This document summarizes topics in chemistry that involve mathematical concepts. It discusses topics like knotted and entangled molecules, fullerenes which won the Nobel Prize in 1996, nanotubes, graphene which won the Nobel Prize in 2010, quantum mechanics applied to chemistry including Schrodinger's cat and octopus, and quantum computing concepts like qubits and quantum cryptography. It provides examples and references for further information on the intersection of mathematics and chemistry.

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7/11/2011, FM UCM
Madrid
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3. The Maths of Chemistry
But are those ALL
maths in chemistry?
There is some nice stuff
out there too!

4. QuirkChemistry
Moebius aromaticity

5. QuirkChemistry
Penrose Staircase

6. QuirkChemistry
Borromean Molecules

7. QuirkChemistry
Trefoil Knotted Molecules
To knot or not to knot,
that’s the question

8. QuirkChemistry
Solomon Ring Molecules

14. QuirkChemistry
Arquimedian Endohedric Molecules

18. Fullerenes, Nobel Prize 1996 chem

19. Fullerenes

20. Endohedral fullerenes: space
ships?
He@C60

21. Nanocars

22. Nanotubes

23. Graphene, Nobel Prize 2010 ph

24. Graphene: light polarizing filter
Nature Photonics 5, 411–415 (2011) (abril 2011)
we demonstrate the operation of a broadband fibre polarizer based on
graphene, an ultrathin two-dimensional carbon material. The out-
coupled light in the telecommunication band shows a strong s-
polarization effect with an extinction ratio of 27 dB. Unlikecan
support transverse-electric-mode surface wave propagation due to
its linear dispersion of Dirac electrons. polarizers made from thin
metal film, a graphene polarizer

25. Not long ago (AJP 5-Abr): from
Schrödinger’s Cat to Schrödinger’s Octopus
Quantum interference of large molecules:
wave-particle duality

26. Schrödinger’s Cat experiment
Dead or alive?
Is card red or black?

27. Qubit
Quantum computing

28. Quantum world
Quantum world Physical systems may be represented by
states in superpostion, e.g:
|alive > |dead >
+
Quantum state: |0 > + |1 >
Quantum bit: qubit
e Criptografia,
2007

29. Einstein-Podolski-Rosen pairs
Quantum Entanglement
Quantum Cryptography

30. Quantum key distribution: most important!
One-time keypad, length of key=length of
message
Generated through EPR pairs Bob
Alice Diagonal
detector basis
Diagonal
polarization filters Horizontal-
vertical
Horizontal-vertical detector basis
polarization filters
Light source
Alice’s bit sequence 1 0 1 1 0 0 1 1 0 0 1 1 1 0
Bob’s detection basis
Bob’s measurement 1 0 0 1 0 0 1 1 0 0 0 1 0 0
Retained bit sequence 1 – – 1 0 0 – 1 0 0 – 1 – 0
Curs d’estiu de
Criptografia, 2007

35. Relation to the Gilbreath
principle and Martin Gardner

40. My preferred chemist: Panoramix
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