Chirality: An Overview David Avnir Institute of Chemistry The Hebrew University of Jerusalem Summer School on Chirality Mainz, 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)

Chiral structures Definition: Chirality is the property of not having not having improper symmetry 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 are mirror-images of each other The difference is that they cannot coincide with each other

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

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

Chiral objects may have other symmetries C3 D3

Induced chirality: Trypsin inhibitors S. Keinan JACS 98

Racemization, enantiomerization Prochirality

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

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

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 The original DLA and its virtual enantiomer Real enantiomers

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

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

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

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

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

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)

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)

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

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)

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

Antibody Catalyzed Reactions (kcat/kun) = 21 000 With D. Shabat F. Grynszpan E. Keinan Chem. Mater., 9, 2258, (1997)

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

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

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

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 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.

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)

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.

Typical CD spectrum L D

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)

NMR – chiral shift reagents

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

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)

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

6. Handedness labelling 

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

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

A spiral DLA and its virtual enantiomer Left Right

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)

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

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?

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!

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)

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

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)

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)

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.

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

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

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

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

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

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 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

We are now ready to start the workshop!