II. Intermolecular Addition Reactions

A. General Reaction Equation

A useful terminology for describing radical addition reactions is given in eq 1. According to this description, when a carbon-centered radical reacts with a carbon–carbon double bond, it adds to the β-carbon atom and creates a new radical center on the α-carbon atom. The letters X, Y, and Z in eq 1 rep­resent sub­stituents attached to the three carbon atoms directly involved in the reaction.

B. Reaction at the Less-Substituted Carbon Atom

A characteristic of radical addition reactions is that a carbon-centered radical adds regio­selec­tively to the less-substituted atom in a C–C multiple bond.^7–10 The reaction shown in Scheme 1 provides a typical example. Other reactions involving double bonds with different sub­stituents (eq 2)¹¹ and double bonds with more than one substituent (eq 3)^12.13 exhibit similar regio­selec­tivity. Explaining regio­selec­tivity in addition reactions begins by noting that they usually are not rever­sible;¹⁴ therefore, infor­ma­tion about transition-state structures is critical to under­standing the selectivity in these kinetically controlled reactions.

C. Transition-State Structure

The structure for the trans­ition state in a radical addition reaction, as determined from mo­lecular-orbital calculations, is shown in ­Figure 1.⁸ Several aspects of this structure affect reac­tion regio­selectivity. The first is that the structure is unsymmetrical.^7,8 An unsymmetrical trans­ition state requires that radical addition to each carbon of the multiple bond represents a distinct reaction pathway; there is no com­mon intermediate. Also, partial σ‑bond for­ma­tion between the α-carbon atom and the incoming, carbon-centered radical causes the groups attached to each of these atoms to assume a decidedly pyra­midal arrangement; thus, reaction causes the groups attached to each cen­ter to move closer together.

D. Factors Controlling Regioselectivity

The unsymmetrical nature of the transition state structure shown in Figure 1 requires that addi­tion to each carbon atom of an unsymmetrically substituted double bond has a different rate constant for reaction. Under­standing regio­selec­tivity in addition reactions then depends upon cor­rectly analyzing the factors con­trol­ling these two rate constants. “The tem­perature dependence of the rate constants is well described by the Arrhenius equation k = Aexp(-E_a /RT). Thus, at a given temperature, the rate variations with radical and substrate substitution can be caused by variations in the fre­quency factor (A) and/or the activation energy (E_a). For polyatomic radicals, the frequency factors span a narrow range... Hence, the large variation in the rate constants is mainly because of variations in the activation energy”.⁸ The major factors deter­mining activation energy [bond strengths, steric effects, stereo­elec­tronic effects, and polar effects] are then the ones that need to be considered in determining reaction regioselectivity.⁸

1. Bond Strengths

A characteristic of many reactions that are similar in nature is that their energies of activation (E_a) can be determined from the Evans–Polanyi relation (eq 4).^8,10 (The Evans–Polanyi relation is discussed in Section I.A. of Chapter 7.) In such situations calculating these energies depends upon deter­min­ing reaction enthalpies (H_r) and establishing values for the two constants in eq 4. For the addition of carbon-centered radicals to C–C double bonds the values for the experimentally deter­mined constants are C=50 kJmol^-1 and α=0.25, when E_a and H_r are expressed in kJmol^-1.^8,15 The number 0.25 for the proportionality constant α means that the enthalpy change, which depends on the difference in the strengths of the bonds being broken and formed, needs to be large for it to have a significant impact on the energy of activation for the reaction. The 0.25 value for α is rea­son­able for a reaction with an early transition state.

2. Steric Effects

Rehybridization of the β-carbon atom from sp² to sp³ takes place dur­ing radical addition (eq 1). The necessary repositioning of groups that this rehybridization requires forces them closer together (i.e., causes group com­pression) as reaction proceeds. Any resistance to group com­pres­sion caused by steric hindrance raises the energy required to reach the transition state for a reac­tion.^8–10 The transition state, therefore, becomes energetically more diffi­cult to attain as the steric size of any of the groups attached to the β‑carbon atom increases. A similar steric com­pression of the groups attached to the carbon atom bearing the radical center in the adding radical also takes place, but the effect should be smaller because a typical radical center has a structure that already is at an inter­mediate stage between sp² and sp³ hybrid­ization.^8–10

In addition to group compression, steric interactions at the transition state also arise between groups attached to the β-carbon atom and those bonded to the adding radical (Figure 1). Exper­i­mental support for significant interaction comes from the finding that the rate constants for radical addition to the β-carbon atom of an alkene change dramatically when sterically demand­ing groups are introduced on this atom.^7,16 In the reactions represented in eq 5 increasing the steric size of the Y group significantly decreases the rate constant for β addition.⁷ While it may be difficult to decide how much rate con­stant reduction is attributable to group compression and how much to inter­action between groups on the β-carbon atom and the incoming radical, the relative rate constants shown in eq 5 leave little doubt that steric effects play a major role in determining the rates of radical addition reac­tions.⁷

Since the separation at the transition state between the adding radical and the α-carbon atom in an addition reaction is considerable (Figure 1), it is reasonable to expect that any steric hind­rance involving α-substituents should be small.^7,16 The relative rate constants shown in eq 6 support this expectation because a dramatic change in the steric size of groups attached to the α‑car­bon atom has only a small effect on the value of these con­stants; the largest and the smallest differ only by a factor of 4.2.⁷

Steric effects have a more important role in determining addition-reaction regioselectivity than do the strengths of the bonds being broken or formed. The reason for this situation can be traced to the nature of the addi­tion pro­cess. In the competing reactions that deter­mine regio­selec­tivity [i.e., addition to either the α or β carbon atom in a multiple bond of an unsatu­rated com­pound] the same number and types of bonds are being broken and formed; con­se­quently, there should be little difference in activation energies for these two reactions based on bond strengths alone.

Although the primary role of steric effects in determining regio­selectivity in radical addition reac­tions is clear, these effects are not always the sole determining factor. It would be difficult, for example, to explain preferential addition to C-2 in the glycal 10 (Scheme 5) on the basis of steric effects alone because C-2 is, if any­thing, more hindered than C-1.^17–19 Clearly, another factor also affects regio­selec­tivity in reactions of this type.

3. Polar Effects

Polar effects are influences on reactivity caused by unequal electron distribution within a molecule or reactive intermediate. In radical addition reactions these effects can originate with sub­stituent groups and can be transmitted to the reacting atoms either through bonds or through space. Polar effects also can arise from electron delocalization that produces unequal electron dis­tribution.

The data shown in eq 7 illustrate the importance that polar effects have on radical addition reactions.⁷ These data describe the relative rate constants for addition of the nucleophilic cyclo­hexyl radical (C₆H₁₁·) to substituted α,β-unsaturated esters. The rate constant is large when a strongly electron-withdrawing substituent (e.g., CN, CO₂Me) is attached to the α‑carbon atom in one of these unsaturated esters. Electron withdrawal from the double bond by either CN or CO₂Me is due primarily to delocalization that shifts electron density to one of these the α-substituents. In the case where the α‑substituent is a methoxycarbonyl group (Z = CO₂Me), the elec­tron-density shift can be seen in the contributing resonance structures shown in Figure 2. Although the polar effects being described are those that exist in the reactants, the rate constants in eq 7 support the idea that these effects remain significant at the transition state.

Polar effects not only explain the difference in rate constants for the reactions shown in eq 7 but they also rationalize the regioselectivity of these reactions. The resonance hybrid pictured in Fig­ure 2 indicates a reduced electron density at the β-carbon atom in the carbon–carbon double bond of the ester; consequently, this atom represents a point of attraction for a nucleophilic radical. In such a situation regioselective, β-carbon-atom addition can be expected. An example of this type of addition is shown in Scheme 6 where the nucleophilic carbohydrate radical 13 adds regio­selectively to the β-carbon atom of the α,β-unsaturated ketone 12.²⁰

Addition of a nucleophilic radical to an electron-rich double bond is too slow to compete with other radical reactions, but if the radical is electrophilic, addition takes place. The dimeth­yl­malonyl radical 11, for example, adds to the electron-rich double bond in the D-glucal 10 (Scheme 5).^17–19 As the resonance hybrid pictured in Figure 3 indicates, C-2 in 10 has greater electron density than C-1; thus, the electrophilic radical 11 not only adds to the double bond in 10 but it does so regioselectivity at C-2 (Scheme 5).

Since steric and polar effects often favor formation of the same product in a radical addition reaction (i.e., that from addition to the least substituted carbon atom in the double bond of the unsat­urated reactant), it is sometimes difficult to determine the relative contribution of each effect to the regioselectivity of a reaction. A series of experiments designed to test these contributions is shown in eq 8.⁷ The first experiment involves addition of the cyclohexyl radical to methyl acrylate (eq 8, R = H). In this reaction both steric and polar effects favor addition of the nucleophilic cyclo­hexyl radical to the less sub­sti­tuted carbon atom in the carbon–carbon double bond, but as the R group becomes steric­ally larger, the regioselectivity of the reac­tion decreases. For the sterically largest R group the favored direction of addition actually changes. The message here is that steric effects can over­whelm polar effects in establishing reaction regio­selectivity, but a sterically quite demanding group (e. g., a t-butyl group) is necessary to over­come a strong polar effect.

Another indication of the significance of polar effects in radical addition reactions can be seen by returning to the Evans-Polanyi relation (eq 4). This relation applies to radical addition reac­tions in which polar factors are not important. For reactions where polar factors are important, energies of activation are lower than those cal­cu­lated from eq 4. In such situ­ations a modified equation (eq 9), one including the multi­plic­ative terms F_n and F_e, reflecting nucleophilic and elec­trophilic polar effects, respectively, is more accurate.^8,15

4. Frontier-Orbital Interactions

Because radical addition reactions have early transition states,⁷ frontier-orbital interactions are able to provide an alternative approach for explaining reaction regioselectivity. The first step in this approach is identifying the frontier orbitals in the reaction of interest; for example, in the addi­tion of the dimethylmalonyl radical 11 to the electron-rich double bond in the D-glucal 10 (Scheme 5), the pri­mary interaction is between the SOMO of 11 and the HOMO of 10 (Figure 10 in Chapter 7). Iden­tifying the frontier-orbital interactions in a reaction does not, by itself, explain reaction regio­selectivity, but orbital identi­fi­cation is a critical first step ­for such understanding because from fron­tier orbitals come the atomic-orbital coefficients that form the basis for explaining regio­selectivity.

Atomic orbital coefficients are valuable in determining the regio­selec­tivity of a reaction with an early transition state because the rate constant for the bond-forming reaction between two atoms in such a reaction depends to a large extent on the magnitude of the coefficients in their interacting frontier orbitals.^17,18 In the reaction pictured in Scheme 5 the most effective bonding is between the radical 11 and C-2 in the D-glucal 10 because the atomic orbital coefficient at C-2 for the HOMO in 10 is larger than that at C‑1 (Figure 4);²¹ con­se­quently, regioselective addition to C-2 is fav­ored.^17,18

Frontier-orbital interactions also explain regio­selec­tivity in the addi­tion reaction shown in Scheme 6, where a nucleophilic radical (13) is adding to an electron-deficient double bond.²⁰ Addi­tion of the radical 13 to C‑4, rather than C-3, in the α,β-unsaturated ketone 12 cannot be explained by steric effects, but frontier-orbital interactions do provide a basis for under­standing the observed regioselectivity. The most important interaction in this case is between the SOMO of 13 and the LUMO of 12. (A justification for this being the primary, frontier-orbital interaction is given in Section IV.B.1 of Chapter 7) For a LUMO such as that in 12 the largest atomic orbital coefficient is associated with the p orbital at C-4 (Figure 4);²¹ consequently, regio­selective addi­tion to C-4 is favored.²²

5. Adduct-Radical Stabilization

Adduct-radical stabilization as a possibility for explaining regio­selec­tive addition of a car­bon-centered radical to a multiple bond is not highly regarded because the exothermic nature of and probable early transition state for radical addi­tion reactions argue against significant, trans­i­tion-state stabilization due to the devel­oping radical. Evidence from study of model compounds that is cited in support of this point of view is that the cyclo­hexyl radical adds more rapidly to acro­lein and acrylonitrile than to sty­rene (eq 10),^7,23 even though a phenyl group is more effective at stabilizing a radical center than is a carbonyl or cyano group.^7,24 This information indicates that adduct-radical stabilization is less im­por­tant than polar effects at the transition state for an addition reaction; thus, polar effects are primarily respon­sible for the differences in reactivity of the un­sat­urated com­pounds, differences such as those shown in eq 10.⁷ (As discussed in Section II.D.2 and seen in eq 6, steric hindrance from the α substituents used in the reactions shown in eq 10 should be inconsequential.) Since reactions between electron-deficient alkenes and nucleophilic radicals are stabilized at the transition state by polar effects, these effects could mask less impor­tant, adduct-radical stabilization. A better test of the importance of adduct-radical sta­bil­ization on regio­selec­tive addition would be one in which polar effects could not be the deter­mining factor.

The addition reactions shown in equations 11 and 12 are ones for which polar effects should be minimal.¹⁰ The similarity in relative rates for the two reactions indicates that adduct-radical stabilization is inconsequential ­at the transition state. These reactions also underscore the difficulty in elim­in­ating completely the influence of polar effects when comparing radical reac­tions. The slightly reduced rate for the reaction shown in eq 12, when compared to that in eq 11, could be due to the effect of the weakly electron-donating methyl group in propene reducing to a small extent the rate of addi­tion of a nucleophilic radical to a slightly more electron-rich double bond. (As men­tioned in Chapter 7, Sections III.C. and III.E., there is not complete agreement about the nucleo­phil­icity of the methyl radical.)

The reaction shown in eq 13 supports the idea that the stability of the developing radical can be a factor in reducing transition-state energy.¹⁰ The greater rate for this reaction, when compared to those shown in equations 11 and 12, can be explained by resonance sta­bilization in the devel­oping radical contributing significantly to transition-state stabilization. The limited data in equa­tions 11-13 are consistent with the idea that adduct-radical stability is only a factor in radical addi­tion reac­tions when such stabili­zation is considerable. Once again, however, polar effects cloud this interpretation. 1,3-Butadiene can be viewed as a molecule in which each double bond has an ethenyl substituent attached. Such a substituent should be elec­tron-with­drawing or, at least, less electron-donating than a methyl group; conse­quently, the double bonds in 1,3-butadiene should be more reactive toward the methyl radical than is the double bond in pro­pene. This difference could explain, at least in part, the difference in relative rates for the reactions shown in eq 12 and eq 13.