chirality: an overview david avnir institute of chemistry the hebrew university of jerusalem summer...
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Chirality: An Overview
David Avnir
Institute of ChemistryThe Hebrew University of Jerusalem
Summer School on ChiralityMainz, August, 15-17, 2011, sponsored by
1 .Definitions and vocabulary
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 )
Definition:Chirality is the property of not having not having improper symmetry
Chiral structures
Improper symmetries:
S4 inversion
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
*Enantiomers are different objects ,but they look very similar
The similarity is because they aremirror-images of each other
The difference is that theycannot coincide with each other
Parity (physicists) = Achirality (the rest of humanity)
Parity violation (PV) :Not having inversion symmetry (many)Not having mirror symmetry (Feynman )
Regular right-handed screw Virtual left handed screw
A chiral object need not have a real enantiomer
Chiral objects may have other symmetries
C3 D3
Induced chirality: Trypsin inhibitors
S. Keinan JACS 98
Racemization, enantiomerization
Prochirality
Chiral crystals
R:P3121 L:P3221
Quartz
SiO4
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
Chiral symmetries
Chiral point-groups : Chiral space-groups :
Metallic Te: Helical P31
The enantiomer: P32
D3-knot
P 61 P 65
P 21
P 21
Chiral crystals may appear in achiral space groups
d(TGGGGT)4
Chirality of mathematical entities
Vectors
Matrices
Operators
Functions
Chaim Dryzun, ChemPhysChem 2011, 12, 197
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?
2 .Chirality and randomness
A chiral object with random features
*What is its enantiomer? *What is the handedness of that tree ?
Diffusion limited aggregates (DLAs)
A random walker(drunken walker)
DLAs are chiral (in 2D)
New concepts are needed to treat this type of chirality
The chirality of a DLA is incidental
Nothing in its construction is associated with left or right handedness
Inherent chirality
The enantiomer of a DLA is virtual
It can never be constructed by repeating the process
Real enantiomers
The original DLA and its virtual enantiomer
Given a pair of DLA enantiomers:
Which is the left-handed?
A convention for left-right exists
Left-handed? Right-handed ?
Incidental and inherent chiralities can appear in the same object:
Spiral chiral DLAs
Two(!) real right-handed near enantiomers
Right (virtual)
Left
Right (real)Right (real)
The concept of real near enantiomers
A chiral object may have an infinite number of near counter-enantiomers
3 .Diastereomeric interactions
Diastereomeric interactions are crucial for:
Synthesis
Separation
Recognition
Detection and analysis
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
In the life-sciences chiral interactions are extremely important
Reason: All biological receptors are chiral; therefore:
The interaction: Left-molecule receptorand the interaction: Right-molecule receptorare different
Therefore, left-handed and right-handed molecules:
*Taste differently
*Can heal or kill (Thalidomide)
*Smell differentlyCarvone
( R) :Spearmint )S(: Caraway (Kümmel)
Thalidomide sedative (R); teratogenic (S)
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
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)
N. Konstom, “Rembrandt’s use of models and mirrors”, BurlingtonMagazine, 99, 94 (1977)
Rembrandt’s 2D-chiral preferences
4 .How are chiral molecules made?
Quite often – a very tedious synthetic route
Enantiomeric excess:
The use of chiral catalysts
Diels-Alder Reaction
K. Lipkowitz et al, J. Am. Chem. Soc., 123, 6710 (2001); Davies, 1996.
Another example of a chiral catalytic process
Faina Gelamn, J. Molec. Catal., A: Chem., 146, 123 (1999)
α-ketogluterate + NH4+ + NADPH
L-Glu + NADP+ +H2O
L-glutamic dehydrogenase@Au
O
O
O
O
OO
O
NH3
O
O
Enzymatic reactions
NH
O
CO 2H
O O
NH
O
CO 2H
O OH
OH
(R)-5 6
Antibody 2H6pH 9.0
+
(R)-7
(2)
(kcat/kun = )21 000
Chem. Mater., 9, 2258, (1997)
Antibody Catalyzed Reactions
WithD. Shabat
F. Grynszpan E. Keinan
Chiral separations
Helicenes
E. Gil-Av, F. Mikes, G. Boshart, J. Chromatogr, 1976, 122, 205
A pair of enantiomers of a [6]-helicene
Silica derivatized with a chiral silylating agent
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 ?
Separation by chiral imprinting
E. Vlieg et al, Angew., 49, 2539 (2010)
De-racemization by grinding
5 .How is chirality detected experimentally?
Quartz, a chiral crystal
R:P3121 L:P3221
The building blocks of quartz :All are chiral!
SiO4 SiSi4 -O(SiO3)7-Si(OSi)4
D. Yogev-Einot, Chem. Mater. 15, 464 (2003)
Le Chatelier, H. Compt. Rend de I'Acad. Sciences 1889, 109, 264.
The optical rotation of quartz: More than 120 years ago
Le Chatelier and his contemporaries
0.97
1.02
1.07
1.12
1.17
98 298 498 698 898 1098
Temperature ( K)
0.54
0.56
0.58
0.6
0.62
0.64
Temperature (°K)
Le
Cha
teli
er
t
Ch
irality, SiS
i4
Chirality t
120 years later: an exact match with quantitative chirality changes
D. Yogev, Tetrahedron: Asymmetry 18, 2295 (2007)
SiSi4
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.
Circular Dichroism
L
D
Typical CD spectrum
Circularly polarized 193 nm
Laser source
Sample:Chiral gold
Electron beam
Detector
Vacuum chamber
Detection of chirality of metals using photoelectrons
Photoelectrons are emitted from the conducting band with different kinetic energies.
H. Behar-Levy, O. Neumann, Ron Naaman, Adv. Mater. 19, 1207 (2007)
NMR – chiral shift reagents
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
We found 21(!) chiral silicate zeoliteswhich 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)
Adsorption of D-histidine (the lower curve) or L-histidine (the higher curve) on Goosecreekite (GOO): The heat flow per injection
The isothermal titration calorimetry (ITC) experiment
L-histidine
With Y. Mastai and A. Shvalb, Bar-Ilan
6 .Handedness labelling
Handedness labeling is an agreed convention ,not an inherent property like chirality itself
Left Right
Handedness labeling of spirals:A convention exists
Following T. A. Cook, “The Curves of Life”, 1914
RightLeft
A spiral DLA and its virtual enantiomer
The hand-and-glove test :Functional handedness and the use of chiral probes
.1Take 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)
Right-handed DLA Left-handed DLA
The hand-and-glove test
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?
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!
The steps:
1. 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)
A method to assign handedness to AB4 (SiO4)species
The Triangle-Method
Yes, but if the definition is arbitrary why this and not another one?
Indeed, let us try another one!
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)
The edge-torsion approach:
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
SiO4 Low-Cristobalite P41212 (no. 92), D. Peacor (1973)
Interesting corollary:
Since handedness is a function of definition, a given object may be at the same time left- or right-handed
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.
The convention for helices:
The plus/minus (P/M) or delta/lambda (/) - helix rules
M or Left handed
helix
T
A
P or Right handed helix;
clockwise
A
T
Definition: Latent handedness -
The inability to assign handedness to a chiral structure under a given relevant convention
-helix A chiral helix with its two enantiomers – but which is left and which is right?
The collapse of the helix handedness convention
The hand-and-glove test :Functional handedness and the use of chiral probes
.1Take 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
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.
Latent-handedness: Two sides of equal perimeter, rotating in opposite directions
1
2
3
R*
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
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.
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.
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
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
Possible chiral non-handed forms of a 2D-potato
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
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
A chiral potato and its virtual enantiomer
*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
The potato lesson
We are now ready to start the workshop!