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David Avnir

Institute of Chemistry

The Hebrew University of Jerusalem

Summer School on Chirality

Mainz, August, 15-17, 2011, sponsored by

"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

Improper symmetries:

S4 inversion

* 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

Induced chirality: Trypsin inhibitors

S. Keinan JACS 98

Racemization, enantiomerization

Prochirality

SiO4

Quartz

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 point-groups:

Chiral space-groups:

Metallic Te: Helical P31

The enantiomer: P32

D3-knot

Chirality of mathematical entities

Vectors

Matrices

Operators

Functions

Chaim Dryzun, ChemPhysChem 2011, 12, 197

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?

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

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

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 receptorsare chiral;therefore:

The interaction: Left-molecule receptor

and the interaction:Right-molecule receptor

are different

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)

Quite often – a very tedious synthetic route

Enantiomeric excess:

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)

(kcat/kun) = 21 000

With

D. Shabat

F. Grynszpan

E. Keinan

Chem. Mater., 9, 2258, (1997)

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?

E. Vlieg et al, Angew., 49, 2539 (2010)

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)

The optical rotation of quartz: More than 120 years ago

Le Chatelier and his contemporaries

Le Chatelier, H. Compt. Rend de I\'Acad. Sciences1889, 109, 264.

Le Chatelier a t/a

Chirality a t/a 0

Temperature (°K)

120 years later: an exact match with quantitative chirality changes

SiSi4

D. Yogev, Tetrahedron: Asymmetry 18, 2295 (2007)

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.

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)

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

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

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)

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?

“what is a left-handed SiO4 tetrahedron?”

one has to invent a convention of handedness for chiral AB4 species.

Let’s do it!

3

2

R*

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: 5.774

2: 4.913

3: 4.369

D. Yogev et al Tetrahedron: Asymmetry18, 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:

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)

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.

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.

A

P or

Right handed helix;

clockwise

The convention for helices:

The plus/minus (P/M) or delta/lambda (/) - helix rules

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

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

3

2

R*

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

* 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

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

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

* 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

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