Keynote lecture at Congress of the International Union of Crystallography, August 2014, Montreal, Canada

1. Insight from energy surfaces:
structure prediction by lattice energy exploration
IUCr Congress, Montreal
August 2014
Graeme M. Day
Chemistry, University of Southampton, UK
www.crystalstructureprediction.net

2. Structure prediction of molecular crystals
lattice energy approach
applications
challenges
12 August (Tuesday)
MS104
Crystal Structure Prediction and Materials Design
MS112
New Approaches to Crystal Structure Prediction

3. Crystal structure prediction (CSP) objectives
Why might CSP be useful?
• Anticipation of polymorphs
• Structure solution
• Design of structure → properties
• We want to be able to reliably predict what is
possible for a given molecule
(or combination of molecules,
for multi-component systems).
• This is not just about predicting one structure, but
a landscape of the energetically feasible
possibilities.
• Providing tools to help anticipate, characterise and
design structures.

4. So, we’re writing programs to solve puzzles?
This is what I tell non-scientists that I do.

5. Poorly fitting pieces
→ many solutions

6. Chemical information
C H O N F

7. Balance of interactions
C H O N F
The energetically optimal solution
is a balance of contributions to
intermolecular interactions:
• Repulsion: U ~ + exp(-aR)
• Dispersion: U ~ - R-6
• Electrostatics: U ~ ± R-1
sterics
& close packing
strong, specific interactions,
& important to long distances

8. structural parameters
energy
structural parameters
optimisationenergy
1) Sample the lattice energy surface
Algorithms we use:
• Monte Carlo
• quasi- or pseudo-random
• simulated annealing
• basin hopping
also in use:
systematic searches; grid-based search;
genetic algorithms; metadynamics …
2) Lattice energy minimise
• Interatomic potentials
• anisotropic atomic models
• Electronic structure methods
3) Remove duplicates
(which we should have)
4) Analyse and interpret
An outline of global lattice energy exploration
sampling

9. First attempts
J. Struct. Chem. (1984), 25, 416-420
• Many solutions with similar energies
• The approach seems to work!
Lowest energy structure (global minimum) is the observed structure

10. Crowded energy landscapes
Many distinct crystal structures.
Very small energy differences.

11. Vox populi
Cryst. Growth & Des. (2006), 6, 1985–1990
http://dx.doi.org/10.1021/cg060313r
Crystal structure prediction
→ low energy possible crystal structures
5 of lowest energy structures (named A-E)
presented to crystallographers at IUCr2005
(Florence)
Allowed to visualise structures and asked to
select the ‘true’ structure.
a) b)
observed
observed
We cannot distinguish the correct from the
‘false’ structures by visual analysis.

12. Position [°2Theta]
5 10 15 20 25 30
XRPD from bulk
simulated from
known structure
crystallisation from nitromethane
XRPD seems to show pure form
Theophylline
Polymorph screening and characterisation
thermodynamically
stable polymorph
with
Mark Eddleston, Bill Jones
Cambridge

13. a different shape from
the rest of sample
5 µm
2 µm
thickness ~ 0.3 µm
electron diffractionTEM image
However, analysis by transmission electron microscopy (TEM) shows two
different morphologies:
Predominant form:
triangular plate-like crystals
These are the known form
10 µm
Less than 1% of sample
TEM analysis of theophylline
These diffraction patterns are inconsistent with
known forms of theophylline.
Chem. Eur. J., (2013), 19, 7883–7888
http://dx.doi.org/10.1002/chem.201204369

14. Yet another form that we observe
(based on TEM and external habit).
~ once in 20 crystallisations, < 1% of sample.
M. D. Eddleston et al, submitted for publication
TEM analysis of theophylline
Chem. Eur. J., (2013), 19, 7883–7888
http://dx.doi.org/10.1002/chem.201204369

15. Applications in characterisation
A) Role of crystal structure prediction in structure characterisation.
• Jointly with diffraction data (powder XRD, TEM)
• In combination with solid state NMR
expt
calc
CSP
chemical shift
calculations
(ss-DFT)
J. Am. Chem. Soc. (2010), 132, 2564–2566
Phys.Chem.Chem.Phys. (2013), 15, 8069-8080.
J. Am. Chem. Soc. (2013), 135, 17501-17507
with
Lyndon Emsley
Lyon

16. 0
5
10
15
20
25
0.25 0.35 0.45 0.55 0.65 0.75
relativeenergy(kJmol-1)
b-hydroquinone
packing coefficient
Importance of the landscape of structures
B) We are changing our interpretation of the many structures on calculated landscapes
• It used to be common to treat all but one structure in predicted sets as “wrong”.
• We should treat these as real possibilities: many of these structures might be
observable under the right conditions, and with the right characterisation tools.
“Why don't we find more polymorphs?”
S. L. Price, Acta Cryst. (2013). B69, p. 313-328
• Also on the landscape: host frameworks. Chem. Eur. J., (2009), 15, 13033.
hydroquinone : C60 complex
See poster
MS112.P05.B663
Jonas Nyman

17. Microporous molecular crystals
prefabricated molecular “pores”
4 x 6 Å diameter
windows
4 x arene faces
axial chirality
window-to-arene packing
→ closed voids
→ formally non-porous
CSP agrees: no window-to-window
alignment in low energy structures
CC1
CC3
CC1
CC3
with
Andy Cooper
Liverpool

18. pure R
racemate
Microporous molecular crystals
predictable packing
Nature (2011), 474, p. 367-371.
Chem. Sci. (2014), 5, 2235-2245.

19. Microporous molecular crystals
predictable packing
X-ray Prediction
Nature (2011), 474, p. 367-371.
Chem. Sci. (2014), 5, 2235-2245.

20. predictable co-crystallisation
and predictable porosity
+
Microporous molecular crystals
predictable co-crystal packing
non-porous
Nature (2011), 474, p. 367-371.

21. Moving towards computational screening
likelihood of observation
relativeenergy
Confidence in computational
screening will depend on:
1) Variability of the target
property among the
predicted structures.
2) Reliability of the
prediction.
Cryst. Growth & Design (2004), 4, 1327
Cryst. Growth & Design (2005), 5, 1023.
See poster
MS112.P01.B659
Josh Campbell

22. Progress…
2002 2005 2006 2007
composition
& structure
co-crystals
structure only
2008 2010 2011
Chem. Eur. J. (2008), 14, 8830;
Chem. Commun. (2010), 46, 2224
Chem. Sci. (2013), 4, 4417.
PCCP (2010), 12, 8466
Int. J. Pharm. (2011), 418, 168
JACS (2006), 128, 14466
PCCP (2007), 9, 1693

23. molecular
connectivity
rigid (one conformer)
QM calculation
Challenges of flexibility: conformer selection
Crystal structure generation
flexible
conformer search
+
QM calculations
ensemble of conformers
conformer selection
Crystal structure generation
x N
Lattice energy minimisations
Inexpensive
Force field methods
Lattice energy minimisations
More difficult: inter-/intra- balance
Hybrid force field / QM models

24. 27 conformers
3 conformers
196 conformers
A conformational explosion
.
.
.
??? conformers
This will scale very badly with size.
Do we need to consider them all?
We lack good guidelines on which
of these are relevant for the
crystalline solid state.

25. A set of pharmaceutical-like molecules
Non-polymorphicPacking polymorphs
Conformational
polymorphs

26. CN1[C@H]2CC[C@@H]1[C@H]([C@H](C2)OC(=O)C3=CC=CC=C3)C(=O)OC
ensemble of conformers & associated energies
Some technical details
Chemical diagram converted to a SMILE, from which an
unbiased 3D structure is generated
Conformer searches
“Low-mode” search for all conformers
Initially force field based (OPLS-AA-2005)
Resulting structures re-optimised: B3LYP/6-31G(d,p) + dispersion correction
(CRYSTAL09)
Chem. Sci. (2014), 5, 3173-3182

27. Some technical details
Optimisation of the crystal structure:
B3LYP/6-31G(d,p) with dispersion correction (CRYSTAL09)
Crystal calculations
A) Single molecule energy at this geometry
(energy of molecule in crystalline geometry)
then
B) Local minimisation
(energy of associated conformer)
molecular strain
Where on the conformational landscape?
Chem. Sci. (2014), 5, 3173-3182

28. Total numbers of conformers
0
50
100
150
200
250
HIBGUV MABZNA SIKRIN FAHNOR ODNPDS COCAIN VEMTOW FIBKUW NEWNIG HAJYUN GALCAX SEVJAF DANQEP CELHIL DADNUR
2418
numberofconformers

29. Energy rank of the crystalline conformer
crystalline
conformer
Where on the conformational
landscapes do we find the
crystalline conformers?
predicted
conformers
increasing
energy
predicted
conformers
increasing
energy
crystalline
conformer
DEconf
DEconf

30. Energy rank of the crystalline conformer
0
20
40
60
80
100
283
conformerrank
* * * * * *
• Most molecules do not adopt their
lowest energy conformer in their crystal
• only 6 of 15 studied here
• 2 of these 6 show conformational
polymorphism
These are adopting high
energy conformations…
for some reason

31. Energetic distribution of all conformers
(all 15 molecules)

32. Why adopt such a high energy conformer?
Global minimum conformer Crystalline conformer
+25.5 kJ/mol
We see an extended conformation, rather than the
lower energy options.
This makes sense: greater intermolecular
stabilisation.
Needs quantification… try surface area.

33. Why adopt such a high energy conformer?
Global minimum conformer Crystalline conformer
+25.5 kJ/mol
AConnolly = 387.7 Å2AConnolly = 321.7 Å2
+66 Å2
We see an extended conformation, rather than the
lower energy options.
This makes sense: greater intermolecular
stabilisation.
Needs quantification… try surface area.
Connolly surface
spherical
probe

34. Why adopt such a high energy conformer?
Global minimum conformer Crystalline conformer
+25.5 kJ/mol
AConnolly = 387.7 Å2AConnolly = 321.7 Å2
+66 Å2
We see an extended conformation, rather than the
lower energy options.
This makes sense: greater intermolecular
stabilisation.
Needs quantification… try surface area.
Connolly surface
spherical
probe
All conformers of this molecule
observed
conformer

35. Importance of accessible surface area
observed
conformers
in red

36. Importance of accessible surface area
All molecules, all conformers

37. Importance of accessible surface area
All molecules, all conformers
• There is clearly a balance of inter- and
intra-molecular energies
• High energy, compact conformations
are not see in crystal structures.
• We thought about conformer selection
rules based on DE and DA.
• Why not unify these? The bias towards
extended conformations reflects
intermolecular stabilisation.

38. Gradient = 0.75 kJ mol-1 Å-2
At least for non-polar surface area, we can
relate increases in lattice energy to
increased molecular surface area.
Molecules with reasonably well
determined sublimation enthalpies:
Surface area → pseudo-energy function
A relationship between molecular
surface area and lattice energy has
been observed.
A. Gavezzotti, JACS (1985), 107, 962.
Chem. Sci. (2014), 5, 3173-3182

39. Global minimum conformer Crystalline conformer
DAConnolly = 66.0 Å2
DEconf = 25.5 kJ mol-1
The increase in potential lattice energy
overcomes the intramolecular energy cost.
Surface area → pseudo-energy function
x 0.75 kJ mol-1 Å-2 → -49.5 kJ mol-1
Chem. Sci. (2014), 5, 3173-3182

40. 0.75 kJ mol-1 Å-2
High energy, compact conformations are
not see in crystal structures
All observed conformers fall
below this line.
Chem. Sci. (2014), 5, 3173-3182
observed
conformers
in red

41. What does this mean for CSP?
More efficient selection of conformers
DEconf,biased = DEconf + 0.75 DAConnolly
An enrichment in observed conformers in
the region of low “energy”.
Observed conformations based on energy.
Need to consider up to approx. 26 kJ/mol.
This would be bad news for structure prediction
(computational or otherwise).
Chem. Sci. (2014), 5, 3173-3182

42. More efficient selection of conformers
0
100
200
300
400
500
600
700
3 5 7 9 11
conformersinobservedDEconf
flexible degrees of freedom
Previous limitation
re-filtering of conformers extends what we can do

43. Take-home
• Computational methods offer an approach to exploring the packing
possibilities that are available to molecules.
• applications in: characterisation, anticipation, screening (design?).
• The applicability of these methods is moving forward:
• larger, more flexible molecules
• multi-component systems
Challenges and limitations remain.
Some structures will remain unpredictable for a long time.

44. current group
Dr Peter Bygrave
Dr David Case
Dr Angeles Pulido
Dr Julien LeJeune
Dr Janliang Yang
Mr Joshua Campbell
Mr Jonas Nyman
Mr Thomas Gee
Mr Hugh Thompson
Acknowledgements
past group members
Dr Tim Cooper
Dr Aurora Cruz Cabeza
Dr Katarzyna Hejczyk
Dr Daniele Tomerini
Mr Andreas Stegmüller
Dr Edward Pyzer-Knapp
Dr Eloisa Angeles
All collaborators,
past and present.