Bond Strengths And Radical Stability

Bond Strengths And Radical Stability

The last two posts have discussed factors which stabilize – and destabilize – free radials. So how do we quantify free-radical stability? Some caution is required – see this note – but if we keep enough variables constant, the strength of C–H bonds (“Bond Dissociation Energies”, or BDE’s) are a pretty good guide to the stability of carbon radicals.

Table of Contents

1. Quantifying Free Radical Stability
2. Why Does H2O Have A Higher Bond Dissociation Energy Than CH4?
3. Bond Dissociation Energy Correlates With Free-Radical Stability
4. Factor #1: Stability Increases In The Order Methyl < Primary < Secondary < Tertiary. Bond Dissociation Energies (BDE’s)
5. Factor#2: Free Radicals Are Stabilized By Resonance. 
6. Factor #3: Free Radials Are Stabilized By Adjacent Atoms With Lone Pairs
7. Factor #4: Across The Periodic Table, Free-Radical Stability Decreases With Increasing Electronegativity
8. Factor #5: Down The Periodic Table, Free-Radical Stability Increases With Increasing Size Of The Atom
9. Factor #6: The Stability Of The Free Radical Decreases As The Orbital Is Held Closer To The Nucleus
10. Factor #7: Electron Withdrawing Groups Destabilize Free Radicals
11. Summary: Quantifying Free-Radical Stability With Bond Dissociation Energies (BDE’s)
12. Notes
13. (Advanced) References and Further Reading

1. Quantifying Free Radical Stability

Over the last two posts we’ve been going through the factors which affect the stability of free radicals.

The bottom line is that radicals are electron deficient and that any factor which either helps to donate electron density to the half-filled orbital, or to spread that unpaired electron out over a larger volume (a.k.a “delocalize” it) will stabilize the radical.

There were a total of six factors we discussed. You might initially find it hard to keep track of the factors we mentioned. That’s OK, because interestingly, there is one measurement which can help us keep all of these factors straight. [EDIT: provided we confine ourselves to some simple examples provided herein]

It’s called Bond Dissociation Energy [BDE]. You might be familiar with it already! There’s probably  a table of bond dissociation energies in your textbook, usually within the first 100 pages or so.

What many people take some time to realize is that BDE is a measure of the energy required for homolytic bond cleavage, and as we discussed earlier, homolytic bond cleavage leads to the formation of free radicals [heterolytic bond cleavage, which is much more common in organic chemistry, leads to the formation of at least one charged species [ions]].

Therefore, BDE is essentially a measure of free radical stability. [EDIT: As Prof. Wenthold points out, the stability of the starting molecule is also a factor to consider. In this post we deal the simple cases of bonds to H that are unstrained, but in cases with strained bonds, bonds weakened by significant electron repulsion, or bonds to very electronegative atoms, corrections must be made for these factors in order to ascertain quantitative free radical stabilities]

The purpose of this post is to help connect the concept of bond dissociation energies with free radical stabilities.

2. Why Does Water Have A Higher Bond Dissociation Energy Than Methane?

Let’s look at a quick representative example. Take two molecules – methane (CH4) and water (H₂O). Which has the weaker bond to H ? Thinking back to some of the chemistry we’ve talked about earlier, such as acid base reactions, it might be tempting to say that O–H is weaker than C–H, since we can think of many strong bases which will deprotonate water [pK_a = 14], but very few that will deprotonate alkanes [pK_a = 50].

However when we look at the BDE’s, we see that HO–H is 118 kcal/mol and H₃C–H is 104 kcal/mol. So the C–H bond is weaker? What gives?

If you’re thinking about BDE’s and acid-base reactions, you’re using the wrong mental model.

Acid base reactions involve heterolytic cleavage and BDE’s are a measure of homolytic cleavage.

Instead of the stability of the ions (heterolytic cleavage!) we need to look at the stability of the free radicals (homolytic cleavage).

Here’s an example of what we need to look at in this case:

Note how we’re forming a H radical in both cases. What’s different is the identity of the other radical.

That leads us to comparing the stability of H₃C•  and HO•  , and we learned previously that [all else being equal]  the stability of free radicals decreases as we go from left to right across the periodic table, since O is more electronegative than C and that partially empty orbital is being held more closely to the positively charged nucleus.  More on that below.

3. Bond Dissociation Energy Is Correlated With Free Radical Stability

The bottom line for this post is that bond dissociation energy is correlated to free radical stability.

Low bond dissociation energies reflect the formation of stable free radicals, and high bond dissociation energies reflect the formation of unstable free radicals.

[EDIT: Caveats apply when extending this discussion beyond the scope discussed in this post. See Note 1]

If we keep one variable constant and vary the other variable, we can analyze the influence of structure on free radical stability.

Here we’re going to keep H as the variable which is the same, and by examine the trends which influence free radical stability in a new light.

Let’s look at these seven factors in turn:

• Stability increases in the order methyl (least stable) < primary < secondary < tertiary (most stable)
• Free radicals are stabilized by resonance
• Free radicals are stabilized by adjacent atoms with lone pairs
• Free radicals increase in stability as the electronegativity of the atom decreases
• Free radicals increase in stability as we go down the periodic table (larger size, more polarizable)
• Free radicals decrease in stability as we go from sp³ to sp² to sp hybridization
  
• Adjacent electron withdrawing groups decrease the stability of free radicals.

4. Factor #1:  Stability increases in the order methyl < primary < secondary < tertiary

Note that the BDE of C-H bonds decreases as we go from methyl to primary to secondary to tertiary. They are easier to break since homolytic bond cleavage results in a more stable radical.

5. Factor #2: Free radicals are stabilized by resonance.

Note the difference in bond strengths between the (primary) C-H bond of propane and of the alkyl C-H bond of propene. The sizeable difference [~13 kcal/mol] is a reflection of the greater stability of the resonance-stabilized “allyl” radical.

Although not directly comparable, look at the C-H bond strength when it is adjacent to two alkenes  [76 kcal/mol]. This “doubly allylic” C–H bond is even weaker, reflecting the fact that a greater number of resonance forms are available for the radical species.

6. Factor #3: Free radicals are stabilized by adjacent atoms with lone pairs.

[This is a subtle point!]. Note the difference in bond strengths between the C-H bond of methane [104 kcal/mol]  and that of methanol [95 kcal/mol]. In between we have the C-H bond of fluoromethane [101 kcal/mol].

Note that even though fluorine is more electronegative than H, the presence of the lone pairs on F is actually stabilizing relative to H.

7. Factor #4: Across the periodic table, free radical stability decreases with increasing electronegativity.

Note the difference between H-CH₃ [104], H-OH [119] and H-F [136].

The most electronegative element has the least stable free radical and this is reflected in the higher bond strength.

8. Factor #5: Down the periodic table, free radical stability increases with increasing size of the atom.

Look how the BDE decreases as we go from H-F [136] to H-Cl [103] to H-Br [87] to H-I [71]. As we should expect by now, the iodide radical is the most stable, since the orbital is larger in size and is therefore “spread out” over a larger volume. further away from the nucleus, therefore “feeling” less effective nuclear charge than would a smaller atom. [thanks to commenter Xylene for this constructive suggestion].

9. Factor #6: The stability of the free radical decreases as the orbital is held closer to the nucleus.

Look what happens to the bond strength as we go from ethane, which is sp³ hybridized [98 kcal/mol] to ethene [sp², 109 kcal/mol] to acetylene [sp, 125 kcal/mol].

This is largely the same effect as #5 above – the farther away from the nucleus the half-filled orbital is, the more stable it will be.

10. Factor #7: electron withdrawing groups destabilize free radicals.

To isolate this effect it’s important to look at examples where the electron-withdrawing group cannot donate a lone pair to the radical (see factor #3). One good example is comparing the C-H strength in ethane vs. trifluoroethane.

11. Summary: Quantifying Free Radical Stability With Bond Dissociation Energies

Hopefully it’s clear by now that where C-H bonds are concerned,  by examining bond dissociation energies, we can discern trends in free-radical stabilities. 

This will be of prime importance in understanding selectivity in free radical reactions: “which free radical forms?”.

A subtle point is that it is also important in understanding fragmentation patterns in mass spectroscopy, but we’re not there yet.
Next Post: Radical Reactions – Why Is Heat Or Light Required? 

Notes

Note 1. More caution is required than I had previously indicated regarding the main thesis of this post – that free radical stabilities are solely reflected by bond strengths. They depend on the stability of both reactant and reagent.

Edits are indicated inline. For more discussion see bottom section.[ TL;DR – the general trends in this post are valid because we discuss bonds to H, but use caution when comparing any other type of bond other than hydrogen.] Thanks to Prof. Paul Wenthold (Purdue University) for his input.

Using the bond strengths (BDE’s) of unstrained bonds to hydrogen is a reasonable method for discerning trends in radical stabilities, as discussed in this post.

However, BDE’s in and of themselves are not reliable for discerning absolute radical stabilities in cases where the bond may be weakened by strain, repulsion between lone pairs, or other factors.
For example the BDE for hydrogen peroxide is 51 kcal/mol, which does NOT imply that the HO• radical is stable, but rather that the O–O bond is destabilized by repulsion between the lone pairs.

Note 2.  In looking at bond strength data there are often differences in 2-3 kcal between different sources. The important part here is not so much the absolute numbers, but the trends. These two files helped when compiling the numbers for this post:

Bond Dissociation Energies

C-H bond strengths

(Advanced) References and Further Reading:

1. Shortcomings of Basing Radical Stabilization Energies on Bond Dissociation Energies of Alkyl Groups to Hydrogen
   Andreas A. Zavitsas, Donald W. Rogers, and Nikita Matsunaga
   The Journal of Organic Chemistry 2010, 75 (16), 5697-5700
   DOI: 1021/jo101127m
   Several textbooks, including some advanced ones, provide radical stabilization energies, and this paper discusses why that may not be the best way to quantify the stability of free radicals.
2. On the Advantages of Hydrocarbon Radical Stabilization Energies Based on R−H Bond Dissociation Energies
   Matthew D. Wodrich, W. Chad McKee, and Paul von Ragué Schleyer
   The Journal of Organic Chemistry 2011, 76 (8), 2439-2447
   DOI: 1021/jo101661c
   This paper addresses some of the shortcomings with the approach used in Ref #1 above. The late Prof. Schleyer was a very influential figure in organic chemistry, and was a pioneer in using computational methods to address interesting problems in organic chemistry.
3. The Radical Stabilization Energy of a Substituted Carbon-Centered Free Radical Depends on Both the Functionality of the Substituent and the Ordinality of the Radical
   Marvin L. Poutsma
   The Journal of Organic Chemistry 2011, 76 (1), 270-276
   DOI: 1021/jo102097n
4. A Single Universal Scale of Radical Stabilization Energies Does Not Exist: Global Bond Dissociation Energies and Radical Thermochemistries Are Described by Combining Two Universal Scales
   Andreas A. Zavitsas
   The Journal of Organic Chemistry 2008, 73 (22), 9022-9026
   DOI: 1021/jo8018768
5. Bond Dissociation Energies by Kinetic Methods
   A. Kerr
   Chemical Reviews 1966, 66 (5), 465-500
   DOI: 10.1021/cr60243a001
   This paper describes experimental techniques for measuring homolytic BDEs.
6. III – Bond energies
   Sidney W. Benson
   Journal of Chemical Education 1965, 42 (9), 502
   DOI: 10.1021/ed042p502
   This paper describes the empirical measurement of homolytic bond dissociation energies. This paper was written by Prof. Benson while at the Stanford Research Institute (now SRI International), a non-profit research center very close to Stanford University. In 1978, Prof. Benson joined Prof. George Olah at USC and helped established the Loker Hydrocarbon Research Institute there.
7. From equilibrium acidities to radical stabilization energies
   Frederick G. Bordwell and Xian Man Zhang
   Accounts of Chemical Research 1993, 26 (9), 510-517
   DOI: 10.1021/ar00033a009
   This paper attempts to correlate the acidity of a proton with the BDE of the corresponding C-H or X-H bond.
8. Ab Initio Calculations of the Relative Resonance Stabilization Energies of Allyl and Benzyl Radicals
   David A. Hrovat and Weston Thatcher Borden
   The Journal of Physical Chemistry 1994, 98 (41), 10460-10464
   DOI: 1021/j100092a014
   The stabilization energy of a vinyl group (in the allyl radical) and a phenyl group (in the benzyl radical) has been calculated to be 15.7 kcal/mol and 12.5 kcal/mol, respectively.
9. Effects of adjacent acceptors and donors on the stabilities of carbon-centered radicals
   G. Bordwell, Xianman Zhang, and Mikhail S. Alnajjar
   Journal of the American Chemical Society 1992, 114 (20), 7623-7629
   DOI: 10.1021/ja00046a003
   Table I in this paper contains stabilization energies of methyl radicals with various substituents (e.g. ·CH₂X).