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Radical Stability—Thermochemical Aspects Johnny Hioe and Hendrik Zipse Department of Chemistry, LMU M¨unchen, M¨unchen, Germany 1 INTRODUCTION is quite challenging. Kinetic data, in contrast, are much more difficult to predict by theory, while the The terms “transient” and “persistent” are used determination of reaction rates can be approached frequently in the scientific literature to describe experimentally with a variety of direct or indirect the kinetic properties of open shell systems in methods, at least for sufficiently fast reactions homogeneous solution.1–5 The hydroxyl radical (see Radical Kinetics and Clocks). Theory and (HO•, 1), for example, is a transient species of experiment pair up nicely in this respect, as a central importance in atmospheric chemistry (see combination of these approaches is able to provide Atmospheric Radical Chemistry), as well as one a comprehensive picture of thermodynamic and of the most important reactive oxygen species kinetic data. (ROS) in aqueous solution, whereas the nitroxide 2,2,6,6-tetramethylpiperidine-1-oxyl, TEMPO (2)is a persistent radical stable enough to be bottled and 2 DEFINITIONS OF RADICAL STABILITY sold in bulk (Figure 1) (see Nitroxides in Synthetic Radical Chemistry). The thermodynamic stability of C-centered radicals However, despite their widespread use, these can be defined in various ways and several options terms are not too helpful for a quantitative approach are discussed in the following.6–10 One of the to radical chemistry as they do not reflect the most often used definitions is based on hydrogen influence of thermochemical driving force and transfer reactions as shown in Scheme 1 for reaction • intrinsic reaction barrier on the observed lifetime. of methyl radical ( CH3, 3) with hydrocarbon In this account, we assemble a large amount of R1R2R3C–H.6,9,11,12 thermodynamic data for (mostly neutral) open shell 1 2 3 • 1 2 3 • systems to provide a foundation for a quantitative RSE(R R R C ) = H298(R R R C ) discussion of reactivity. This type of data will, + for example, show that reactions of radical 1 H298(CH4) are typically much more exothermic than those 1 2 3 − H298(R R R C–H) of radical 2. Thermodynamic data for open shell − • systems can be computed with comparable ease H298( CH3) (1a) for stable as well as for unstable systems, while RSE(R1R2R3C•) = BDE(R1R2R3C–H) the experimental determination of quantities such − as the heat of formation of a particular radical BDE(CH3–H) (1b) Encyclopedia of Radicals in Chemistry, Biology and Materials, Online 2012 John Wiley & Sons, Ltd. This article is 2012 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Radicals in Chemistry, Biology and Materials in 2012 by John Wiley & Sons, Ltd. DOI: 10.1002/9780470971253.rad012 2 BASIC CONCEPTS AND METHODOLOGIES to stabilizing interactions between the unpaired spin and the three methyl substituents in radical (4)or OH O N whether this also reflects other components such as 1 steric strain in the closed shell reference system isobutane (4H) cannot be seen from the results 2 in Table 1. For further discussion of alternative Figure 1 Hydroxyl radical 1 and 2,2,6,6-tetramethylpiperi- approaches to defining radical stability, we also dine-1-oxyl radical (TEMPO) 2. include here data for hydroxymethyl radical (5) and fluoromethyl radical (6). The C–H bond energies in The reaction energy of the reaction in Scheme 1 methanol (5H) and fluoromethane (6H) are smaller is often referred to as the radical stabilization • than that in methane (3H), implying a stabilizing energy (RSE) of radical R and is, of course, influence of HO- and F-substituents on the radical identical to the difference in homolytic C–H bond center according to (1). energies in the two closed shell systems CH3–H • From a conceptional point of view, it is also (3H) and R–H. The RSE value of R can thus important to note that (1) is an isodesmic reaction, equally well be expressed by (1a) or by (1b) which is defined as a reaction with retention of and is negative for systems more stable than 15,16 • the number of bonds of a given formal type. the methyl radical CH (3). Expression (1b) 3 This implies that RSE values can be computed quite makes it also clear that theoretically calculated and experimentally measured bond dissociation energy accurately even with moderately accurate quantum (BDE) data can conveniently be combined to mechanical methods (Table 1). Alternative defini- express the stability of radicals in a quantitative tions to characterize the stability of carbon-centered way. Using the above definition, the stability radicals in a quantitative way have been pro- • of tert-butyl radical ((CH3)3C , 4) amounts to posed, which circumvent the cleavage of C–H −38.9 ± 2.9kJmol−1 when using experimentally bonds.14, 17–19 This involves the cleavage of a fully measured heats of formation13 or to −29.1 ± apolar C–C bond in the formal dimer of the respec- 0.7kJmol−1 using energies derived from G3-level tive radicals. Using again the methyl radical as a calculations (Table 1). Whether these values are due (nonstabilized) reference system and accounting for H H ∆H H + 298 + R H R3 H R 3 (1) H R H 1 R 1 R2 H 2 33H Scheme 1 Isodesmic hydrogen transfer reaction defining the RSE of C-centered radicals. • Table 1 RSE values for tert-butyl radical ((CH3)3C , 4), hydroxymethyl radical • • ( CH2OH, 5), and fluoromethyl radical ( CH2F, 6) calculated according to (1). Method RSE (kJ mol−1) Exp.a −38.9 ± 2.913 • G3 −28.4 C(CH3)3 (4) G3B3 −29.8 G3(MP2)-RAD −28.5 Exp.a −37.4 ± 0.613 • CH2OH (5) G3B3 −33.5 G3(MP2)-RAD −32.3 Exp.a −15.5 ± 4.213 • CH2F (6) G3B3 −13.4 G3(MP2)-RAD −12.8 a The following experimentally measured BDE values (see Ref. 13) have been used to calculate −1 RSE values: BDE(CH3–H) =+439.3 ± 0.4 kJ mol ;BDE((CH3)3C–H) =+400.4 ± 2.9 kJ −1 −1 −1 mol ;BDE(FCH2–H) =+423.8 ± 4.2 kJ mol ;BDE(HOCH2–H) =+401.9 ± 0.6 kJ mol . Encyclopedia of Radicals in Chemistry, Biology and Materials, Online 2012 John Wiley & Sons, Ltd. This article is 2012 John Wiley & Sons, Ltd. This article was published in the Encyclopedia of Radicals in Chemistry, Biology and Materials in 2012 by John Wiley & Sons, Ltd. DOI: 10.1002/9780470971253.rad012 RADICAL STABILITY—THERMOCHEMICAL ASPECTS 3 the fact that two radicals are generated simultane- close proximity to previous estimates.20–22 RSE ously in this process leads to (2) as the defining values calculated according to (2) therefore, need equation (Table 2). to be corrected for these additional interactions to extract the true substituent effect on radical RSE(R1R2R3C•) = 0.5[BDE(R1R2R3C–CR1R2R3) stability.14, 17–19 Following the approach pioneered by Zavitsas et al., this leads to corrected RSE − − • BDE(CH3 CH3)](2) −1 values of RSEZ((CH3)3C , 4) =−5.1kJmol , • −1 RSEZ( CH2OH, 5) =−8.5kJmol , and RSE • −1 While this definition avoids most of the pitfalls of Z( CH2F, 6) =+13.7kJmol (Table 2). In con- using the C–H BDE process presented first, it also trast to the results obtained from (1), this implies does have its own problems. These are mainly con- that fluorine substituents directly attached to the nected to cases, in which the two halves of the sym- radical center are destabilizing. A third way of metric dimer reference system interact through more quantifying radical stability involves the cleavage than just the central covalent bond. For the dimer of of a C–C bond in a nonsymmetric reference tert-butyl radical (4) we may, for example, assume compound14, 17–19: the presence of steric interactions, whose relief on C–C bond dissociation will artificially stabilize 1 2 3 • 1 2 3 RSE(R R R C ) = BDE(R R R C–CH3) radical 4. Two additional cases worthy of consider- − − ation are ethylene glycol (HOCH2CH2OH), whose BDE(CH3 CH3)) (3) • cleavage leads to hydroxymethyl radical ( CH2OH, 5), and 1,2-difluoromethane (FCH2CH2F), whose This definition solves a number of problems • cleavage generates the fluoromethyl radical ( CH2F, arising from steric or stereoelectronic interactions 6). In the first of these systems, the two halves in the symmetric reference compounds discussed communicate through an internal hydrogen bond above. Without addition of any correction terms, this and additional stereoelectronic effects, while in leads to the results shown in Table 3. For all three the second example only the latter aspect remains. systems considered here, the RSE values obtained This leads in both of these systems to a preference from (3) are very close to the RSEZ values resulting for gauche conformations. The magnitude of the from the combination of (2) with the correction gauche effect in 1,2-difluoroethane can be quan- terms proposed by Zavitsas.14 tified through the gauche/anti enthalpy difference The defining equation (1) for measuring stabil- as −1.8 kJ mol−1 at G3(MP2)-RAD level, in ities of carbon-centered radicals can be adapted • • Table 2 RSE values for tert-butyl radical ((CH3)3C , 4), hydroxymethyl radical ( CH2OH, 5), and • fluoromethyl radical ( CH2F, 6) according to (2). Conformation Method RSE (kJ mol−1) Exp.a −27.4 ± 2.113 • G3B3 −16.1 C(CH3)3 (4) G3(MP2)-RAD −15.0 14 G3(MP2)-RAD −5.1(RSEZ) Exp.a −9.6 ± 3.213 gauche G3B3 7.5 • CH2OH (5) gauche G3(MP2)-RAD −6.8 anti G3(MP2)-RAD −10.8 14 anti G3(MP2)-RAD −8.5(RSEZ) Exp.a −4.6 ± 4.213 gauche G3B3 +7.9 • CH2F (6) gauche G3(MP2)-RAD +8.1 anti G3(MP2)-RAD +6.3 14 anti G3(MP2)-RAD +13.7(RSEZ) a The following experimentally measured BDE values (see Ref.
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