At the beginning of this series I said that the fact that carbon forms 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:
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 bicycle[2.2.1]heptane (also called “norbornane”) with 1 double bond.
3 different constitutional isomers are possible. But only one has ever been observed.
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.
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?
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]
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.
Bredt, You’ve Got It Going On
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)
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.
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 nitrogen 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”
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.