Chirality: An Overview David Avnir Institute of Chemistry The Hebrew University of Jerusalem Summer School on Chirality Mainz, August, 15-17, 2011, sponsored by
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
Induced chirality: Trypsin inhibitors S. Keinan JACS 98
Racemization, enantiomerization Prochirality
Chiral crystals 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 symmetries Chiral point-groups: Chiral space-groups: Metallic Te: Helical P31 The enantiomer: P32 D3-knot
P 21 P 21 P 61 P 65 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?
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
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
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 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:
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)
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 -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?
De-racemization by grinding E. Vlieg et al, Angew., 49, 2539 (2010)
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)
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.
Chirality, SiSi4 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 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.