If C60 is a cage – then what?

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image at: commons.wikimedia.org/wiki/File:Endohedral_fu...

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You cannot close a cage with only hexagons you need exactly 12 pentagons And 12x5 = 60 !

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But stable if separated This structure is unstable ©

This molecule is stable ©

The Isolated Pentagon Rule (IPR) For stability the pentagons must not abut H.W. Kroto. Nature 329 (1987), pp. 529–531. T.G. Schmalz, W.A. Seitz, D.J. Klein and G.E. Hite. J. Am. Chem. Soc. 110 (1988) pp. 1113–1127. ©

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No cage between C60 and C70 can have all pentagons isolated So if C60 is a cage then the next possible stable cage –is C70 …this nailed it for me

C70

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C24 last of this family No C22 possible

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The soccer ball is special as all the black pentagonal patches are isolated ©

When we realised it was the same pattern as football …how could it be wrong? ©

The first giant fullerene C240 with Ken McKay Nature 1988 Sussex NNC

Sussex NNC C960 Ken McKay

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The Pentagon Isolation Rule (PIR) Obviously if 12 pentagons are needed to close a cage then one needs at least 60 carbon atoms to form one without abutting pentagons which we know are bad news from Organic Chemistry ©

But one cannot tile a flat floor with pentagons

And one can tile a flat floor with hexagons

David Jones pseudonym of Daedalus in the New Scientist (1966)

no matter how large can only close if there are exactly A sheet of hexagons no matter how large can only close if there are exactly 12 pentagons interspersed

But with pentagons…..

There is also a problem when you try to tile a flat surface with hexagons around a pentagon

But if we do not constrain to a flat surface and allow the network to curve

And intersperse some more pentagons

We find that when we include exactly 12 pentagons the network will curve completely and the network closes into a cage

Rice Sussex NNC

©

must have abutting pentagons C62, C64, C66 and C68 must have abutting pentagons Sussex NNC

Sussex NNC

After C60 the next fullerene which can have non abutting pentagons is C70 Sussex NNC

If C60 is a cage

If C60 is a cage then C70 MUST be the next magic number

Pentagon Isolation Rule prediction If C60 is a cage then C70 MUST be the next magic number Pentagon Isolation Rule prediction Kroto 1986 and Schmalz et al 1986