Stability of Carbon-Centered Radicals: Effect of Functional Groups on the Energetics of Addition of Molecular Oxygen

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1 Stability of Carbon-Centered Radicals: Effect of Functional Groups on the Energetics of Addition of Molecular Oxygen JAMES S. WRIGHT, HOOMAN SHADNIA, LEONID L. CHEPELEV Department of Chemistry, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada K1S 5B6 Received 16 June 2008; Revised 8 August 2008; Accepted 14 August Published online 29 September 2008 in Wiley InterScience ( Abstract: In this paper we examine a series of hydrocarbons with structural features which cause a weakening of the C H bond. We use theoretical calculations to explore whether the carbon-centered radicals R which are created after breaking the bond can be stabilized enough so that they resist the addition of molecular oxygen, i.e. where the reaction R 1 O 2? ROO becomes energetically unfavorable. Calculations using a B3LYP-based method provide accurate bond dissociation enthalpies (BDEs) for R H and R OO bonds, as well as Gibbs free energy changes for the addition reaction. The data show strong correlations between R OO and R H BDEs for a wide variety of structures. They also show an equally strong correlation between the R OO BDE and the unpaired spin density at the site of addition. Using these data we examine the major functional group categories proposed in several experimental studies, and assess their relative importance. Finally, we combine effects to try to optimize resistance to the addition of molecular oxygen, an important factor in designing carbon-based antioxidants. q 2008 Wiley Periodicals, Inc. J Comput Chem 30: , 2009 Key words: carbon-centered radicals; antioxidants; bond dissociation enthalpy Introduction Carbon-centered radicals can be formed by a variety of initiating processes, where a C H bond in the molecule is broken to form the initial radical C (generically denoted R ). In the presence of atmospheric oxygen, R will usually add molecular oxygen to give the corresponding peroxyl radical ROO. 1 These reactive peroxyl radicals can oxidize other materials, e.g., in a biological environment they can start a chain reaction of lipid peroxidation, converting lipid (L H) into lipid hydroperoxide. Because of this problematic feature associated with carbon reactivity, antioxidants designed both for chemical and biological systems typically contain a weak O H bond leading to formation of an oxygen-centered radical. 2 5 Criteria for an effective oxygen-radical based antioxidant, denoted AO H, are (i) the AO H bond should be weak, i.e., the parent molecule is a good hydrogen donor, (ii) the radical AO should react only slowly with substrate, and (iii) the radical AO should be unreactive toward molecular oxygen to avoid generating peroxyl radicals. Phenolic antioxidants ArOH by appropriate use of substituents can be designed to satisfy (i), whereas (ii) depends on substrate but is satisfied when ArO H bonds are sufficiently weak, and (iii) is always satisfied, since an oxygen radical ArO does not add molecular oxygen to form the trioxyl radical ArOOO. Hence, the predominant importance of phenolic compounds is as industrial and biological antioxidants. Discussion of the use of antioxidants based on carbon radicals is relatively recent. However, the experimental study of carbon-centered radicals has been under investigation for many years, see Griller and Ingold in These authors distinguish between stable radical and persistent radical in terms of the tendency to add molecular oxygen (persistent radicals do not). One way to approach the problem experimentally is to generate a radical R from the parent hydrocarbon RH in the presence of molecular oxygen, and then examine the formation of the adduct ROO, from which an equilibrium constant can be derived. From rate measurements, Scaiano et al. 7 designate a carbon-centered radical to be long-lived if its reaction rate with oxygen is slow on the time scale of an ESR or laser flash photolysis (LFP) experiment (ca. 1 ms). Another useful experimental approach that was applied to lipid peroxidation studies 8 is to measure stability of the product ROO by way of measuring rates for the reverse reaction, ROO? R 1 O 2, termed b-fragmentation. Recently, Scaiano et al. 7,9 11 examined factors that might stabilize a carbon-centered radical. As a test of stability, they measured rates of addition of molecular oxygen to carbon radicals using LFP and identified five factors that led to diminished reac- Correspondence to: J. S. Wright; jim_wright@carleton.ca Contract/grant sponsor: NSERC, Canada q 2008 Wiley Periodicals, Inc.

2 Stability of Carbon-Centered Radicals 1017 tivity. These were (i) benzylic resonance stabilization, (ii) unpaired spin delocalization onto oxygen or other (unreactive) heteroatom, (iii) stereoelectronic effects, (iv) electron-withdrawing effects, and (v) steric effects. From this work, they determined that benzolactones and substituted fluorenes were unreactive. In later work, Scaiano and coworkers 10 showed that nitrile derivatives or para-nitro substituents on phenyl rings attached to the carbon center significantly decreased the reactivity toward oxygen. 11 This series of papers and other recent developments (ref. 12 and references therein) have generated renewed interest in the creation of stable carbon-centered radicals as a starting point for new antioxidants. A number of theoretical papers have also looked into the origin of carbon radical stability. Attention was focused particularly on the captodative effect, in which the carbon center is simultaneously substituted with an electron-withdrawing substituent and an electron-donating substituent, causing a synergistic weakening of the C H bond Davidson et al., 15 for example, found that the most stabilizing donor-acceptor combinations were [NH 2, CHO] and [OH, CHO], with combinations involving CN and a donor showing only modest stabilization. Other theoretical works, e.g., that of Boyd et al., 16 has examined the structure and properties of peroxyl radicals, which also led to an analysis of the dissociation into a carbon radical and molecular oxygen. The careful measurement accompanied by the calculation of carbon-oxygen bond dissociation enthalpies (BDE) in peroxyl radicals by Kranenburg et al. 17 (hereafter KCCM) provides a solid basis for comparison for any theoretical approach used to examine radical stability. A useful discussion of how various substituents stabilize carbon-centered radicals was given by Henry et al., 18 (hereafter HPMR), where they considered the interaction between a 2p carbon orbital and either p-acceptors, lone pair donors, or alkyl groups. Also, a discussion of factors relevant to lipid peroxidation or oxygen addition in general was given by Pratt et al. 8 In this article, we calculate gas-phase R H and R OO (BDEs), Gibbs free energies for the addition reaction, and unpaired spin densities in the radical. Then, we examine the various categories used by Scaiano and coworkers and attempt to evaluate their importance. Finally, we use these observations to predict the existence of some highly stabilized carbon-centered radicals. Method of Calculation KCCM 17 determined BDE(R H) and BDE(R OO ) by using photoacoustic calorimetry and compared with their own density functional theory (DFT) calculations. They list 18 experimental values of the BDE for R H ranging over values from 105 to 77 kcal mol 21 and 13 experimental values for R OO over a range from 37 to 12 kcal mol 21. In general, their DFT calculations underestimated the R H BDE by 0 5 kcal mol 21 and R OO by 0 6 kcal mol 21. They used differences in BDE relative to methane to improve agreement between theory and experiment, but the errors are large enough that we have chosen a slightly different DFT approach. We established in another work that we can calculate the absolute BDE(R H) for small hydrocarbons and aromatic systems to within 1 2 kcal mol 21 using a DFT method, we termed it as the Medium Level Model 2 (MLM2). 19 MLM2 obtains the geometry and frequency using the B3LYP functional with a 6-31G(d) basis set, and the final (single-point) energy using the G(2d,2p) basis set for the parent R H and the radical R. Frequencies are scaled by the factor , 20 the energy of R is calculated using an open shell (RO)B3LYP functional, and the energy of atomic hydrogen is set to its exact value, hartree. In standard notation, the method is denoted (RO)B3LYP/6-3111G(2d,2p)//B3LYP/6-31G(d)/B3LYP/6-31G(d). For brevity, the two basis sets G(2d,2p) and 6-31G(d) will be denoted Large and Small, respectively. However, MLM2 was shown to be less accurate for bonds of type C O. 21 Rather than switch functionals, we adopted a consistent B3LYP methodology termed MLM3, which gave good agreement with experiment for a variety of molecular properties, including C H and X-Y BDEs, where [X,Y] 5 C,N,O,F,S. 22 For the present application, MLM3 is identical to MLM2 except that (i) the H-atom energy is restored to its Large basis value of hartree, a difference of 1.35 kcal mol, and (ii) an open-shell correction (OSC) of 12.0 kcal mol 21 is added to the energy of each (doublet) radical. In the case of R H? R 1 H, then, MLM3 relative to MLM2 raises the absolute enthalpy of R by kcal mol 21 but lowers the enthalpy of the H- atom by 1.35 kcal mol 21, making the net change in R H BDE kcal mol 21. (Therefore, for methane the BDE is kcal mol 21 in MLM2, but kcal mol 21 in MLM3.)For R 1 O 2, no correction term is applied to triplet oxygen, but the (doublet state) OSC is applied to both R and ROO, so that all correction terms cancel and enthalpy changes for the R OO BDE using MLM3 and MLM2 are the same. All structures for parent and radical were first subjected to a conformer search using AM1 or occasionally PM3 (when AM1 gave suspicious structures), using the Spartan 02 program. 23 Conformers within 1 kcal mol 21 of the minimum energy conformer were sent to the Gaussian 03 program 24 for the B3LYP calculations. The most stable conformers for parent and radical were then determined by B3LYP/Small geometry optimization. (Note that the ROB3LYP/Large energetics are accurate, but prone to switches of electronic state at the open-shell (RO) stage and must be monitored carefully.) Gas-phase enthalpies and Gibbs free energies were determined at these potential minima. A useful guide to the preferred position of substitution is to examine the spin density in the resulting radical, since the carbon atom containing the most unpaired spin density is usually the thermodynamically preferred site of oxygen addition. An exception to this statement occurs when the site of highest spin density is a heteroatom (N,O); in that case, the preferred site of O 2 attack is the carbon atom with highest spin density. The unpaired spin density, q spin, was obtained at the final calculation step using UB3LYP/Large. 8 We tested the MLM3 method for five molecules from the data set of KCCM, with BDE values for R OO ranging from 12 to 33 kcal mol 21. BDE data were calculated for methyl, ethyl, benzyl, allyl, and cyclohexadienyl radicals, which form a representative set spanning the range of the KCCM data. Table 1 shows a comparison between their BDE data for R H and

3 1018 Wright, Shadnia, and Chepelev Vol. 30, No. 7 Table 1. Comparison of Calculated Bond Dissociation Enthalpy (BDE) at 298 K for R H? R 1 H and R OO? R 1 O 2 (Triplet Ground State) to Literature Values. 16 Radical BDE (R H) (UB3LYP) a BDE (R H) (MLM3) b BDE (R H) BDE (R OO ) BDE (R OO ) BDE (R OO ) (Expt.) c (UB3LYP) a (MLM3) b (Expt.) c Methyl Ethyl Allyl CycloHD e Benzyl MAD d All units in kcal mol 21. a Unrestricted B3LYP method used for radical, radical-oo, and O 2. Data from Kranenburg et al. 16 ; basis set is 6-31G(d) throughout. b Restricted MLM3 method (this work) used for parent molecule, radical, radical-oo, and O 2. This method uses ROB3LYP/6-3111G(2d,2p) basis for energy; see text for description. c Experimental values obtained or quoted by Kranenburg et al. 16 d Mean absolute deviation. e Cyclohexadienyl radical formed from 1,4-cyclohexadiene. R OO and data from the present calculations, along with experimental values. It can be seen that MLM3 provides considerably improved calculated values for the R H BDE (MAD kcal mol 21 ) and for R OO (MAD kcal mol 21 ). This level of accuracy is certainly adequate to discuss trends in the stability of carbon radicals. Also of interest is the gas-phase Gibbs free energy change for oxygen addition, defined in the opposite sense to the R OO BDE, i.e., we define DG 0 add FOR R 1 O 2? ROO. Therefore, positive values for the R OO BDE and negative Gibbs free energy changes for DG 0 add both indicate that oxygen will add to the carbon radical. Figure 1 shows structures for a large set of hydrocarbons of interest, where only the radical is shown. The structures shown are for dissociation of the weakest C H bond in the parent molecule. Often oxygen will add at this same position, although not always, for example, in the allyl radical B1 the two ends of the molecules are symmetry-equivalent and addition will necessarily occur at each equally. In other cases, the different positions of attack in the radical are not symmetry-equivalent, e.g., as in the pentadienyl radical where oxygen addition can occur at the ends or in the middle of the chain. In this case, there is higher q spin at the middle position; this is shown by an asterisk in Figure 1. Since O 2 may add preferentially at this position there is a double entry in Table 2, i.e., B3 (end) and B3 0 (middle). Results and Discussion 0 BDE Values, DG add, q spin Table 2 shows the gas-phase R H and R OO BDE values, DG 0 add and spin densities for the structures in Figure 1. Antioxidant activity depends on the R H BDE, but the persistence of the radical in an oxygen environment depends on the R OO BDE. Figure 2 shows the BDE for R OO plotted versus the BDE for R H. In agreement with most 17 but not all 8 previous work, we obtain a strong correlation, where the BDEs are related by BDE (R OO ) BDE (R H), with correlation coefficient R Here, the range in BDE (R H) is 55 kcal mol 21, with a standard deviation of 4 kcal mol 21 ; outliers on this graph include the alkyl-substituted and diamino radicals. Entropy effects are not expected to change the picture but just in case, Figure 3 shows a plot of the BDE (R OO ) vs. DG 0 add. The correlation is excellent with only one outlier, giving DG 0 add BDE(R OO ). The small standard deviation of 0.7 kcal mol 21 shows that entropy differences for (R OO 2 R ) between different compounds essentially cancel out, so that BDE (R OO ) and DG 0 add can essentially be used interchangeably as a measure of R OO stability. Note that there is an entropy penalty of 10.5 kcal mol 21 caused by combining R and O 2, which is constant for the series. This means that when the BDE (R OO ) drops to ca. 10 kcal mol 21, the addition of oxygen is no longer favored. Clearly this applies to many of the compounds studied in this article. Figure 4 displays plot of BDE (R OO ) vs. (U)B3LYP/ Large spin density. There are actually two correlations on this plot, the main correlation shows BDE (R OO ) q spin. Here, the BDE (R OO ) data span over 50 kcal mol 21 with a standard deviation of 3.8 kcal mol 21, thus the quality of this correlation is very similar to that in Figure 2. However, the outliers of first correlation can be described in a second correlation of BDE (R OO ) q spin. These will be discussed in the following context. Structures and Categories Structures in Figure 1 are arranged approximately into categories given by Scaiano and coworkers. 9 Category A consists of simple substituents surrounding a carbon radical. B has conjugative delocalizing groups and their (oxygen) heteroatom analogues. C

4 Stability of Carbon-Centered Radicals 1019 Figure 1. Structures, showing position of carbon radical formed after abstraction of an H-atom.

5 1020 Wright, Shadnia, and Chepelev Vol. 30, No. 7 Table 2. Gas-Phase Bond Dissociation Enthalpy (BDE) for R H and R OO, free energy of addition DG 0 add (R 1 O 2 ), and spin densities for molecules in Figure 1. Table 2. (Continued) No. BDE (R H) BDE (R OO ) DGadd0 (R 1 O 2 ) q spin (UB3LYP) No. BDE (R H) BDE (R OO ) DG 0 add (R 1 O 2 ) q spin (UB3LYP) A A A A A A A A A A B B B B B B B B B C C C C C D D D E E E E E F F F F G G G G G H H I I I I I I I I J J J J J J J J All values calculated for gas phase using MLM3 method in kcal mol 21. contains benzylic resonance stabilizers, D has the o, m, p-substituents for nitrotoluene, E contains simple lactones and isolactones, F has captodative substituents, G allows spin delocalization onto heteroatoms, H examines stereoelectronic effects, I makes use of some combinations, and finally J shows a number of molecules designed to maximize carbon radical stability. Simple Substituents A1-A4 show the familiar effect of increasing methyl substitution on a carbon radical. 18 Thus for methyl (A2), dimethyl (A3), or trimethyl-substituted (A4) carbon radicals, the decrease in R H BDE goes according to the sequence 4.5, 3.5, 2.8 kcal mol 21, showing the formation of an increasingly stabilized carbon radical but with an attenuated effect for each additional methyl substituent. A well-accepted measure of radical stabilization energy (RSE) compares the substituent to an H-atom in methane and is defined as RSE 5 BDE (CH 3 H) 2 BDE (XCH 2 H) (for discussion see HPMR and references therein). The RSE values are therefore 4.5, 8.0, and 10.8 kcal mol 21 for the series of increasingly methylated methyl radicals. Molecular oxygen will add to all these radicals, forming a weak covalent bond of ca. 32 kcal mol 21, i.e., the BDE remains essentially invariant to methyl substitution. The Gibbs free energy change for formation of ROO from R and O 2 is strongly negative (Table 2, kcal mol 21 ) for methyl radical (A1). The origin of the RSE from alkyl groups and other substituents has been discussed previously. 18 The stabilization of methyl radical by methyl substitution is caused by hyperconjugation. Here, the unpaired spin in the methyl radical is in a carbon 2p orbital, which interacts with a pseudo-p orbital formed from a combination of the substituent r CH bonding orbitals of appropriate symmetry. In this way, a pseudo-p bond is created which lowers the energy of two electrons, whereas the energy of the carbon 2p-orbital is raised into a p* MO; the net effect is a oneelectron stabilization. Judging from Figure 2, hyperconjugative substituents or multiple electron donors do not obey a linear relationship between R H and R OO BDE values, e.g., methylated and diamino methyl radicals are outliers. Results for A8-A10 show the effect of adding the lone-pair donor groups methoxy, amino, and diamino. The methoxy substituent in A8 weakens the C H BDE as much as three methyl groups, similar to the effect on the O H BDE in phenol, whereas the stronger amino donor A9 weakens the R H bond

6 Stability of Carbon-Centered Radicals 1021 Conjugative Delocalization Allylic and pentadienylic systems are known to form relatively stable carbon radicals (e.g., see ref. 16 for a discussion of allylic stabilization). The stability of the radical arises through conjugative delocalization, i.e., by extending the p-chain which contains the odd electron. For propene? allyl (B1), the C H BDE drops by a full 17.6 kcal mol 21 relative to methane, whereas the R OO BDE drops by almost as much at 14.2 kcal mol 21. Thus, there is a much reduced tendency to add oxygen to the allyl radical, consistent with the relatively low q spin Pentadiene (B3) and cyclopentadiene (B5) strongly lower both BDEs; note that DG 0 add for cyclopentadienyl radical is positive. It is easy to see the reason for stabilization of a methyl radical by a vinyl substituent, which falls into the class of p- acceptor. 18 Thus, for three electrons in an allylic p-system which is formed, two go into a stabilized p-bonding MO and the third into a non-bonding MO, resulting in a net two-electron stabilization. The same two-electron stabilization argument applies for a butadienyl substituent at a methyl radical site. Hence, vinyl and butadienyl are superior functional groups. The carbonyl group, shown in B2, is a less effective substituent than vinyl at stabilizing the carbon radical. This is no doubt because carbonyl is an electron-withdrawing group that destabilizes the radical, even though p-conjugation adds some stability. Figure 2. Correlation between BDE (R OO ) and BDE (R H). All values in kcal mol 21. by a full 13.2 kcal mol 21. Interestingly, among this group only the methoxy subsituent shows an appreciable weakening of the R OO BDE. These groups act as lone pair donors because for the interaction between amino and methyl, for example, it is the lone pair on N which interacts with 2p on carbon to form p and p* MOs. Thus, the energy of two electrons is lowered where one is raised, again a net 1-electron stabilization. Note that structure A10 is a significant outlier from the correlation of R OO BDE vs. q spin (Fig. 4) with an unexpectedly large BDE given its unpaired spin density of Chart 1 shows one of the possible types of interaction that causes extra stabilization of the adduct. On the right-hand structure, the amino groups have undergone an umbrella inversion toward the OO group. This is a result of the partially positively charged H- atoms interacting with the partial negative charge on oxygen and causing an unusual increase in the R OO bond dissociation enthalpy. Structures A5-A7, containing the electron-withdrawing groups CF 3, NO 2, and CN, show a progressive decline in C H BDE (106.5? 101.1? 96.7, respectively), also accompanied by a decrease in spin density (1.06? 0.94? 0.86) on the radical center and a significant decrease in R OO BDE. The spin density shows how effectively the attached functional group can delocalize the odd electron, and for this purpose CN is significantly more effective than NO 2. Figure 3. Gibbs free energy of addition DG 0 add BDE (R OO ). All values in kcal mol 21. for R 1 O 2 vs.

7 1022 Wright, Shadnia, and Chepelev Vol. 30, No. 7 Chart 2. Oxygen adduct in pentadienyl radical is favored at the end, not the middle, due to the better conjugation effect in B3. Figure 4. BDE (R OO ) vs. unpaired spin density. Squares, solid line: Main set of points. Circles, dashed line: Deviant points due to structural differences between parent R H and adduct R OO. Table 2 shows a double entry for B3, consistent with the fact that the spin density at the central carbon is higher than that at the end (0.53 vs. 0.51). In general, oxygen attack would favor the position of higher spin density. However, Table 2 shows that in this case the Gibbs free energy of addition favors the end position, i.e., the value for DG 0 add is more negative for B3 (21.9 kcal mol 21 ) than for B3 0 (13.7 kcal mol 21 ). A simple explanation is shown in Chart 2 (see also ref. 25). When O 2 adds to pentadienyl radical, addition at the end is favored because this allows conjugation over the four remaining carbon atoms. On the other hand, when attack is at the middle, a skipped diene is formed with complete loss of conjugation, and the Gibbs free energy penalty for forming the latter is 5.6 kcal mol 21. We conclude that spin density in the parent molecule is an important predictor for the site of addition, but that delocalization in the product is more dominant in determining the preferred location of oxygen addition. It is also of interest to terminate the conjugated system with oxygen, thus converting the vinyl substituent in B1 into the electron-withdrawing carbonyl group in B2. As stated earlier, this significantly increases the C H BDE (88? 95 kcal mol 21 ) but has much less effect on the R OO BDE. Compare B3 and B4, where the chain has been extended, both of which have an identical R OO BDE at the low value of ca. 12 kcal mol 21, corresponding to very slightly negative values for DG 0 add. The skipped diene B6, a familiar motif in fatty acid chemistry, has the advantages of the same delocalized pentadienyl radical as B3, but less stability in the parent due to the lack of conjugation. As a result, the R H BDE has dropped down to 74.1 kcal mol 21, the R OO BDE is reduced to 6.5 kcal mol 21 and DG 0 add has become positive at 13.7 kcal mol21. Thus the RSE is a full 32 kcal mol 21 relative to methyl, and the (slightly) positive value of DG 0 add indicates the beginning of resistance to oxygen addition. These results are consistent with the kinetic studies of Tallman et al. 25 who studied the mechanism of linoleate oxidation. They found that the peroxyl radical with oxygen at the center of the pentadienyl chain easily split off oxygen and reformed the original pentadienyl radical, whereas oxygen remained bound more strongly at the end of the chain. Continuing in this direction by adding another vinyl substituent, B7 now corresponds to a triple-skipped diene. There is no conjugation in the parent but extensive (cross) conjugation in the radical. This is reflected in the low spin density of 0.48 on the central carbon, the nearly complete disappearance of the R OO BDE and the strongly positive value of DG 0 add kcal mol 21. In fact, the radical is non-planar, with the vinyl groups twisted by 348 with respect to each other (propeller orientation). Nevertheless, the trivinyl-substituted methyl radical is significantly more stable than divinyl, unlike the case when there are phenyl substituents. The loss of stabilization in the case of triphenylmethyl radical is due to the more severe twist angle of 538. InB7 just as in B6 it is energetically preferable to add oxygen at the end of a chain, thereby allowing more extensive delocalization in the remaining molecule (see Chart 2). Although it has lower spin density at this position than in the middle (0.38 vs. 0.48), this is nevertheless denoted B7 0 (Table 2). Clearly addition at the end is preferred by 7.8 kcal mol 21. Benzylic Resonance Stabilization Chart 1. Electrostatic stabilization of adduct by umbrella inversion of amino groups. Structures C1-C5 explore variations in benzylic resonance stabilization for the substituents phenyl, diphenyl, triphenyl, a-naphthyl, and indenyl. Surprisingly, the phenyl substituent (creating the benzyl radical, C1) is less effective at stabilizing methyl radical than the vinyl substituent (creating the allyl radical, B1).

8 Stability of Carbon-Centered Radicals 1023 Chart 3. Unpaired spin densities on indenyl radical. with the unsubstituted benzyl (C1) shows only modest differences, with para- being most resistant to oxygen addition (but only different from unsubstituted benzyl by ca. 2.5 kcal mol 21 ). Inspection of spin densities shows that q spin in benzyl and 0.74 in p-nitrobenzyl (D3); in D3 there is indeed some small spin density on N. From Figure 4 this change in spin density should cause a decrease in BDE R OO by ca. 3 kcal mol 21, which is close to the observed 2.5 kcal mol 21. However, we cannot explain from these model calculations why Scaiano and coworkers 12 observed such a profound rate enhancement effect caused by p-nitro substitution in the isobenzofuranyl system (Chart 4, replacing R¼H with R¼NO 2 ). Thus, we calculate an RSE for phenyl and 17.6 kcal mol 21 for vinyl, which is in good agreement with previous work using the accurate CBS-RAD method. 18,26 This observation also holds for two phenyl groups (C2), which are less effective than two vinyl groups (B6). Surprisingly, the triphenyl-substituted methyl radical (C3) is very similar in properties to diphenyl C2. This can be attributed to the further loss of conjugation caused by the severe propeller twist in C3. The a-naphthyl substituent (C4) is very little better than phenyl at stabilizing the carbon radical. However, the indenyl radical (C5) is an effective stabilizer, providing a low R H BDE (80.4) and a positive DG 0 add. Viewed from one perspective, the indenyl radical is stabilized by phenyl on one side (leading to benzylic resonance) and vinyl on the other (allylic resonance), so that the spin density has dropped to a relatively low This is the lowest value in the series C1-C5. Inspection of C5 (Chart 3) shows that indenyl benefits mostly from allylic resonance in the five-membered ring, allowing q spin at the two symmetry-equivalent positions. Ortho, Meta, Para Effects Scaiano and coworkers 12 reported that the presence of a para- NO 2 group dramatically slowed the reaction rate of isobenzofuranyl radicals with oxygen, Chart 4. Thus the experimental result showed a rate decrease of ca M 21 s 21 on adding only paranitro substitution. Structures D1-D3 show the calculated effect of adding an ortho-, meta-, or para-no 2 functional group to the simpler benzyl radical. Considering the BDE(ROO ) comparison Chart 4. Reaction of isobenzofuranyl radicals with oxygen. Lactones, Isolactones The five-membered lactone ring E1 is interesting relative to the previously discussed molecules in that it has a low R H BDE (76.9 kcal mol 21 ) combined with a very positive DG 0 add (ca. 110 kcal mol 21 ). However, the isolactone E2 shares an identical radical with lactone E1. Because E2 forms an oxygen adduct which is much more stable than E1 (with BDE R OO of 9.5 rather than 0.6 kcal mol 21, oxygen addition will occur preferentially as shown for E2. The hybrid structure E3 is a poor radical stabilizer and therefore not of interest. Surprisingly, the benzolactone E4 forms a less stable radical (BDE R H kcal mol 21 ) than the simple lactone E1 (76.9 kcal mol 21 ), and with a less positive DG 0 add (15.3 kcal mol21 ), a higher spin density, etc. As earlier, the vinyl group adjacent to the radical site in E1 and E2 is superior to phenyl in E4 at causing resistance to oxygen addition. Examination of spin densities shows extreme delocalization in E1, mostly to the opposite allylic carbon but also on the carbonyl oxygen. The reason for the poor performance of the benzolactone is that the possibility of allylic delocalization is lost in the benzolactone, and the result is that the simple lactone is a more effective spin delocalizer. Captodative Stabilization Structures F1-F4 show that the captodative effect can accomplish substantial weakening of C H bond and C O bond using only two small substituents. Thus for NH 2 and NMe 2 as donors, and NO 2 and CHO as acceptors, Table 2 shows remarkably low BDEs for such small molecules, with BDE (R H) ranging from 71 to 81 kcal mol 21 and also very low values for R OO, ranging from 4 to 8 kcal mol 21. Thus these molecules are almost unbound with respect to oxygen addition, with a very weak covalent bond approaching the range normally found only for hydrogen bonds. The carbonyl group forms a more powerful p-acceptor than nitro, but the NMe 2 group offers only a slight improvement over the amino group. Thus F2 and F4, containing CHO, are superior to F1 and F3, containing NO 2 as the electron-withdrawing group. The most effective combination in this series is F4, Me 2 N CH 2 CHO, with DG 0 add kcal mol21. These results are in general agreement with Davidson et al. 15 confirming the importance of the captodative stabilization obtained by combining the amino and carbonyl groups around a carbon radical.

9 1024 Wright, Shadnia, and Chepelev Vol. 30, No. 7 Spin Delocalization on Heteroatom G1-G4 begin with a substituted cyclohexadienyl ring and then abstract an H-atom at the position shown (Fig. 1). The very low R H BDEs (61 76 kcal mol 21 ) result from the fact that an aromatic benzyl-type radical forms in G2-G4. In fact, oxygen substitution will occur but at the benzylic site when possible, rather than at the abstraction site shown, hence the double entry in Table 1 for G2, G2 0.InG2 attack at the site shown is strongly endergonic (DG 0 add 5117 kcal mol21 ) but this is misleading, since the benzyl site of attack is so strongly favored (DG 0 add kcal mol 21,inG2 0 ). However, by placing a heteroatom in the benzylic position, as in the dieneimine G3, we retain a very low R H BDE (66.4 kcal mol 21 ) with a negative value for R OO BDE kcal mol 21, corresponding to the highly positive DG 0 add kcal mol21. A similar although less dramatic result holds for the dienone form in G4, which is best represented as a phenoxyl radical. Spin densities are indeed exceptionally low on the indicated carbon in G3 (q spin ), because so much spin density has been transferred to the heteroatom N. A less extreme but still important result applies to the dienone G4, where the unpaired spin on carbon is 0.40 but on oxygen it is Therefore, the structures G3 and G4 should be very resistant to oxygen addition. Stereoelectronic Effects Benzylic resonance is weakened in the diphenylmethyl radical C2 because of the twisting of the methyl groups, but the fluorene molecule H1 forces coplanarity of the phenyl groups with the radical site. A similar effect is achieved in the oxygen-substituted H2, which has a six-membered ring connecting phenyl groups. The relevant comparison for the constrained radical H1 is the (unconstrained) diphenylmethyl radical C2. Table 1 shows essentially no difference for this pair, so that the fluorenyl radical is no improvement over diphenylmethyl. However H2, a hydrocarbon analog of phenoxazine, represents a better starting point than fluorene H1 since it has a lower BDE (75.5 vs kcal mol 21 ) and a more positive DG 0 add (12.1 vs kcal mol 21 ). Combined Effects Figure 5. Structure J9: Dome-shaped phenalene (R H), planar phenalenyl radical (R ), and planar oxygen adduct. The oxygen is far away and weakly bound. We next consider I1-I4 that contain some obvious combinations of the effects described earlier. In all cases, the C H bond is broken at the cyclohexadienyl carbon, as in G1. We borrow from the theme in G2, anticipating benzyl attack, and provide captodative stabilization at the (incipient) benzyl radical. Thus, I1 adds a CHO acceptor group at the benzyl radical site. The R H BDE in I1 drops to 58.9 kcal mol 21, and DG 0 add rises to kcal mol 21. However, oxygen attack will preferentially occur at the benzyl carbon (I1 0 ), with DG 0 add much less favorable at 11.0 kcal mol 21. Oxygen attack at the benzyl site also occurs for I2, but now the captodatively stabilized benzyl containing NH 2 (donor) and CHO (acceptor) groups shows an R H BDE of only 50.4 kcal mol 21 and DG 0 add for benzyl attack is now 19.0 kcal mol 21, much more resistant to oxygen addition. The nitro group (I3) substituted for CHO shows similar properties. Thus, these compounds combine the features of a cyclohexadienyl group with captodative stabilization at the benzyl site. The result is very low R H BDEs and several fairly positive values of DG 0 add. Novel Molecules J1, phenalene, is an unusual molecule (although not unknown, see ref. 27), which forms a very stable p-radical. It has a nonplanar parent, which is conjugated only along the periphery of the molecule. The phenalenyl radical is perfectly planar and therefore has improved conjugation relative to both parent and oxygen adduct; resonance structures can be drawn showing partial aromaticity. The result is an amazingly small R H BDE of only 15.9 kcal mol 21 with a very low spin density of 0.12 at the center. This suggests that attack may preferentially occur at a ring position where the spin density is higher, even though this would be accompanied by a loss of aromaticity. J1 still retains a weak R OO bond of 4.4 kcal mol 21 but the oxygen positioning is very unusual. Figure 5 shows that the O 2 is very far (ca. 3.0 Å) from the central carbon and sits in a broad van der Waals minimum, where the bound frequency is only 23 cm 21. In fact, the interaction in the adduct is sufficiently weak that the carbon skeleton remains planar. This weak interaction is not well described by DFT but does serve to emphasize the unique stability of the phenalenyl carbon-centered radical. J2, oxatriangulene, borrows from H2 and J1 but surrounds the carbon radical by oxygen-linked rings. The parent is domeshaped, the radical is planar, and the oxygen adduct is in turn dome-shaped (Fig. 5). Therefore, because of the fully planar and highly stabilized radical, the BDE should be relatively small for R H, and because of the destabilized adduct (loss of conjugation due to non-planarity), the BDE for R OO should also be small. The result is good but not spectacular: the BDE for R OO has dropped to 1.7 kcal mol 21, i.e., almost disappeared, and DG 0 add has risen to 19.3 kcal mol21. In this case and in general as DG 0 add becomes positive, we find a long weak R OO bond with distances ranging from 1.55 to 1.6 Å. Thus for the strongly bound methyl-oo, the bond distance is Å, whereas for weakly bound J2 adduct the R OO distance increases to Å; in Figure 6, the oxygen molecule is drawn as unbound. (Using the GaussView Viewer associated with Gaussian 98, bonds between carbon and oxygen are not drawn when the distance exceeds 1.55 Å.)

10 Stability of Carbon-Centered Radicals 1025 Conclusions Figure 6. Structure J2: Dome-shaped oxatriangulenium Parent (R H), planar radical (R ), and dome-shaped oxygen adduct R OO. Structures J3 and J4 exploit themes from fatty acid chemistry. 9 J3 uses two hexadienyl substituents to delocalize the unpaired spin, giving DG 0 add kcal mol21. Clearly this structure could be extended to another such chain (trihexadienylmethane), and extrapolating from the trivinyl case (B6) this should lead to DG 0 add in excess of 120 kcal mol21. J4 follows on the trivinyl substituent B7 but extends the delocalization to three butadienyl substituents. Formerly isolated in the parent, these groups are fully (cross) conjugated in the radical, giving a high DG 0 add kcal mol21. Finally, J5 is similar to J4 except that it uses three styrenyl groups instead of three butadienyl groups. The styrenyl functional group has been shown to be an effective radical stabilizing group in weakening the BDE of phenolic antioxidants. 28 Thus the molecule should improve on the trivinyl-substituted B7 and it does, with DG 0 add kcal mol 21 (vs. 9.6 for B7). Structures J3 0, J4 0, and J5 0 show more favorable Gibbs free energy changes are possible at alternative sites, either at the ends (J3 0, J4 0 ) or at the position allylic to the central carbon (J5 0 ). All these alternative sites increase conjugation in the adduct and hence are favored. Kinetic Considerations In this article, we have only used thermodynamic data as a predictor of antioxidant effectiveness, but it is reaction rates which determine antioxidant usefulness in practice. There have been a number of discussions in the literature, particularly by Zavitsas (personal communication), 29 regarding the relative rates between hydrocarbons R H and peroxyl radicals (e.g., ROO ) versus rates between hydrocarbons and carbon-centered radicals (e.g., methyl). Thus, Zavitsas estimates activation barriers for transfer from an oxygen center, i.e., ROO H OR 0 (type O H O) to be generally significantly lower than barriers for transfer from a carbon center ROO H R 0 (type O H C). 29 This suggests that the practical use of such antioxidants, except possibly for industrial processes at high temperatures, may be problematic. Indeed, Barclay 29 found that the commercially used carbon radical-based antioxidant HP-136 (Barclay, personal communication), and also studied by Scaiano et al., 8 failed to inhibit the oxidation of cumene, a situation in which even a weak phenolic antioxidant showed some inhibition. However, recent advances by Scaiano and coworkers (ref. 12 and references therein) in creating antioxidants based on carbon radicals have shown new possibilities for development in this area. The MLM3 method gives BDEs for R H andr OO of sufficient accuracy to be useful for the purposes of this article, although all calculations were restricted to the gas phase. Thus this article deals exclusively with H-atom transfer reactions. A good linear correlation was obtained between R OO and R H BDEs for a variety of compounds. Gibbs free energies of addition and R OO BDEs can essentially be used interchangeably because of their near-perfect linear correlation. R OO BDEs are also well correlated with unpaired spin densities, with smaller spin density leading to a weaker bond. Simplifying the earlier observations, to design molecules with stable radicals which resist oxygen addition, probably the first approach is to attempt to delocalize the unpaired spin. Thus, when the maximum q spin is 0.50 or less, Table 2 shows that all DG 0 add values are positive. A more important stabilizing force occurs, however, when the delocalization in the adduct is more extensive than in the parent R H. Using categories defined in previous work, particularly by Scaiano et al., 7,9 11 we are able to make the following generalizations: (1) alkyl groups and lone pair donors show little effect on the BDE for R OO, but electron withdrawing groups weaken the R OO bond, especially the cyano group; (2) conjugative delocalization, particularly with one or more vinyl groups, is very effective for weakening the R OO bond, as well as lowering the R H BDE. Thus conjugative delocalization provides an important, if not the most important, stabilizer for carbon-centered radicals. The skipped diene form (divinyl substituents in the parent R H) shows the largest effect in this category, resulting in a positive DG 0 add ; (3) benzylic resonance weakens both R H and R OO bonds, as expected. However, vinyl is a more powerful functional group than phenyl, because allyl radical distributes spin density more effectively than benzyl, where it tends to concentrate on the benzylic (exocyclic) carbon; (4) simple ortho-, meta-, and para-effects using the NO 2 group are minor, when considering stabilization of the benzyl radical; (5) lactones and to a lesser extent isolactones are important stabilizing groups, but benzolactones offer only a small improvement over lactones; (6) captodative stabilization provides a very strong radical stabilizing force, and the carbonyl acceptor seems to be special in this respect; (7) starting from cyclohexadienyl radical, spin delocalization onto a heteroatom is a useful design strategy; (8) the improvement in desired properties by using stereoelectronic effects in our examples (i.e., fluorene) is small, relative to unconstrained phenyl groups. Thus, stereoelectronic effects using the fluorenyl group are weak, although introduction of an oxygen into a six-membered ring adjacent to benzenes results in somewhat better stabilization; (9) considering all of the aforementioned effects, we have tabulated Gibbs free energies of addition for a variety of molecules, approximately half of which will be resistant to the addition of molecular oxygen. One must be careful, however, to account for alternative sites of oxygen attack, which may in fact undergo addition. With insights gained from the earlier calculations, we considered the design of novel antioxidants with a highly positive DG 0 add, corresponding to an ultra weak R OO bond (or none at all) and a correspondingly low R H BDE value. One way to begin is to design a molecule with a very weak C H bond,

11 1026 Wright, Shadnia, and Chepelev Vol. 30, No. 7 since values of the R OO BDE and R H BDE are highly correlated. A simpler way is to design for strong delocalization of the unpaired spin density, which is well correlated with the R OO BDE. This can be rapidly explored for the radical in question, without considering the parent or the oxygen adduct. In nonpolar solutions, the formation of R from parent molecule R H by an H-atom transfer mechanism should be dominant, and the addition reaction will become very slow for molecules with the large positive values of DG 0 add reported here. Particularly given the very low values of the R H BDE for some of these compounds, direct reaction with molecular oxygen (autoxidation) and subsequent chain reactions would usually be a concern, but these molecules are expressly designed to resist oxygen addition so this will not be a factor. In this article, we have not considered the fate of the long-lived carbon-centered radicals, which deserves further attention. Creation of novel antioxidants based on carbon-centered radicals should be possible based on the earlier considerations. One factor that needs to be addressed is that the rate of H-atom transfer between C HO is inherently slower than between O HO, i.e., activation barriers for the latter exchange are lower. However, it is probable that since the best molecules in our list of structures have extremely low C H BDEs, the barrier heights for atom transfer should also be relatively low. Another area that needs more exploration is the intentional destabilization of the parent molecule, so that strain is relieved as the carbon radical is formed. Structures C2, C3, J1, and J2 illustrate this point. We have designed another series of molecules that systematically test this approach and have obtained very weak C H bonds. These results will be reported in a separate publication. Acknowledgments The authors thank Drs. Tony Durst, Ross Barclay, and Tito Scaiano for helpful comments. References 1. Maillard, B.; Ingold, K. U.; Scaiano, J. C. J Am Chem Soc 1985, 105, Burton, G. W.; Doba, T.; Gabe, E. J.; Hughes, L.; Lee, F. L.; Prasad, L.; Ingold, K. U. J Am Chem Soc 1985, 107, Burton, G.; Ingold, K. U. Acc Chem Res 1986, 19, Shi, H.; Noguchi, N.; Niki, E. Free Rad Biol Med 1999, 27, Halliwell, B.; Gutteridge, J. M. C. Free Radicals in Biology and Medicine; Oxford University Press: Oxford, Griller, D.; Ingold, K. U. Acc Chem Res 1976, 9, Scaiano, J. C.; Martin, A.; Yap, G. P. A.; Ingold, K. U. Org Lett 2000, 2, Pratt, D. A.; Mills, J. H.; Porter, N. A. J Am Chem Soc 2003, 125, Bejan, E. V.; Font-Sanchis, E.; Scaiano, J. C. Org Lett 2001, 3, Font-Sanchis, E.; Aliaga, C.; Focsaneanu, K.-S.; Scaiano, J. C. Chem Commun 2002, 15, Font-Sanchis, E.; Aliaga, C.; Cornejo, R.; Scaiano, J. C. Org Lett 2003, 5, Frenette, M.; Aliaga, C.; Font-Sanchis, E.; Scaiano, J. C. Org Lett 2004, 6, Viehe, H. G.; Janousek, Z.; Merenyi, R.; Stella, L. Acc Chem Res 1985, 18, Pasto, D. J. J Am Chem Soc 1988, 110, Davidson, E. R.; Chakravorty, S.; Gajewski, J. J. New J Chem 1997, 21, Boyd, S. L.; Boyd, R. J.; Barclay, R. R. C. J Am Chem Soc 1990, 112, Kranenburg, M.; Ciriano, M. V.; Cherkasov, A.; Mulder, P. J Phys Chem A 2000, 104, Henry, D. J.; Parkinson, C. J.; Mayer, P. M.; Radom, L. J Phys Chem A 2003, 105, DiLabio, G. A.; Pratt, D. A.; LoFaro, A.; Wright, J. S. J Phys Chem A 1999, 103, Scott, A. P.; Radom, L. J Phys Chem 1996, 100, DiLabio, G. A.; Pratt, D. A. J Phys Chem A 2000, 104, Wright, J. S.; Rowley, C. R.; Chepelev, L. L. Mol Phys 2005, 103, Wavefunction Inc. SPARTAN 02; Wavefunction Inc.: Irvine, CA, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, Tallman, K. A.; Pratt, D. A.; Porter, N. A. J Am Chem Soc 2001, 123, Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A., Jr. J Chem Phys 1996, 104, Zheng, S.; Lan, J.; Khan, S. I.; Rubin, Y. J Am Chem Soc 2003, 125, Charron, M. MSc Thesis, University of Ottawa, Ottawa, Canada, Zavitsas, A. A. J Am Chem Soc 1998, 120, 6578.