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
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
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
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.
So, we’re writing programs to solve puzzles?
This is what I tell non-scientists that I do.
Poorly fitting pieces → many solutions
Chemical information
C H O N F
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
structural parameters
ener
gy
structural parameters
optimisation en
ergy
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
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
Crowded energy landscapes
Many distinct crystal structures.
Very small energy differences.
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)
observ
ed
observ
ed
We cannot distinguish the correct from the
‘false’ structures by visual analysis.
0
5000
10000
Counts
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
a different shape from the rest of sample
5 µm 2 µm
thickness ~ 0.3 µm
electron diffraction TEM 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
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
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
0
5
10
15
20
25
0.25 0.35 0.45 0.55 0.65 0.75
rela
tive e
nerg
y (
kJ m
ol-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
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
pure R
racemate
Microporous molecular crystals predictable packing
Nature (2011), 474, p. 367-371. Chem. Sci. (2014), 5, 2235-2245.
Microporous molecular crystals predictable packing
X-ray Prediction
Nature (2011), 474, p. 367-371. Chem. Sci. (2014), 5, 2235-2245.
predictable co-crystallisation and predictable porosity
+
Microporous molecular crystals predictable co-crystal packing
non-porous
Nature (2011), 474, p. 367-371.
Moving towards computational screening
likelihood of observation
rela
tive
en
ergy
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
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
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
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.
A set of pharmaceutical-like molecules
Non-polymorphic Packing polymorphs Conformational
polymorphs
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
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
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
nu
mb
er
of
con
form
ers
Energy rank of the crystalline conformer
crystalline
conformer
Where on the conformational
landscapes do we find the
crystalline conformers?
predicted
conformers
incre
asin
g
energ
y
predicted
conformers
incre
asin
g
energ
y
crystalline
conformer
DEconf
DEconf
Energy rank of the crystalline conformer
0
20
40
60
80
100
283
con
form
er r
ank
* * * * * *
• 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
Energetic distribution of all conformers (all 15 molecules)
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.
Why adopt such a high energy conformer?
Global minimum conformer Crystalline conformer
+25.5 kJ/mol
AConnolly = 387.7 Å2 AConnolly = 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
Why adopt such a high energy conformer?
Global minimum conformer Crystalline conformer
+25.5 kJ/mol
AConnolly = 387.7 Å2 AConnolly = 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
Importance of accessible surface area
observed conformers
in red
Importance of accessible surface area
All molecules, all conformers
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.
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
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
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
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
More efficient selection of conformers
0
100
200
300
400
500
600
700
3 5 7 9 11
con
form
ers
in o
bse
rve
d D
E con
f
flexible degrees of freedom
Previous limitation
re-filtering of conformers extends what we can do
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.
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.