Between 1985 and 1990 more than half a dozen publications claimed we were wrong

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

2

One can tile a flat floor with squares

And one can tile a flat floor with hexagons

But one cannot tile a flat floor with pentagons

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

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 allow curvature

And add some more pentagons

We find that with 12 pentagons the network closes into a cage

© The Pentagon Isolation Rule (PIR) Now if 12 pentagons are needed to close a cage 60 carbon atoms are needed if adjacent pentagons areto be avoided we know adjacent pentagons are bad news from our Organic Chemistry

© Then we realised it was the same pattern as football So how could it be wrong?

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Then while building models like this little boy

I guessed that C 62, C 64, C 66 and C 68 cannot close unless some pentagons are adjacent but we knew that C 70 CAN! This was proven mathematically by Schmalz et al in Galveston

C 70 The cage solution explained why 60 and 70 were both special

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Then again while playing around with models like this little boy

C 28 should be special - a tetravalent “Superatom” atom H W Kroto, Nature, 329, 529 (1987) Polaroid image of the first molecular model of C 28

Mass spectrum of laser vapourised graphite (Rice 1985) C 28

C 28 Ti

28 Paul Dunk and Alan Marshall U

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The first giant fullerene C 240 with Ken McKay Nature 1988

C 540 made by Ken McKay

C 60 C 240 C 540 C 960 The Giant Fullerenes with Ken McKay Nature 331, 328 (1988) Sussex NNC

C 28 Sussex NNC

Exxon Data Cox et al JACS (1988) Sussex NNC Assignment

©

The Pentagon Isolation Rule (PIR)

Sussex NNC Rice

Sussex NNC

After C 60 the next fullerene which can have non abutting pentagons is C 70

If C 60 is a cage

then C 70 MUST be the next magic number

If C 60 is a cage then C 70 MUST be the next magic number Pentagon Isolation Rule prediction Kroto 1986 and Schmalz et al 1986

© So… C 60 is the smallest cage that can avoid abutting pentagons

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

David Jones in a fun article published under the pseudonym of Daedalus in the New Scientist (1966) pointed out that a sheet of hexagons no matter how large could only close if there were exactly 12 pentagons interspersed

© The Pentagon Isolation Rule (PIR) C 60 is the smallest fullerene that can avoid abutting pentagons

Sussex NNC C 24

Sussex NNC C 20

Sussex NNC It is not possible to make a C 22 cage

NB – Paquette’s Group had synthesised Dodecahedrane C 20 H 20 in 1982, three years before the discovery of C 60

With hindsight C 20 H 20 can be recognised as the fully hydrogenated derivative of C 20 the smallest possible and almost certainly least stable fullerene

With hindsight C 20 H 20 can be recognised as the fully hydrogenated derivative of C 20 the smallest possible and least stable fullerene

C 50 Cl 10 was isolated in 2004

C n+2 rule (4n+3)-1 rule yields 11, 15, 19, 23 C 15 + C 19 + C 23 +

C 28 ”superatom” analogue of sp 3 carbon atom Suggests T d C 28 H 4 Nature (1987) Support C 28 U tetravalent (Smalley and coworkers) C 28 H 4 Sussex NNC

Kroto and Walton Chem Phys Letts 1993 C 24 H 12

C 32 H 2

C 36 H 12

C 50 H 10 predicted to be stable 1993

Sussex NNC The Oddfellas ?

C 20 ? Sussex NNC

C 20 ? Sussex NNC

The Multiplet Pentagon Isolation Rule

Sussex NNC

NB – Paquette’s Group had synthesised Dodecahedrane C 20 H 20 in 1982, three years before the discovery of C 60 With hindsight C 20 H 20 can be recognised as the fully hydrogenated derivative of C 20 the smallest possible and least stable fullerene

NB – Paquette’s Group had synthesised Dodecahedrane C 20 H 20 in 1982, three years before the discovery of C 60 With hindsight C 20 H 20 can be recognised as the fully hydrogenated derivative of C 20 the smallest possible and least stable fullerene

Sussex NNC

Moses Gomberg’s Free Radical (1901) triphenyl methyl CPh 3 -CPh 3 ⇄. CPh 3 +. CPh 3

C 28 H 4

C 50 H 10

Sussex NNC Rice

Sussex NNC

C 28 H 4

Exxon Data Cox et al JACS (1988) Sussex NNC Assignment

BuckyWorld ©

Sussex NNC