The Derived Crystal Packing Model:
a Way to Predict Crystal Structures
and Structural Phenomena
Claire GERVAIS
Present Address: Department of Chemistry and Biochemistry,
University of Berne, Switzerland
Introduction
N O2
O2N
NO2
Molecule
Crystal structure
Expected
physical properties
Real crystals
Real
physical properties
Introduction
Twinning
Polymorphism
?
Lamellar epitaxy
Concomitant
crystallization
Introduction
Twinning
Polymorphism
Analogy between crystal packings
Lamellar epitaxy
Concomitant
crystallization
Introduction
Crystal structure prediction
Derived Crystal Packing model
Analysis and prediction of
structural phenomena
Derived Crystal Packing Model
Slice (PF3)
Mother phase
Ribbon (PF1)
Ribbon (PF2)
Step I : Analysis of the mother phase and extraction of
periodic fragments (PF)
Derived Crystal Packing Model
PF1
Daughter phase 5
Daughter phase 1
PF2
PF3
Daughter phase 4
Daughter phase 2
Daughter phase 3
Step II: Generation of daughter phase(s) by adding new
symmetry operators to PF
Consequences of Structural
Similarities between Mother and
Daughter Phases ?
Expression of the Daughter Phases
Two-step procedure to generate new phases:
• Extraction of periodic fragments
• Addition of symmetry operators
Mother phase
Daughter phase
Expression of the Daughter Phases
Lattice energy difference
determined by interactions
between PFs
Provided a PF with strong intermolecular interactions,
Similar lattice energies
Expression of the Daughter Phases
Concomitant crystallization
Similar growth unit
Expression of the Daughter Phases
• Aminoff and Broomé (Z. Krist., 80, 1931):
[…] The transition structure is that of a possible polymorphic
modification of the structure or else that of a modification which
could be plausible for that substance.”
• Dauphiné twin of quartz a:
Individual Twin zone Individual
Quartz a
Quartz a
Trigonal
hexagonal
Quartz b
Trigonal
Expression of the Daughter Phases
During crystal growth: Continuation of the lattice…
…Or formation of twins or epitaxies.
Growth
Twinning of MP
Underlying
expression of DP at
the twin zone
Expression of the Daughter Phases
During crystal growth: Continuation of the lattice…
…Or formation of twins or epitaxies.
Growth
Epitaxy of DP
on MP
Expression of the Daughter Phases
Structural relationships between mother and daughter phases :
• Similar lattice energies: similar stability
• Same growth unit: similar conditions of growth
Polymorphism
(Concomitant)
Twinning,
Epitaxy
Applications of the DCP Model
Resolution of racemic mixtures
Design of polar structures
Verification of structural purity
Help in crystal structure prediction
Resolution of Racemic Mixtures
The DCP model can generate racemic compounds
from enantiomer structures and vice versa
Chiral PF
Chiral mother phase
+ Symmetry of second
kind
Racemic daughter phase
If structural relationships + close lattice energies between
chiral and racemic structures …
Resolution of Racemic Mixtures
Stable conglomerate
Diffusion rate is too low
Growth rate is too high
R
RS S
S
R
SS R S
R R
R S RS R S
R R
S S RS
S R S
S S S RS
RRRRR
Growth of R
The local
supersaturation of S
enantiomer is too high
S
R
R
R
S
R
S
RS
S
RRRRR
RRRRR
2D nucleation of S
SSSSS
RRRRR
RRRRR
Resolution of Racemic Mixtures
Stable conglomerate
• Several examples:
– 5-ethyl-5-methyl-hydantoin (see poster),
– Hexahelicene,
– a-amino-acids,
– Triazolylketone,
– Ammonium salts…
Existence or generation
of competitive racemic compounds
Torbeev et al., J. Phys. Chem. B, 2003, 107, 13523-13531 and references (7)
Resolution of Racemic Mixtures
Stable racemic compound
R
RS S
S
R
SS R S
R R
R S RS R S
RRRRR
S S S S S
SSSSS
RRRRR
Growth of R,S
RRRRR
S S S S S
RRRRR
S S S S S
RRRRR
S S S S S
Resolution of Racemic Mixtures
R S RS S
R
S S R R R S R Tailor-made additive R to inhibit
R R R nucleation of R,S and R nuclei
R
S S R
but…
S
R
…2D nucleation of R,S
R R RR R
S S SS S
RR R RR
SSSSS
SSSSS
SSSSS
SSSSS
SSSSS
RRR RR
RRRRR
RRRRR
S S S S S
RRRRR
S S S S S
SSSSS
SSSSS
SSSSS
SSSSS
RRRRR
S S S S S
Resolution of Racemic Mixtures
• Already observed experimentally for alanine:
– I. Weissbuch et al. Chem. Mater. 1994, 6, 1258-1268
– See Poster
Existence of structural
relationships between chiral and
racemic phases (2D layer)
Resolution of Racemic Mixtures
• Generation of daughter phases with similar lattice
energies and structures:
– Lamellar epitaxy between two enantiomers
hinders preferential crystallization
– Epitaxy enantiomer / racemic compound
structures hinders resolution by tailor-made
additives
The DCP model could be of help to predict these problems
Design of Polar Structures
• Design of 2D polar layers by crystal engineering
D
A
Building block
2D polar layer
S. George et al., NJC, 2003
V. Videnova-Adrabinska et al., J. Mater. Chem., 2000
Design of Polar Structures
• Generation of polar and non-polar 3D phases by
the DCP model
D
A
Building block
2D polar layer
3D daughter phases
Design of Polar Structures
• Chances to obtain polar structures driven by the
stability of the different daughter phases
Variation of the building block
(Substituants)
D
Stable polar phases
R
A
C. Gervais, submitted to Mol. Cryst. Liq. Cryst. & Poster
Help in Structure Prediction
• When polymorphism is of importance (drugs,
pigments…):
Known mother phase
Daughter phase 1
Daughter phase 2
Daughter phase 3
Verification of Structural Purity
C. Gervais, G. Coquerel, Acta Cryst B. 2002, 58, 662 & Poster
Help in Structure Prediction
• Complementary tool to ab initio methods:
Rank
1
2
3
4
…
Daughter phases
Xth
Structure Xth has to be taken into consideration
Conclusion
Twinning
Polymorphism
?
Lamellar epitaxy
Concomitant
crystallization
Conclusion
Twinning
71H, TNT, ZNPPA…
Kuleshova, Cryst. Reports. 2002 & 2003
Many examples!
Polymorphism
DCP model
Lamellar epitaxy
12H, a-aminoacids, hexahelicene…
Concomitant
crystallization
TNT,
ZNPPA…
Conclusion
Particular phenomena for
chiral and polar compounds
Twins and epitaxies
Crystal structures
Mother phase
Daughter phases
Conclusion
Particular phenomena for
chiral and polar compounds
Twins and epitaxies
Crystal structures
For the moment, it’s not automatic !
Conclusion
Automation of the model at:
Unité de Croissance Cristalline, de Chromatographie et
de Modélisation Moléculaire
(Director: Prof. Gérard Coquerel)
UPRES EA 2659, IRCOF,
University of Rouen,
76821 Mont-Saint-Aignan CEDEX,
France
Conclusion
• Automation of the model
– PBC analysis to extract the most energetic
PFs
– Use of Transformation Matrices to
generate new 3D packings
• Further developments in the field of
chirality and polarity
• Extension to other types of compounds
or phases (organometallics, solvates,
hydrates…)
Thanks To:
• Prof. Gérard Coquerel who proposed me to
develop this idea during my PhD. thesis
• Prof. Jürg Hulliger who introduced me in the field
of polarity
• All the authors named in this presentation who
gave me the opportunity to apply the model to
nice examples
• All of you !
For further information and
examples, see Poster …
Gérard Coquerel and me!
Help in Structure Prediction
Modafinil crystallises in various polymorphic forms and
solvates
Form I: P21/a (Z’=2)
a = 14.517Å
b = 9.710Å
c = 20.875Å
b = 110.14Å
Help in Structure Prediction
• Form III detected experimentally
• X-ray powder diffraction (XRPD) pattern closely
similar to that of form I
BUT...
Help in Structure Prediction
BUT… Twinned crystals
with dendritic growth
20m
Great difficulty to resolve the structure by Single
Crystal X-ray diffraction
Application of the DCP model
Help in Structure Prediction
Form I (P21/a, Z’=2)
Help in Structure Prediction
Form I (P21/a, Z’=2)
Hydrophobic PF
(two independent
molecules)
Hydrophilic PF
(one molecule)
The two molecules of the asymmetric unit have close conformations
Help in Structure Prediction
Hydrophobic PF
Regeneration of an
H-bond network
Help in Structure Prediction
Hydrophobic PF
Pna21 with Z’=2
Help in Structure Prediction
Hydrophilic PF
Help in Structure Prediction
Hydrophilic PF
Suppression of symmetries
contained in the PF
Help in Structure Prediction
Hydrophilic PF
Pna21 with Z’=2
Help in Structure Prediction
Hydrophilic slice
(one molecule)
Suppression of symmetries
Hydrophobic slice
(two molecules)
Regeneration of the H-bond
network
Daughter Phase Pna21
Z’=2
Help in Structure Prediction
Daughter Phase
Form III
Good match between the XRPD patterns
Help in Structure Prediction
Recently, single crystals of form III have been
obtained, and the crystal structure resolved….
Pna21 , Z’=2
Crystal packing match with the daughter
phase generated
M. Pauchet, C. Gervais, G. Coquerel et al., Cryst. Growth Des.
(submitted)