Bredt’s Rule (And Summary of Cycloalkanes)

Bredt’s Rule: Why Don’t Bridgehead Double Bonds Form?

This post is all about Bredt’s Rule (1924): double  bonds cannot be placed at the bridgehead of a  bridged ring system. We review the key points from our chapter on cycloalkanes, dive into Bredt’s rule, explain what’s  going on in Bredt’s rule (spoiler: poor orbital overlap between p-orbitals)  and then (Note 1) show that  it’s  actually more like “Bredt’s Strongly Worded Suggestion” since there  are indeed some molecules which possess bridgehead olefins. And we also cover bridgehead amides.

Table of Contents

1. Cycloalkanes: What We’ve Learned So Far
2. Bredt’s Rule: A Double Bond Cannot Be Placed At The Bridgehead  Of A Bridged Ring System
3. Bredt’s Rule Explained:  Bridgehead  Double Bonds Have  Poor Orbital Overlap
4. Summary: Bredt’s Rule
5. Notes
6. (Advanced) References and Further Reading

1. What We’ve Learned So Far About Cycloalkanes

At the beginning of this series on cycloalkanes we saw that carbon’s ability to form rings leads to all kinds of interesting consequences that follow logically from the rules of structure and bonding in organic chemistry, but nevertheless would have been hard to predict from first principles. Among them, we’ve seen that:

• 3 and 4 membered rings have significant ring strain (a combination of “angle strain” and “torsional strain”)
• Rings of size <8 cannot turn inside-out, meaning that configurations of substituents relative to each other are locked. The simple way to say this is that it leads to the existence of cis and trans isomers for the disubstituted cases ( sometimes called “geometric isomers”) – e.g. cis– and trans- 1,2-dimethylcyclohexane.
• The most stable conformation of cyclohexane is the chair conformation in which all the groups along each C–C bond are staggered relative to each other. In the cyclohexane chair, there are two orientations of substituents on tetrahedral carbon: straight up/down relative to the ring (“axial”) and in the plane of the ring (“equatorial”).
• Cyclohexane chairs can undergo “flips” whereby all equatorial groups become axial and all axial groups become equatorial. This occurs rapidly at room temperature – so rapidly that in most cases at room temperature, the signals corresponding to each individual chair cannot be observed by our most useful tool (NMR spectroscopy) – instead, an average is observed. The activation energy for a chair flip is about 10 kcal/mol, since in order for a chair to “flip”,  the molecule must pass through the strained “half-chair” conformation (about 10 kcal/mol higher in energy than the chair).
• Axial substituents lead to greater torsional strain than equatorial substituents, since they experience two additional “gauche” interactions with the hydrogens on the ring carbons located two bonds away. Another way to look at the same phenomenon is to think of the axial group interacting with each of the axial hydrogens (“diaxial” interactions). For methylcyclohexane, the conformation where methyl is axial is 1.70 kcal/mol more unstable than the conformation where the methyl is equatorial, a number referred to as the “A-value” for CH₃.  A-values have been measured for a large number of mono substituted cyclohexanes.  In particular, the A-value for t-butyl is so high (>4.5 kcal/mol) that cyclohexane rings with a t-butyl substituent are essentially “locked” in the position where the t-butyl is equatorial.
• A-values are additive. With di- and trisubstituted cyclohexanes, we can use A-values to determine which chair conformation is most stable.
• The stereochemistry of fused rings can have a huge effect on the shape of the molecule. In cis-decalin, the molecule adopts a “tent” or “cup” shape where there is a concave and convex face. Trans-decalin is much more flat. Additionally, cis-decalin can undergo chair flips on each of its cyclohexanes, but trans-decalin is “locked” in position since a ring flip would lead to too much strain (essentially this would create the equivalent of a trans-double bond in a six membered ring, which is too unstable to form).
• “Bridged bicyclic”  and “spiro” ring junctions are also possible.  In bridged bicyclic molecules, the two bridgeheads are separated by “bridges” containing at least one carbon. In “spiro” fused molecules, the two rings are both joined at the same carbon.

Again, even if you are a genius, it would have been extremely difficult, if not impossible,  for you to predict all this behaviour based solely on knowing the rules of chemical bonding. Many of these phenomena were first observed experimentally and the explanations provided post-hoc. That’s why I keep repeating the reminder that organic chemistry is very much an empirical science.

In this , the last post on this series on cycloalkanes, we’ll talk about a final surprising and interesting consequence of the fact that carbon can form rings.  It goes like this:

2. A double bond cannot be placed at the bridgehead of a bridged ring system unless the rings are large enough.

Let’s go through this. Imagine drawing a version of bicyclo[2.2.1]heptane (also called “norbornane”) with 1 double bond. 

3 different constitutional isomers are possible. But only one has ever  been observed. 

Back in 1924, German chemist Julius Bredt was working on bicyclic molecules with these (and related) ring systems, and made the following generalization:

This observation came to be known as “Bredt’s rule“. Note that no deep explanation was offered at the time – merely the observation that these bridgehead double bonds do not form.

3. Bridgehead Double Bonds Have Poor Orbital Overlap

Looking at a model, and knowing what we know now about bonding, especially that of π bonds – can you think of a reason why bridgehead alkenes might be unstable?

via GIPHY

Remember what is required in order for a π bond to form – we require overlap between the two adjacent p orbitals. In other words, they must be in the same plane, lined up like the plastic men on a foosball table.

Look closely at the bridgehead C-H bond in the model above. Note how it’s almost sticking straight out to the side of the molecule, especially with respect to the C-H bond on the adjacent carbon.

The normal geometry for a sp² hybridized carbon is trigonal planar. However, due to the constraints placed on it by being part of multiple rings, the bridgehead carbon becomes “pyramidalized“, that is to say, somewhat like a pyramid (non-planar). In other words it has a very atypical shape for an sp² hybridized carbon.

Since the model above doesn’t show p-orbitals,  I’ve taken a photo of a model where the two  p-orbitals are roughly indicated by the bridgehead C-H bond, and red loopy looking thingy on the adjacent carbon. Note that when we look along the  C–C bond containing the bridgehead carbon, we see that the adjacent p orbitals are “staggered” with respect to each other. In other words there is very little orbital overlap. Poor overlap = poor bonding! [Note 2]

Summary: Bredt’s Rule

I didn’t show what the overlap in the other possible constitutional isomer would look like (the third case in the second diagram, above) but trust me when I say that the overlap is even worse.

So the bottom line for today is bridgehead double bonds are unstable due to poor orbital overlap. 

Here endeth the lesson for the vast majority of readers. However, if you’re interested, you can continue reading to learn about how our understanding of Bredt’s rule has evolved since 1924.

Notes

Exceptions To Bredt’s Rule, and Bridgehead Amides

Bredt, You’ve Got It Going On 

Exceptions To Bredt’s Rule

In the intervening years the question of bridgehead double bonds has been studied in considerably more detail. The review by Shea (academic paywall)  although more than 30 years old, is still a very useful primer on the topic. Of particular interest is that several natural products have been isolated that contain bridgehead double bonds, such as CP-225,917 (left) and Taxol (right)

 What gives? These molecules are clearly stable. Why might bridgehead double bonds be allowed in these cases, but not in the case of norbornene, above?

It has to do with the greater flexibility that accompanies larger ring sizes. It turns out that the stability of bridgehead double bonds roughly mirrors the stability of the largest trans-cycloalkene that contains the double bond.

Neither trans-cyclohexene nor trans-cycloheptene are stable enough to exist at room temperature (too much ring strain); nor have the bridgehead alkenes in a parent ring of 6 or 7 been observed as anything other than transient intermediates.

However, trans-cyclooctene is a stable molecule – and likewise, bicyclo[3.3.1]non-1-ene is a stable compound.. Observing bridgehead double bonds in molecules with parent ring sizes of 9  (CP-225,917) and 10 (Taxol) is therefore to be expected, since trans-cyclononene and trans cyclodecene are stable molecules, as are all the higher cycloalkenes.

Bridgehead Amides

If you are still reading this, you must be a nerd, so one last wrinkle.

Amide bonds are generally difficult to break – certainly much more so than those of esters or acid chlorides.  This is a good thing for us – strong peptide bonds make for stable proteins. One of the reasons is the considerable double-bond character between C and N as shown in the right-hand resonance form, a consequence of nitrogen’s considerable electron -donating ability.

What happens when the nitrogen is at a bridgehead, especially in a small ring system?

Needless to say the overlap between the lone pair on N and the carbonyl carbon is now extremely poor. This results in a  considerably weaker C-N bond, one that is very easily cleaved by moderate nucleophiles.

In 2006 Brian Stoltz’ group at Caltech succeeded in isolating the HBF₄ salt of the bridgehead amide above. Short and interesting paper.

Note 1: Another way of stating Bredt’s rule (once you learn about elimination reactions, is the following: “Elimination to give a double bond in a bridged bicyclic system always leads away from the bridgehead”

Bredt’s observations:

Note 2: In fact, double bonds of this type are predicted to have “diradical” character. Attempts to form bridgehead double bonds in rings of sizes 6 and 7 are often accompanied by phenomena such as dimerization and trapping of O₂, which are clear indicators of radical intermediates.

(Advanced) References and Further Reading

1. Über sterische Hinderung in Brückenringen (Bredtsche Regel) und über die meso‐trans‐Stellung in kondensierten Ringsystemen des Hexamethylens
   J. Bredt
   Justus Liebigs Annalen der Chemie 1924, 437 (1), 1-13
   DOI: 10.1002/jlac.19244370102
   The original paper by Bredt, noting the difficulty of synthesizing bicyclic compounds with a double bond at the bridgehead position.
2. Bredt’s Rule of Double Bonds in Atomic-Bridged-Ring Structures
   Frank S. Fawcett
   Chemical Reviews 1950, 47 (2), 219-274
   DOI: 1021/cr60147a003
   An old review from 1950 that compiles experimental observations to that date in support of Bredt’s Rule.
3. Bicyclo[3.3.1]non-1-ene
   James A. Marshall and Hermann Faubl
   Journal of the American Chemical Society 1967, 89 (23), 5965-5966
   DOI: 1021/ja00999a049
4. The Decarboxylation of β-Keto Acids. II. An Investigation of the Bredt Rule in Bicyclo[3.2.1]octane Systems
   James P. Ferris and Nathan C. Miller
   Journal of the American Chemical Society 1966 88 (15), 3522-3527
   DOI: 10.1021/ja00967a011
   A study of decarboxylation rates in bridged bicyclic keto acids, where the rate of decarboxylation is found to be strongly dependent on orbital overlap of the departing C-CO2H bond with the neighboring carbonyl. Good exam question material.
5. Bredt’s rule. Bicyclo[3.3.1]non-1-ene
   John R. Wiseman
   Journal of the American Chemical Society 1967, 89 (23), 5966-5968
   DOI: 10.1021/ja00999a050
   The above two back-to-back papers are on the same topic – the successful synthesis and isolation of the smallest compound with a bridgehead olefin.
6. Bredt’s rule. III. Synthesis and chemistry of bicyclo[3.3.1]non-1-ene
   John R. Wiseman and Wayne A. Pletcher
   Journal of the American Chemical Society 1970, 92 (4), 956-962
   DOI: 10.1021/ja00707a035
   This followup paper to Wiseman’s communication (Ref #4) provides more details on the synthesis and reactivity of the ‘Anti-Bredt’ olefin, bicyclo[3.3.1]non-1-ene.
7. Bredt Compounds and the Bredt Rule
   Dr. Gert Köbrich
   Angew. Chem. Int. Ed. 1973, 12 (6), 464-473
   DOI: 10.1002/anie.197304641
   As the structural basis for Bredt’s Rule became clear, it was evident that the prohibition against bridgehead double bonds would not be absolute.
8. Recent developments in the synthesis, structure and chemistry of bridgehead alkenes
   Kenneth J. Shea
   Tetrahedron 1980, 36 (12), 1683-1715
   DOI: 1016/0040-4020(80)80067-6
   This review summarizes work that took place after Fawcett’s review (Ref #2) and includes information on the successful synthesis of compounds with bridgehead alkenes.
9. Strained bridgehead double bonds
   Philip M. Warner
   Chemical Reviews 1989, 89 (5), 1067-1093
   DOI: 1021/cr00095a007
   A more recent review, this includes information on the successful synthesis of ‘anti-Bredt’ hydrocarbons.
10. Natural Products with Anti‐Bredt and Bridgehead Double Bonds
    Jeffrey Y. W. Mak Dr. Rebecca H. Pouwer Assoc. Prof. Craig M. Williams
    Angew. Chem. Int. Ed. 2014, 53 (50), 13664-13688
    DOI: 10.1002/anie.201400932
    This review covers the synthesis of natural products with bridgehead olefins. Compounds that have bridgehead double bonds and are otherwise stable are also known as ‘Anti-Bredt’ olefins, since they defy Bredt’s Rule.
11. Synthesis and structural analysis of 2-quinuclidonium tetrafluoroborate
    Tani, K., Stoltz, B.
    Nature 2006, 441, 731–734
    DOI: 10.1038/nature04842
    A landmark paper on the synthesis and unambiguous characterization (by X-ray spectroscopy) on potentially the smallest bridgehead amide.
12. Formation of Anti-Bredt Olefins from Bridgehead Carbene Precursors:  A Computational Study
    Michael Geise and Christopher M. Hadad
    Journal of the American Chemical Society 2000, 122 (24), 5861-5865
    DOI: 10.1021/ja000295g
    This paper examines computationally whether ‘Anti-Bredt’ olefins can be formed by formation of the bridgehead carbene followed by rearrangement. In the conclusion, the paper states, “this study has shown that the equilibria for rearrangement of bridgehead carbenes to anti-Bredt olefins lie heavily on the side of the olefin. Also, the calculated intrinsic barriers to rearrangement are all easily accessible under most reaction conditions, with the largest barrier being 7.4 kcal/mol”. Now, all we need is experimental evidence!
13. Does 1‐Norbornene Exist?
    R. Keese and E.‐P. Krebs
    Angew. Chem. Int. Ed. 1972, 11 (6), 518-520
    DOI: 10.1002/anie.197205181
    1-norbornene, the smallest bicyclic bridgehead olefin which has been investigated experimentally, has not been directly observed or characterized. Instead it has been trapped as an adduct with furan, suggesting that it formed as an intermediate.
14. Evaluation and prediction of the stability of bridgehead olefins
    Wilhelm F. Maier and Paul Von Rague Schleyer
    Journal of the American Chemical Society 1981, 103 (8), 1891-1900
    DOI: 10.1021/ja00398a003
    This is a rather comprehensive computational study. Prof. Schleyer has calculated the strain energy and heat of formation of >50 bridgehead olefins, in order to determine trends based on structure.