Before thinking about why tertiary radicals are 'stable', you need to have some kind of understanding about the structure of radicals. Show
Carbon centered radicals adopt similar geometries to carbocations: three coordinate and planar. Whereas carbocations have an empty p-orbital, radicals have a singularly occupied p-orbital. Overall the geometry is usually described as sp2 if we're thinking about hybridisation. (*) With the structure of the radical now defined, we can think about what gives the tertiary radical such stability, and to do that we need to discuss what hyperconjugation is. A good place to start (other than a textbook) might be the IUPAC definition from the Gold book:
Essentially, in the sp2 geometry, adjacent C-H bonds are able to interact with the vacant p-orbital, donating a small amount of electron density in order to stabilise the electron deficient p-orbital. Individual C-H bonds to not exert a particularly strong stabilising effect, however, in a t-butyl cation/radical, there are 9 adjacent C-H bonds, each donating a very small amount of electron density, the sum of which amounts to a net overall stabilisation relative to primary radicals. Whilst this explains the stability of the tert-butyl radical, there are other mechanisms of stabilisation for radicals which carbocations are not able to participate in. Due to the single electron in the p-orbital, radicals can also be stabilised by resonance, in a similar (but not identical) way to lone pairs or carbanions. A classic example is a radical generated next to a C=O group or C=C group. Both of these effects discussed (hyper conjugation and resonance) are thermodynamic effects. The stabilisation is lowering the energy, making the radical less reactive. (*) In the case of radicals, this is a bit misleading, theres a lot of spectroscopic and computational evidence to suggest that radicals deviate from planarity towards a pyramidal structure (the idea of hybridisation and sp2 doesn't hold up well)- especially when electron withdrawing groups such as fluorine are bonded to the radical centre. From the point of view of undergraduate chemistry this is largely irrelevant, however, given that the planar model explains the features of radical reactions that we're usually interest in, as organic chemists rather than theoreticians (EPR studies are one place in which the planar model falls down, the measured values don't correlate well to a completely flat carbon centre). Last updated: August 30th, 2022 | What Factors Affect Free-Radical Stability? In the last post we introduced free radicals – neutral, electron-deficient chemical species with a partially filled orbital – and learned that they are highly reactive intermediates in organic chemistry. In this post we’ll cover two of the most important concepts concerning these species: their geometry, and their stability. It’s this latter concept that we’ll see is particularly important for understanding many free-radical reactions in organic chemistry. [Spoiler: the factors that affect free radical stability are the same factors that stabilize carbocations [discussed previously here] Table of Contents 1. Stability Of Free Radicals Increases In The Order Methyl < Primary < Secondary < TertiaryLet’s talk a bit about stability first, and then circle back to their structure. Being electron deficient, you might already have a hunch regarding factors that might stabilize free radicals. Waaaay back, we talked about how a considerable portion of organic chemistry can be explained simply by understanding that: 1) opposite charges attract (and like charges repel), and 2) the stability of charges increases if it can be spread out over a greater volume. These still apply here! Electron poor species are stabilized by neighboring atoms that can donate electron density. [“if you’re poor, it helps to have rich neighbors”]. The most common way to interpret “rich neighbors” here is the observation that increasing the number of alkyl groups on the carbon bearing the free radical increases its stability. Radical stability increases in the order methyl < primary < secondary < tertiary. [For a second, more conceptually complex example, see the bottom of the post]. [Note 1] 2. Free Radicals Are Stabilized by Delocalization (“Resonance”)Secondly, we have also learned that any factor which can lead to the electron deficient site being delocalized [spread out] over a larger area will also stabilize electron poor species. Previously, for example, we’ve seen that the positive charge of a carbocation is considerably stabilized when it is adjacent to a π bond. That’s because the carbocation is sp2 hybridized and bears an empty p orbital, allowing for overlap with the adjacent p orbitals and therefore leading the positive charge to be delocalized over multiple carbon atoms, in a manner that is most easily grasped by drawing resonance structures. Carbocations are flat – so it’s easy to see how the p orbital could be in line with adjacent p orbitals of a double bond. But what about the geometry of free radicals? 3. The Geometry of Free Radicals Is That Of A “Shallow Pyramid”, Which Allows For Overlap Of The Half-Filled p-Orbital With Adjacent Pi BondsIf we draw out the electrons in a typical alkyl free radical, we see that there are three bonding pairs and a single unpaired electron, for a total of four occupied orbitals. By analogy to, say, amines, we might expect that the hybridization of the molecule to be sp3 and geometry of a free radical would be trigonal pyramidal. That’s actually a good approximation, except that the “pyramid” is a little shallower than it is for molecules which have a full lone pair.[Note 2] When the free radical is adjacent to a π bond, there’s a significant stabilization to be obtained if the p orbitals are all in line so they can overlap [“conjugation”] with each other. Overlap is increased (and the molecule’s energy lowered) if the “shallow pyramid” is flattened out. It’s a good approximation to think of a free radical adjacent to a π bond as being “sp2” hybridized. So what does this all boil down to? The electron-deficient free radical can be delocalized over multiple carbons. Therefore, free radicals are stabilized by resonance. 4. The Same Factors Which Stabilize Free Radicals Also Stabilize CarbocationsIf you read the article on the stabilization of carbocations, you might notice something: the same factors which stabilize free radicals are also the same factors which stabilize carbocations! Quiz time: one of the most stable free radicals known is the triphenylmethyl radical, discovered by Moses Gomberg in 1900. In the absence of oxygen, this radical is indefinitely stable at room temperature. Can you identify the factors which might make this free radical particularly stable? Next Post: What Factors Destabilize Free Radicals? NotesNote 1. Stabilization of Free Radicals By Adjacent Lone Pairs In addition to alkyl groups, free radicals are also stabilized by adjacent groups with lone pairs, such as oxygen and nitrogen. At first thought, oxygen might not seem like much of an electron donating group, since it’s quite electronegative. However, oxygen does have two lone pairs of electrons. How might these be involved? The adjacent oxygen atom can donate electron density to the half-empty p orbital, which is a stabilizing interaction. The orbital picture looks like this. Note 2. One note for advanced students – the “shallow pyramid” has a low barrier to inversion. This means that if a free radical is formed from an optically active chiral center, rapid racemization generally ensues. (Advanced) References and Further Reading
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