I have a new favorite molecule: adamantane. As you probably know, someone is said to be ‘adamant’ if they are unshakeable, immovable, inflexible, unwavering, uncompromising, resolute, resolved, determined, firm, rigid, or steadfast. But ‘adamant’ is also a legendary mineral, and the etymology is the same as that for ‘diamond’.
The molecule adamantane, shown above, features 10 carbon atoms arranged just like a small portion of a diamond crystal! It’s a bit easier to see this if you ignore the 16 hydrogen atoms and focus on the carbon atoms and bonds between those:
It’s a somewhat strange shape.
Puzzle 1. Give a clear, elegant description of this shape.
Puzzle 2. What is its symmetry group? This is really two questions: I’m asking about the symmetry group of this shape as an abstract graph, but also the symmetry group of this graph as embedded in 3d Euclidean space, counting both rotations and reflections.
Puzzle 3. How many ‘kinds’ of carbon atoms does adamantane have? In other words, when we let the symmetry group of this graph act on the set of vertices, how many orbits are there? (Again this is really two questions, depending on which symmetry group we use.)
Puzzle 4. How many kinds of bonds between carbon atoms does adamantane have? In other words, when we let the symmetry group of this graph act on the set of edges, how many orbits are there? (Again, this is really two questions.)
You can see the relation between adamantane and a diamond if you look carefully at a diamond crystal, as shown in this image by H. K. D. H. Bhadeshia:
or this one by Greg Egan:
Even with these pictures at hand, I find it a bit tough to see the adamantane pattern lurking in the diamond! Look again:
Adamantane has an interesting history. The possibility of its existence was first suggested by a chemist named Decker at a conference in 1924. Decker called this molecule ‘decaterpene’, and registered surprise that nobody had made it yet. After some failed attempts, it was first synthesized by the Croatian-Swiss chemist Vladimir Prelog in 1941. He later won the Nobel prize for his work on stereochemistry.
However, long before it was synthesized, adamantane was isolated from petroleum by the Czech chemists Landa, Machacek and Mzourek! They did it in 1932. They only managed to make a few milligrams of the stuff, but we now know that petroleum naturally contains between .0001% and 0.03% adamantane!
Adamantane can be crystallized:
but ironically, the crystals are rather soft. It’s all that hydrogen. It’s also amusing that adamantane has an odor: supposedly it smells like camphor!
Adamantane is just the simplest of the molecules called diamondoids.
These are a few:
1 is adamantane.
2 is called diamantane.
3 is called triamantane.
4 is called isotetramantane, and it comes in two mirror-image forms.
Here are some better pictures of diamantane:
People have done lots of chemical reactions with diamondoids. Here are some things they’ve done with the next one, pentamantane:
Many different diamondoids occur naturally in petroleum. Though the carbon in diamonds is not biological in origin, the carbon in diamondoids found in petroleum is. This was shown by studying ratios of carbon isotopes.
Eric Drexler has proposed using diamondoids for nanotechnology, but he’s talking about larger molecules than those shown here.
For more fun along these lines, try:
• Diamonds and triamonds, Azimuth, 11 April 2016.