometries of the TSs for the dialkyl- and diarylnitroxyl self-exchange reactions. Instead, our calculations find that the much faster Ph₂NO^• + Ph₂NOH self-exchange reaction is due to the greater electronic delocalization provided by the phenyl groups in the transition structure. The CVT barrier for Ph₂NO(^•/H) self-exchange reaction, 5.6 kcal mol⁻¹, is 9−10 kcal mol⁻¹ lower than the CVT barriers for the ^tBu₂NO(^•/H) and TEMPO(H) self-exchange reactions (15.7, 14.5 kcal mol⁻¹, respectively).

Because the reaction barriers for the arylhydroxylamines are lower than those for the dialkylhydroxylamines, the former reactions can proceed by passage over, or close to the top of the barriers, without the need for substantial tunneling. In contrast, the higher reaction barriers on the potential energy surfaces for the dialkylhydroxylamine reactions lead to both H and D preferentially tunneling through the barriers. Tunneling produces the low E_a and A values and the high H/D KIEs that we have both measured and calculated for the dialkylnitroxyl radical + dialkylhydroxylamine reactions.

While many discussions of tunneling emphasize the distance over which the H or D transfers must occur, in this case the O-H bond distances in the reactant complexes and transition structures are calculated to be quite similar for the reactions of dialkylhydroxylamines vs. those of arylhydroxylamines. The results of our calculations suggest that the former reactions show the experimental indications of tunneling while the latter do not because of the different barrier heights for degenerate HAT in these two types of hydroxylamines. These studies thus appear to be an experimental example of the well-known theoretical result that barrier height is as key a factor as barrier width in determining the probability of tunneling in a chemical reaction.³

Conclusions

Hydrogen atom transfer from dialkylhydroxylamines to dialkylnitroxyl radicals predominantly involves hydrogen tunneling. This has been shown through a combination of experimental and computational studies. Experimentally, the kinetics of three pseudo-self exchange reactions have been examined. For the reactions of 4-oxo-TEMPO^• with TEMPO-H (eq 2) and 4-MeO-TEMPO-H (eq 3), the activation parameters and H/D kinetic isotope effects (Tables 2-4) suggest that tunneling is important in both H and D transfers. The measured ratios of k_H/k_D = 21−23 ± 4 correspond to intrinsic KIEs of ca. 40 at 298 K, given the 98 ± 1% deuterium enrichment of the hydroxylamines. Computational studies of the (CH₃)₂NO^• + (CH₃)₂NOH model reaction, using the small-curvature tunneling (SCT) approximation, also find substantial tunneling by both H and D. The reaction of ^tBu₂NO^• with TEMPO-H (eq 4) has very unusual activation parameters, with E_a(D) < E_a(H) and log(A_H/A_D) ≈ 3.

The properties of these pseudo self-exchange reactions of dialkylhydroxylamines contrast with related reactions of arylhydroxylamines. Aryl-substituted hydroxylamines generally react with higher rate constants and very small KIEs (< 2). Calculations indicate that the Ph₂NO^• + Ph₂NOH self-exchange has a 9−10 kcal mol⁻¹ lower barrier than the ^tBu₂NO^• + ^tBu₂NOH and TEMPO + TEMPO-H self-exchange reactions, due to greater electron delocalization in the [Ph₂NO.._H.._ONPh2]^• transition structure. The picture that emerges from these studies is that the self-exchange reactions of the dialkylhydroxylamines involve tunneling of both H and D, while the related reactions of arylhydroxylamines proceed over or close to the top of the reaction barriers. This dichotomy is due to the higher barriers for the dialkylhydroxylamine reactions, rather than to differences in the geometries of the reactant complexes or transition structures between the two types of hydroxylamines.

Experimental

Physical Techniques and Instrumentation

¹H (500 MHz) and ¹³C{¹H} (126 MHz) NMR were recorded on Bruker Avance spectrometers, referenced to a residual solvent peak, and reported as: δ (multiplicity, assignment, number of protons). The error for NMR integration is estimated to be ±10%. Lorentzian line fitting for accurate integration was done using NUTS.²⁵ Electrospray ionization mass spectra (ESI/MS) were obtained on a Bruker Esquire-LC ion trap mass spectrometer and reported as m/z, with samples infused as MeCN solutions. UV-vis spectra were acquired with a Hewlett-Packard 8453 diode array spectrophotometer, and reported as λ_max/nm (ε/M⁻¹ cm⁻¹). IR spectra were obtained as CD₃CN, CD₂Cl₂, or CCl₄ solutions in a NaCl solution cell, using a Bruker Vector 33 or Perkin Elmer 1720 FT-IR spectrometer, and reported in cm⁻¹. UV-vis stopped-flow measurements were obtained on an OLIS RSM-1000 stopped-flow spectrophotometer. Elemental analyses were performed by Atlantic Microlab (Norcross, GA). All reactions were performed in the absence of air using standard glove box/vacuum line techniques.

Materials

All reagent grade solvents were purchased from Fisher Scientific, EMD Chemicals, or Honeywell Burdick & Jackson (for anhydrous MeCN). Deuterated solvents were obtained from Cambridge Isotope Laboratories. CD₃CN was dried over CaH₂, vacuum transferred to P₂O₅, and over to CaH₂, then to a dry glass flask. CD₂Cl₂ was dried over CaH₂, and vacuum transferred to a dry glass flask. TEMPO^•, 4-oxo-TEMPO^•, 4-MeO-TEMPO^•, and ^tBu₂NO^• were purchased from Aldrich, and were sublimed onto a cold-finger apparatus before use. UV-vis (MeCN): TEMPO^•, 460 (10.3); 4-oxo-TEMPO^•, 440 (5.5); 4-MeO-TEMPO^•, 460 (10.4); ^tBu₂NO^•, 454 (8.9). UV-vis (CH₂Cl₂): TEMPO^•, 460 (11.1); 4-oxo-TEMPO^•, 446 (6.0); 4-MeO-TEMPO^•, 462 (11.0); ^tBu₂NO^•, 450 (9.0). UV-vis (CCl₄): TEMPO^•, 471 (12.2); 4-oxo-TEMPO^•, 450 (7.1). Anal. Calcd (Found) for TEMPO^• (C₉H₁₈NO): C, 69.18 (69.14); H, 11.61 (11.65); N, 8.96 (9.09); for 4-oxo-TEMPO^• (C₉H₁₆NO₂): C, 63.50 (63.61); H, 9.47 (9.51); N, 8.23 (8.19); for 4-MeO-TEMPO^• (C₁₀H₂₀NO₂): C, 64.48 (64.64); H, 10.82 (10.97); N, 7.52 (7.47); for ^tBu₂NO^• (C₈H₁₈NO): C, 66.62 (66.87); H, 12.58 (12.79); N, 9.71 (9.61).

TEMPO-H was prepared according to literature procedures.^{58 1}H NMR (CD₃CN): δ 1.06 (s, CH₃, 12H), 1.45 (s, CH₂, 6H; the C3/C5 and C4 signals are coincident), 5.34 (br s, OH, 1H). ¹H NMR (CD₂Cl₂): δ 1.10 (s, CH₃, 12H), 1.46 (s, CH₂, 6H), 4.31 (br s, OH, 1H). ¹³C{¹H} NMR (CD₃CN): δ 17.78 (C4), 26.11 (CH₃), 40.16 (C3), 58.78 (C2). Anal. Calcd (Found) for TEMPO-H (C₉H₁₉NO): C, 68.74 (69.01); H, 12.18 (12.39); N, 8.91 (8.82). TEMPO-D was prepared analogously to TEMPO-H, using (CD₃)₂CO/D₂O (99.9% D in D₂O) as the solvent; it was 98 ± 1% OD by NMR integration. Anal. Calcd (Found) for TEMPO-D (C₉H₁₈DNO): C, 68.30 (67.42); H, 12.10 (12.21); N, 8.85 (8.68). IR: ν_OH/ν_OD = 3495/2592 (CD₃CN), 3583/2648 (CD₂Cl₂), 3597/2658 (CCl₄).

Preparation of 4-MeO-TEMPO-H

A suspension of 4-MeO-TEMPO^• (2.00 g, 10.7 mmol) and Na₂S₂O₄ (3.60 g, 20.7 mmol) in Me₂CO/H₂O (15 mL each) was stirred for 30 min at room temperature under N₂. The solvent was then partially evacuated under vacuum to remove Me₂CO. The leftover aqueous layer was extracted with Et₂O (3 × 20 mL), and the solvent was evacuated to dryness to give the crude product, which was purified by sublimation to a cold finger, yielding 951 mg of white powder (48%). ¹H NMR (CD₃CN): δ 1.09, 1.10 (s, CH₃, 6H each); 1.25, 1.90 (m, CH₂, 2H each); 3.25 (s, OCH₃, 3H); 3.46 (m, 4-CH, 1H); 5.37 (br s, OH, 1H). ¹H NMR (CD₂Cl₂): δ 1.16, 1.20 (s, CH₃, 6H each); 1.33, 1.90 (m, CH₂, 2H each); 3.32 (s, OCH₃, 3H); 3.44 (m, 4-CH, 1H); 4.51 (br s, OH, 1H). ¹³C{¹H} NMR (CD₃CN): δ 20.83, 32.74 (CH₃); 45.25 (C3); 55.77 (OCH₃); 59.22 (C2); 72.57 (C4). ESI/MS⁺: 188 [M + H]⁺, 170 [M – OH]⁺. Anal. Calcd (Found) for 4-MeO-TEMPO-H (C₁₀H₂₁NO₂): C, 64.13 (64.28); H, 11.30 (11.31); N, 7.48 (7.49). 4-MeO-TEMPO-D was prepared analogously using (CD₃)₂CO/D₂O (99.9% D in D₂O) and was 98 ± 1% OD by NMR integration. Anal. Calcd (Found) for 4-MeO-TEMPO-D (C₁₀H₂₀DNO₂): C, 63.79 (63.92); H, 11.24 (11.37); N, 7.44 (7.55). IR (CD₃CN): ν_OH/ν_OD = 3492/2584.

¹H NMR Equilibrium Measurements

A typical experiment involved a J-Young sealable NMR tube being loaded with 4-oxo-TEMPO^• (48 mg, 0.28 mmol) and TEMPO-H(D) (76 mg, 0.48 mmol) in 0.5 mL CD₃CN or CD₂Cl₂ to form an equilibrium mixture with 4-oxo-TEMPOH(D) and TEMPO^•. ¹H NMR spectra of the sample were obtained at 278−318 K. All chemical species have resolvable peaks, whose integrations were determined by Lorentzian line fitting using NUTS.²⁵ An equilibrium constant was calculated at each temperature from the ratios of the peak areas, corrected for the number of protons for each peak. The experiment was repeated with 4-oxo-TEMPO^•/TEMPO-H(D) = 32 mg/51 mg, and 24 mg/38 mg and the reported K at each temperature is the average of three runs. The errors on K are 2σ of the variation of measured values. The errors on ΔH^o and ΔS^o are 2σ errors from the least-squares linear fit using KaleidaGraph⁵⁹ to the Van't Hoff equation.

¹H NMR of TEMPO^• in CD₃CN: −29.74 (3,5-CH₂, 4H), −16.51 (CH₃, 12H), 15.33 (4-CH₂, 2H); in CD₂Cl₂: −27.97 (3,5-CH₂, 4H), −15.14 (CH₃, 12H), 15.19 (4-CH₂, 2H). ¹H NMR of 4-oxo-TEMPO^• in CD₃CN: −7.78 (CH₃, 12H), 1.80 (3,5-CH₂, broad, 4H, overlaps with residual solvent [CH₂DCN] peak); in CD₂Cl₂: −7.12 (CH₃, 12H), 2.22 (3,5-CH₂, 4H). ¹H NMR of 4-MeO-TEMPO^• in CD₃CN: −33.89, −20.42 (3,5-CH₂, 2H each); −29.43, −1.74 (CH₃, 6H each); 3.07 (OCH₃, 3H); 8.67 (4-CH, 1H). ¹H NMR of ^tBu₂NO^• (s, ^tBu) in CD₃CN: −6.67; in CD₂Cl₂: −6.20. 4-oxo-TEMPO-H and ^tBu₂NOH were not isolated but were generated in situ in reactions 2 and 4, respectively. ¹H NMR of 4-oxo-TEMPO-H in CD₃CN: 1.22 (s, CH₃, 12H); 2.39 (s, CH₂, 4H); in CD₂Cl₂: 1.24 (s, CH₃, 12H); 2.49 (s, CH₂, 4H). ¹H NMR of ^tBu₂NOH (s, ^tBu) in CD₃CN: 1.23; in CD₂Cl₂: 1.31.

UV-Vis Stopped-Flow Kinetic Measurements

Solutions of 4-oxo-TEMPO^• (12−24 mM) and TEMPO-H(D) (118−584 mM) in MeCN or CH₂Cl₂ were prepared and loaded into gas-tight syringes inside a N₂ glovebox. The stopped-flow apparatus was flushed with the solvent, and a background spectrum was acquired. The syringes were immediately loaded onto the stopped-flow apparatus to minimize air exposure. The stopped-flow drive syringes were flushed with the reagents, then filled and allowed to thermally equilibrate. A minimum of six kinetic runs were performed for each set of concentrations at 278−318 K in MeCN or at 273−308 K in CH₂Cl₂ for reaction 2. The contents of the two syringes were rapidly mixed at equal volume resulting in half of the original concentrations (5.9−12 mM 4-oxo-TEMPO^• and 59−292 mM TEMPO-D). Kinetic data were analyzed using SPECFIT global analysis software²⁸ to determine the rate constants. Under pseudo-first order conditions (≥ 10 equiv TEMPO-H(D)), k_obs values were derived from fitting an A → B model at each [TEMPO-H(D)], and second order rate constants were obtained from plotting k_obs versus [TEMPO-H(D)] (Figure 3). Under second order conditions, the data were fit to an opposing second order equilibrium model, A + B ⇄ C + D (A and C colored), with a fixed equilibrium constant (Table 1). Reaction 2 was also performed in CCl₄ at 298 K under pseudo-first order conditions (≥ 10 equiv TEMPO-H(D)). Temperature dependent measurements of reaction 3 used similar amounts of 4-oxo-TEMPO^• and 4-MeOTEMPO-H(D) in MeCN; for reaction 4, 12−139 mM ^tBu₂NO^• and 118−237 mM TEMPO-H(D) in MeCN or CH₂Cl₂ were used (as the initial concentrations right after stopped-flow mixing). The errors on k are 2σ of the variation of measured values. The errors on the activation parameters are 2σ from the least-squares linear fit using KaleidaGraph⁵⁹ to the Eyring or Arrhenius equation.