Chirality and Achirality in Crystal Structures H. D. Flack and G. Bernardinelli University of Geneva, Switzerland www.flack.ch/howard/cristallo/ publcns.html
Chirality and Achirality in Crystal Structures H. D. Flack and G. Bernardinelli University of Geneva, Switzerland .
Dec 16, 2015
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Chirality and Achirality in Crystal Structures
H. D. Flack and G. Bernardinelli
University of Geneva, Switzerland
www.flack.ch/howard/cristallo/publcns.html
L- and D- quartz
Chirality in Chemistry
Hans Erni’s drawing
Kelvin’s definition of chirality
Lord Kelvin
Modern definitions of Chirality
• IUPAC: The geometric property of a rigid object (or spatial arrangement of point or atoms) of being non-superposable by pure rotation and translation on its image formed by inversion through a point; the symmetry group of such an object contains no symmetry operations of the second kind ( 1, m, 3, 4, 6). When the object is superposable by pure rotation and translation on its inverted image, the object is described as being achiral; the symmetry group of such an object contains symmetry operations of the second kind.
• Barron: True chirality is exhibited by systems that exist in two distinct enantiomorphic states that are interconverted by space inversion by not by time reversal combined with any proper spatial rotation.
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
CA
NC
NA
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
Optical activity in crystals and molecules
Single crystalMolecules
gas or liquid
Achiralm, mm2,4,42m: Yes
Other point groups: NoNo
Chiral Yes
Enantiopure: Yes
Racemate: No
Enantiomeric mixture: Yes
Useful terms
Enantiomorph: One of a pair of chiral objects or models of opposite chirality sense.
Enantiomer: One of a pair of chiral molecular entities of opposite chirality sense.
Racemate: An equimolar mixture of a pair of enantiomers.
IUPAC Basic Terminology of Stereochemistry http://www.chem.qmul.ac.uk/iupac/stereo/
Crystal structures formed from chiral and achiral molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules
Chiral molecules
enantiopure
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules permitted
Chiral molecules
enantiopure
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules permitted permitted
Chiral molecules
enantiopure
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules permitted permitted
Chiral molecules
enantiopureforbidden
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules permitted permitted
Chiral molecules
enantiopureforbidden permitted
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules permitted permitted
Chiral molecules
enantiopureforbidden permitted
Chiral molecules
racematepermitted
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules permitted permitted
Chiral molecules
enantiopureforbidden permitted
Chiral molecules
racematepermitted permitted
Chiral molecules
enantiomeric mixture
() o-tyrosine
Crystal structures formed from chiral and achiral molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules permitted permitted
Chiral molecules
enantiopureforbidden permitted
Chiral molecules
racematepermitted permitted
Chiral molecules
enantiomeric mixturelike enantiopure? like enantiopure?
Idealized binary phase diagrams for enantiomeric mixtures
Conglomerate - phase diagram
Racemic structure formation – phase diagram
-(1-naphthoxy) propionic acid & -(1-naphthyl) propionic acid
m-fluoromandelic acid & m-chlorophenyl hydracylic acid
Free energy vs temperature
Solid solution formation
Methyprylon
Methyprylon 3D
Crossing isodimorphism with two minima
Melting point diagram of methyprylon
Methyprylon cell dimensions and optical activity
Einem glücklichen Zufall ist zu verdanken, dass in der Fraktion A beide Modifikationen entdeckt wurden.
Solid solution formation
Frederic Stanley Kipping 1863 - 1949
Prelog’s L- and D- quartz
Brazil twin of quartz
Hexahelicene
From racemic solution From enantiopure solution
Characterisation of enantiomers for absolute configuration determination
Optical activity CD spectrum (circular dichroism) Enantioselective (chiral) chromatography
E. P. Kündig, M. Kondratenko, F. Robvieux, G. Bernardinelli, (2003). Organometallics, 22, -
CrOC
OCO
O
Space group P212121; crystals grown from racemate; refinements using the above configuration:
Crystal 1: Flack parameter x = 0.36(4); ee = 28(8)%
Crystal 2: Flack parameter x = 0.90(3); ee = -80(6)%
CD spectra, from crystal 1 and crystal 2 in solution, normalised to allow for the volume of the crystal.
E. P. Kündig, M. Kondratenko, F. Robvieux, G. Bernardinelli, (2003). Organometallics, 22, -
ee(x-ray) / ee(x-ray) = -0.35(10); CD(350) / CD(350) = -0.42
P. Müller, D. Riegert, G. Bernardinelli, (2003). Helv. Chim. Acta 86, -
NH
SO2
CH3
H
13
6
Space group P21; Flack parameter x = -0.03(12)
CD spectrum flat; []D = 0.7
Substance ee = 43%, semi-preparative separation by HPLC
Enantiomer composing the single crystal used for X-ray diffraction was unequivocally identified by HPLC.
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
4/m 3 6/m
(m 3)
222 422 32 622 23
432
1 2 4 3 6
4mm 3m 6mm m mm2
4 42m
6 6m2 43m
32 geometric crystal classes
Anti-wurtzite
Mn1–y FeyS, y 0.05; P63mc; Flack parameter x = 0.02(4)
“ . . . is found to crystallize in the inverse wurtzite structure, i.e. the wurtzite-type structure but with the opposite absolute configuration, which can be named anti-wurtzite.”
Point group 6mm contains symmetry operations of the second kind, e.g. m.
The crystal structure is achiral.
There is no ‘opposite absolute configuration’.
Anti-wurtzite is just wurtzite in another orientation.
Anti-wurtzite
Model for Flack parameter: C = (1-x) X + xX .
The macroscopic crystal C is treated as a mixture of an
oriented crystal structure X and its inverted structureX in
variable proportion.
Point group 6mm contains symmetry operations of the
second kind, e.g. m. The crystal structure is achiral.
X andX are not identical but may be brought into
congruence by making a pure rotation.
Symmetry elements in point groups 6/mmm and 6mmInternational Tables for Crystallography Vol. A
6/mmm 6mm
Point groups 6/mmm and 6mm
Point groups 6/mmm and 6mm
1 6 3 2[001] 32 65
m[100] m[210] m[110] m[120] m[010] m[110]
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
Point groups 6/mmm and 6mm
1 6 3 2[001] 32 65
m[100] m[210] m[110] m[120] m[010] m[110]
6/mmm
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
Point groups 6/mmm and 6mm
1 6 3 2[001] 32 65
m[100] m[210] m[110] m[120] m[010] m[110]
6mm
6/mmm
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
Point groups 6/mmm and 6mm
1 6 3 2[001] 32 65
m[100] m[210] m[110] m[120] m[010] m[110]
6mm
6/mmm
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
Point groups 6/mmm and 6mm
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
Equivalent twin operations for 6mm in 6/mmm
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
Achiral crystal structures formed from enantiopure molecules
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules
Chiral molecules
enantiopureforbidden
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
La Coupe du Roi
The End
On ne peut être trop prudent dans les conclusions à déduire de l’expérience, lorsque l’on a affaire à des substances quelquefois si semblables en apparence, et qui peuvent être au fond si différentes.
Louis Pasteur (1848)
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