1. If C60 is a cage – then what?

2. 1

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

4. 2

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

6. 3

7. But stable if separated This structure is unstable

8. This molecule is stable

9. 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.

10. 4

11. 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

12. C70

13. 5

14. C24 last of this family
No C22 possible

15. 6

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

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

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

20. Sussex NNC
C Ken McKay

22. 6

23. 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

24. But one cannot tile a flat floor with pentagons

25. And one can tile a flat floor with hexagons

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

27. 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

28. But with pentagons…..

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

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

31. And intersperse some more pentagons

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

34. Rice
Sussex NNC

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

37. Sussex NNC

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

39. If C60 is a cage

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

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