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 (m3m)
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 (m3m)
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 (m3m)
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 (m3m)
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 (m3m)
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 (m3m)
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 (m3m)
222 422
32 622 23
432
NC
1 2 4 3 6
CA
4/m 3 6/m
(m 3)
4mm 3m 6mm
m mm2
NA4 42m
6 6m2 43m
32 geometric crystal classes
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
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 (m3m)
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 (m3m)
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
Achiral
Single crystal
Molecules
gas or liquid
m, mm2,4,42m: Yes
Other point groups: No
No
Enantiopure: Yes
Chiral
Yes
Racemate: No
Enantiomeric
mixture: Yes
Optical activity in crystals and molecules
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/
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
Achiral molecules
Chiral
crystal structure
permitted
Chiral molecules
enantiopure
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral molecules
Achiral
crystal structure
Chiral
crystal structure
permitted
permitted
Chiral molecules
enantiopure
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral molecules
Chiral molecules
enantiopure
Chiral molecules
racemate
Achiral
crystal structure
Chiral
crystal structure
permitted
permitted
forbidden
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral molecules
Chiral molecules
enantiopure
Chiral molecules
racemate
Achiral
crystal structure
Chiral
crystal structure
permitted
permitted
forbidden
permitted
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral molecules
Chiral molecules
enantiopure
Chiral molecules
racemate
Achiral
crystal structure
Chiral
crystal structure
permitted
permitted
forbidden
permitted
permitted
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
Achiral molecules
Chiral molecules
enantiopure
Chiral molecules
racemate
Achiral
crystal structure
Chiral
crystal structure
permitted
permitted
forbidden
permitted
permitted
permitted
Chiral molecules
enantiomeric mixture
Crystal structures formed from chiral and achiral molecules
() o-tyrosine
Achiral molecules
Chiral molecules
enantiopure
Chiral molecules
racemate
Chiral molecules
enantiomeric mixture
Achiral
crystal structure
Chiral
crystal structure
permitted
permitted
forbidden
permitted
permitted
permitted
like enantiopure?
like enantiopure?
Crystal structures formed from chiral and achiral molecules
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
Einem glücklichen Zufall ist zu verdanken, dass in der Fraktion A beide
Modifikationen entdeckt wurden.
Methyprylon cell dimensions and optical activity
Solid solution formation
Frederic Stanley Kipping 1863 - 1949
Prelog’s L- and D- quartz
Brazil twin of quartz
From racemic solution
From enantiopure solution
Hexahelicene
Characterisation of enantiomers for
absolute configuration determination
 Optical activity
 CD spectrum (circular dichroism)
 Enantioselective (chiral) chromatography
Cr
OC
O
OC
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
E. P. Kündig, M. Kondratenko, F. Robvieux, G. Bernardinelli, (2003).
Organometallics, 22, -
H
SO2
6
3
1
N
H
CH3
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.
P. Müller, D. Riegert, G. Bernardinelli, (2003). Helv. Chim. Acta 86, -
1 2/m mmm
4/mmm 3m
6/mmm (m3m)
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 + xX .
 The macroscopic crystal C is treated as a mixture of an
oriented crystal structure X and its inverted structureX in
variable proportion.
 Point group 6mm contains symmetry operations of the
second kind, e.g. m. The crystal structure is achiral.
 X andX are not identical but may be brought into
congruence by making a pure rotation.
6/mmm
6mm
Symmetry elements in point groups 6/mmm and 6mm
International Tables for Crystallography Vol. A
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]
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
6/mmm
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
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
6/mmm
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
2[100] 2[110] 2[010] 2[120] 2[110] 2[210]
1 65 35 m[001] 3 6
6/mmm
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
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
Achiral
crystal structure
Chiral
crystal structure
Achiral molecules
Chiral molecules
enantiopure
Chiral molecules
racemate
forbidden
Chiral molecules
enantiomeric mixture
Achiral crystal structures formed from enantiopure molecules
La Coupe du Roi
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)
The End