3Kelvin'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)
4Chiral structures Definition: Chirality is the property of not having not having improper symmetryImproper symmetries:S inversion
5A 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 aremirror-images of each other
6* Enantiomers are different objects, but they look very similarThe similarity is because they aremirror-images of each otherThe difference is that theycannot coincide with each other
7Parity (physicists) = Achirality (the rest of humanity) Parity violation (PV):Not having inversion symmetry (many)Not having mirror symmetry (Feynman )
8A chiral object need not have a real enantiomer Regular right-handed screw Virtual left handed screw
12Chiral 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
14P 21 Chiral crystals may appear in achiral space groups d(TGGGGT)4
15Chirality of mathematical entities VectorsMatricesOperatorsFunctionsChaim Dryzun, ChemPhysChem 2011, 12, 197
16Labeling of the enantiomers CIP rulesBased on ordering the colors according to given rules of hierarchyBut the CIP rules collapse when all colors are the same.What then is a left-handed SiO4 tetrahedron?
28Diastereomeric interactions are crucial for: Synthesis Separation RecognitionDetection and analysis
29Comfortable 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-LgComfortable vs. Very awkward
30In 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
31sedative (R); teratogenic (S) Therefore, left-handed and right-handed molecules:* Taste differently* Can heal or kill (Thalidomide)* Smell differentlyCarvone(R): Spearmint (S): Caraway(Kümmel)Thalidomidesedative (R); teratogenic (S)
32Chiral perception interactions with the brain * The left and right hemispheres of the brain are very unequal* Therefore, no mirror symmetry – the brain is chiralSpecifically: the brain is a chiral information receptorTherefore, left and right objects must be perceived differently by the brain
33Psychology 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)
34Rembrandt’s 2D-chiral preferences N. Konstom, “Rembrandt’s use of models and mirrors”, BurlingtonMagazine, 99, 94 (1977)
47The building blocks of quartz: All are chiral!SiO4SiSi4-O(SiO3)7-Si(OSi)4D. Yogev-Einot, Chem. Mater. 15, 464 (2003)
48Le Chatelier and his contemporaries The optical rotation of quartz: More than 120 years agoLe Chatelier and his contemporariesLe Chatelier, H. Compt. Rend de I'Acad. Sciences 1889, 109, 264.
49120 years later: an exact match with quantitative chirality changes Temperature (°K)Le Chatelier a t/aChirality, SiSi4Chirality a t/a 0SiSi4D. Yogev, Tetrahedron: Asymmetry 18, 2295 (2007)
50Circular 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/STherefore absorption spectra are slightly different.That difference-spectrum is the CD spectrum.
52Detection of chirality of metals using photoelectrons Sample:Chiral goldElectron beamDetectorLaser sourceVacuum chamberCircularly polarized 193 nmPhotoelectrons are emitted from the conducting band with different kinetic energies.H. Behar-Levy, O. Neumann, Ron Naaman, Adv. Mater. 19, 1207 (2007)
54Out of over 700 zeolite structures only 5 are recognized as chiral Chiral zeolitesEnantioselective in:* Catalysis* Heterogeneous chemistry* chromatography* separation-scienceKnown:Zeolite-like, open-pore crystals, MOF’s, etc.Out of over 700 zeolite structures only 5 are recognized as chiralDesired:Chiral aluminosilicate zeolites
55We found 21(!) chiral silicate zeolites which have been under the nose all the time!a. Goosecreekite. b. Bikitaite. c. The two enantiomeric forms of NabesiteCh. Dryzun et al, J. Mater. Chem., 19, 2062 (2009)Editor’s Choice, Science, 323, 1266 (2009)
56The isothermal titration calorimetry (ITC) experiment L-histidineAdsorption of D-histidine (the lower curve) or L-histidine (the higher curve) on Goosecreekite (GOO): The heat flow per injectionWith Y. Mastai and A. Shvalb, Bar-Ilan
58Handedness labeling is an agreed convention, not an inherent property like chirality itself
59Handedness labeling of spirals: A convention existsLeft RightFollowing T. A. Cook, “The Curves of Life”, 1914
60A spiral DLA and its virtual enantiomer LeftRight
61The hand-and-glove test: Functional handedness and the use of chiral probesTake an enantiomeric pair of chiral probes – the letter e - with defined handedness:Left Rightby the spiral convention2. Interact each with your object and measure the degree of interaction3. The “winning” e determines the functional handedness(diastereomeric interactions)
62The hand-and-glove test Right-handed DLALeft-handed DLA
63But the CIP rules collapse when all colors are the same. CIP rules for handedness assignmentBased on ordering the colors according to given rules of hierarchyBut the CIP rules collapse when all colors are the same.What then is a left-handed SiO4 tetrahedron?
64To 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!
65A method to assign handedness to AB4 (SiO4)species The Triangle-MethodThe 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)123R*1: 5.7742: 4.9133: 4.369D. Yogev et al Tetrahedron: Asymmetry 18, 2295 (2007)
66Yes, but if the definition is arbitrary why this and not another one? Indeed, let us try another one!
67The 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)
68Interesting 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 rulesInteresting corollary:Since handedness is a function of definition, a given object may be at the same time left- or right-handedSiO4 Low-Cristobalite P41212 (no. 92), D. Peacor (1973)
69It 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.
70The convention for helices: The plus/minus (P/M) or delta/lambda (/) - helix rulesP or Right handed helix;clockwiseATTAM or Left handed helix
71The collapse of the helix handedness convention A chiral helix with its two enantiomers – but which is left and which is right?-helixDefinition: Latent handedness -The inability to assign handedness to a chiral structure under a given relevant convention
72The hand-and-glove test: Functional handedness and the use of chiral probesTake an enantiomeric pair of chiral probes – the letter e - with defined handedness:Left rightby the spiral convention2. Interact each with your object3. The “winning” e determines the functional handednessLatent-handedness: There is no winning e
73The 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.123R*Latent-handedness: Two sides of equal perimeter, rotating in opposite directions
74Latent-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
75Proof 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.
76Chiral 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.
77Enantiomerization 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
79The 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
81And 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
82Conversion 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
83A 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 potatoA chiral potato and its virtual enantiomer