1. Chirality: An Overview
David Avnir
Institute of Chemistry
The Hebrew University of Jerusalem
Summer School on Chirality
Mainz, August, 15-17, 2011, sponsored by

2. 1. Definitions and vocabulary

3. Kelvin's definition:
"I call any geometrical figure, or group of points, chiral, and say it has chirality, if its image in a plane mirror, ideally realized, cannot be brought to coincide with itself.”
(Lord Kelvin, 1904, The Baltimore Lectures)

4. Chiral structures Definition:
Chirality is the property of not having not having improper symmetry
Improper symmetries:
S inversion

5. A positive definition
* Chirality: The property of having for the same object a left-form and a right-form
* This left and right forms are called enantiomers
* The enantiomers are
mirror-images of each other

6. * Enantiomers are different objects,
but they look very similar
The similarity is because they are
mirror-images of each other
The difference is that they
cannot coincide with each other

7. Parity (physicists) = Achirality (the rest of humanity)
Parity violation (PV):
Not having inversion symmetry (many)
Not having mirror symmetry (Feynman )

8. A chiral object need not have a real enantiomer
Regular right-handed screw Virtual left handed screw

9. Chiral objects may have other symmetries
C D3

10. Induced chirality: Trypsin inhibitors
S. Keinan JACS 98

11. Racemization, enantiomerization
Prochirality

12. Chiral crystals Quartz SiO4 R:P3121 L:P3221
A crystal is chiral if its symmetry space group is composed of proper symmetry operations only:
Cn rotations (n = 1, 2, 3, 4, 6) and helix roto-translations (Cn, n = 2 (zig-zag), 3, 4 and 6, followed by translation parallel to the rotation axis

13. Chiral symmetries Chiral point-groups: Chiral space-groups:
Metallic Te: Helical P31
The enantiomer: P32
D3-knot

14. P 21 Chiral crystals may appear in achiral space groups d(TGGGGT)4

15. Chirality of mathematical entities
Vectors
Matrices
Operators
Functions
Chaim Dryzun, ChemPhysChem 2011, 12, 197

16. Labeling of the enantiomers
CIP rules
Based on ordering the colors according to given rules of hierarchy
But the CIP rules collapse when all colors are the same.
What then is a left-handed SiO4 tetrahedron?

17. 2. Chirality and randomness

18. A chiral object with random features
* What is its enantiomer?
* What is the handedness of that tree?

19. Diffusion limited aggregates (DLAs)
A random walker
(drunken walker)

20. DLAs are chiral (in 2D)
New concepts are needed to treat this type of chirality

21. The chirality of a DLA is incidental
Nothing in its construction is associated with left or right handedness
Inherent chirality

22. The enantiomer of a DLA is virtual
It can never be constructed by repeating the process
The original DLA and its virtual enantiomer
Real enantiomers

23. Which is the left-handed?
Given a pair of DLA enantiomers:
Which is the left-handed?
Left-handed? Right-handed?
A convention for left-right exists

24. Incidental and inherent chiralities can appear in the same object: Spiral chiral DLAs

25. The concept of real near enantiomers
Left
Right (virtual)
Right (real)
Right (real)
Two(!) real right-handed near enantiomers

26. A chiral object may have an infinite number of near counter-enantiomers

27. 3. Diastereomeric interactions

28. Diastereomeric interactions are crucial for: Synthesis Separation
Recognition
Detection and analysis

29. Comfortable vs. Very awkward
Diastereomerism:
The difference in interaction between each enantiomer of a pair, with another chiral object.
The interaction between a right-hand (Rh) and a right-glove (Rg) is different from the interaction of a right-hand (Rh) with a left-glove (Lg)
Two different interactions:
Rh-Rg Rh-Lg
Comfortable vs. Very awkward

30. In the life-sciences chiral interactions are extremely important
Reason: All biological receptors are chiral; therefore:
The interaction: Left-molecule receptor
and the interaction: Right-molecule receptor
are different

31. sedative (R); teratogenic (S)
Therefore, left-handed and right-handed molecules:
* Taste differently
* Can heal or kill (Thalidomide)
* Smell differently
Carvone
(R): Spearmint (S): Caraway
(Kümmel)
Thalidomide
sedative (R); teratogenic (S)

32. Chiral perception interactions with the brain
* The left and right hemispheres of the brain are very unequal
* Therefore, no mirror symmetry – the brain is chiral
Specifically: the brain is a chiral information receptor
Therefore, left and right objects must be perceived differently by the brain

33. Psychology of aesthetic perception
“When some pictures are mirror reversed, aesthetic evaluations of them change dramatically.”
“When a painting is viewed in a mirror… even the meaning can change…”
“ The first major finding… was that paintings containing left-to-right directional cues were preferred…”
A. M. Mead and J. P. McLaughlin, Brain and Cognition, 20, 300 (1992)

34. Rembrandt’s 2D-chiral preferences
N. Konstom, “Rembrandt’s use of models and mirrors”, Burlington
Magazine, 99, 94 (1977)

35. 4. How are chiral molecules made?

36. Quite often – a very tedious synthetic route
Enantiomeric excess:

37. The use of chiral catalysts
Diels-Alder Reaction
K. Lipkowitz et al, J. Am. Chem. Soc., 123, 6710 (2001); Davies, 1996.

38. Another example of a chiral catalytic process
Faina Gelamn, J. Molec. Catal., A: Chem., 146, 123 (1999)

39. L-glutamic dehydrogenase@Au
Enzymatic reactions
L-glutamic
α-ketogluterate + NH4+ + NADPH
L-Glu + NADP+ +H2O

40. Antibody Catalyzed Reactions
(kcat/kun) =
With
D. Shabat
F. Grynszpan
E. Keinan
Chem. Mater., 9, 2258, (1997)

41. Chiral separations Helicenes A pair of enantiomers of a [6]-helicene
Silica derivatized with a chiral silylating agent
E. Gil-Av, F. Mikes, G. Boshart, J. Chromatogr, 1976, 122, 205

42. Enantioselectivity (resolution factor)
as a function of the number of rings in the helicene
Question: Is there a relation between this behavior and the degree of chirality of helicenes?

43. Separation by chiral imprinting

44. De-racemization by grinding
E. Vlieg et al, Angew., 49, 2539 (2010)

45. 5. How is chirality detected experimentally?

46. Quartz, a chiral crystal
R:P L:P3221

47. The building blocks of quartz:
All are chiral!
SiO4
SiSi4
-O(SiO3)7-
Si(OSi)4
D. Yogev-Einot, Chem. Mater. 15, 464 (2003)

48. Le Chatelier and his contemporaries
The optical rotation of quartz: More than 120 years ago
Le Chatelier and his contemporaries
Le Chatelier, H. Compt. Rend de I'Acad. Sciences 1889, 109, 264.

49. 120 years later: an exact match with quantitative chirality changes
Temperature (°K)
Le Chatelier a t/a
Chirality, SiSi4
Chirality a t/a 0
SiSi4
D. Yogev, Tetrahedron: Asymmetry 18, 2295 (2007)

50. Circular Dichroism Circular dichroism (CD):
Left-handed cirularly polarized light (L-CPL) and right-handed light (R-CPL) interact differently with a chiral molecule, say S:
“Diastereomer 1”: L-CPL/S
“Diastereomer 2”: R-CPL/S
Therefore absorption spectra are slightly different.
That difference-spectrum is the CD spectrum.

51. Typical CD spectrum L D

52. Detection of chirality of metals using photoelectrons
Sample:
Chiral gold
Electron beam
Detector
Laser source
Vacuum chamber
Circularly polarized 193 nm
Photoelectrons are emitted from the conducting band with different kinetic energies.
H. Behar-Levy, O. Neumann, Ron Naaman, Adv. Mater. 19, 1207 (2007)

53. NMR – chiral shift reagents

54. Out of over 700 zeolite structures only 5 are recognized as chiral
Chiral zeolites
Enantioselective in:
* Catalysis
* Heterogeneous chemistry
* chromatography
* separation-science
Known:
Zeolite-like, open-pore crystals, MOF’s, etc.
Out of over 700 zeolite structures only 5 are recognized as chiral
Desired:
Chiral aluminosilicate zeolites

55. We found 21(!) chiral silicate zeolites
which have been under the nose all the time!
a. Goosecreekite. b. Bikitaite. c. The two enantiomeric forms of Nabesite
Ch. Dryzun et al, J. Mater. Chem., 19, 2062 (2009)
Editor’s Choice, Science, 323, 1266 (2009)

56. The isothermal titration calorimetry (ITC) experiment
L-histidine
Adsorption of D-histidine (the lower curve) or L-histidine (the higher curve) on Goosecreekite (GOO): The heat flow per injection
With Y. Mastai and A. Shvalb, Bar-Ilan

57. 6. Handedness labelling 

58. Handedness labeling is an agreed convention,
not an inherent property like chirality itself

59. Handedness labeling of spirals:
A convention exists
Left Right
Following T. A. Cook, “The Curves of Life”, 1914

60. A spiral DLA and its virtual enantiomer
Left
Right

61. The hand-and-glove test:
Functional handedness and the use of chiral probes
Take an enantiomeric pair of chiral probes – the letter e - with defined handedness:
Left Right
by the spiral convention
2. Interact each with your object and measure the degree of interaction
3. The “winning” e determines the functional handedness
(diastereomeric interactions)

62. The hand-and-glove test
Right-handed DLA
Left-handed DLA

63. But the CIP rules collapse when all colors are the same.
CIP rules for handedness assignment
Based on ordering the colors according to given rules of hierarchy
But the CIP rules collapse when all colors are the same.
What then is a left-handed SiO4 tetrahedron?

64. To answer the question
“what is a left-handed SiO4 tetrahedron?”
one has to invent a convention of handedness for chiral AB4 species.
Let’s do it!

65. A method to assign handedness to AB4 (SiO4)species
The Triangle-Method
The steps:
Find the triangle with the maximal perimeter.
2. Check the direction from the longest edge to the shortest one, facing the triangle.
3. Clockwise rotation (shown) is a right handed tetrahedron.
(The CIP logic of hierarchy) 1 2 3 R*
1: 5.774
2: 4.913
3: 4.369
D. Yogev et al Tetrahedron: Asymmetry 18, 2295 (2007)

66. Yes, but if the definition is arbitrary why this and not another one?
Indeed, let us try another one!

67. The edge-torsion approach:
The edge-torsion approach:
1. Project one edge onto the other - three angles form.
2. Select the smallest angle from the three.
3. Check the angle direction from top to bottom
(Right-handedness is shown)

68. Interesting corollary:
Could it be that the same object is right-handed by one definition and left-handed by the other?
Yes.
Example: SiO4 of Low-Cristobalite:
Left handed by the torsion rules; right handed by the triangles rules
Interesting corollary:
Since handedness is a function of definition, a given object may be at the same time left- or right-handed
SiO4 Low-Cristobalite P41212 (no. 92), D. Peacor (1973)

69. It is not possible to define handedness in a unique way.
Thesis:
It is not possible to define handedness in a unique way.
Stronger Thesis:
For each agreed labeling method there is at least one chiral object for which it is not possible to tell if it is Left or Right.

70. The convention for helices:
The plus/minus (P/M) or delta/lambda (/) - helix rules
P or 
Right handed helix;
clockwise A T T A
M or 
Left handed helix

71. The collapse of the helix handedness convention
A chiral helix with its two enantiomers – but which is left and which is right?
-helix
Definition: Latent handedness -
The inability to assign handedness to a chiral structure under a given relevant convention

72. The hand-and-glove test:
Functional handedness and the use of chiral probes
Take an enantiomeric pair of chiral probes – the letter e - with defined handedness:
Left right
by the spiral convention
2. Interact each with your object
3. The “winning” e determines the functional handedness
Latent-handedness: There is no winning e

73. The triangle method:
* Find the triangular-side with the maximal perimeter.
* Check the direction from the longest edge to the shortest one, facing the triangle.
* Clockwise rotation (shown) is a right handed tetrahedron. 1 2 3 R*
Latent-handedness: Two sides of equal perimeter, rotating in opposite directions

74. Latent-handedness: Two equal angles of opposite rotation direction
The Torsion Method:
* Project one edge onto the other along the line which connects them; three angles form.
* Select the smallest angle from the three.
* Check the angle direction and assign the helix notation (, right handedness is shown).
Latent-handedness: Two equal angles of opposite rotation direction

75. Proof of the stronger thesis, which stated:
For each agreed labeling method there is at least one chiral object for which it is not possible to tell if it is Left or Right.

76. Chiral Enantiomerization route
* A continuous process that converts one enantiomer (say, left) to the opposite one (right),
* and where all intermediate structures along the route are chiral.

77. Enantiomerization of a left-hand to a right-hand glove:
Along the process there must be a partially pealed-off glove where the sense of left converts to the sense of right; that is where the definition collapses

79. The argument:
Along any chiral enantiomerization route there must be a chiral point where “leftness” changes into “rightness” – the latent-handedness structure – and the handedness definition collapses
“Left” gradually changes into Right

80. Possible chiral non-handed forms of a 2D-potato

81. And it gets crazier:
Let us define for the nonhanded 2D-potato a new *left-right* definition.
That nonhanded potato can enantiomerize to its mirror image;
and a new non-handed potato emerges for which the new definition will not hold!
…and so on ad infinitum

82. Conversion of a (chiral) potato to its virtual enantiomer
There is an infinite number of chiral enantiomerization routes from the “left” to the “right” potato.
Ruch, 60’s

83. A chiral potato and its virtual enantiomer
The potato lesson
* Because there is an infinite number of enantiomerization routes, there is an infinite number of non-handed potatoes
* Each of these can serve as a reference of “what is left”.
* Therefore there is an infinite number of ways to define the handedness of a potato
A chiral potato and its virtual enantiomer

85. We are now ready to start the workshop!