Computational studies of Polymorphs: Computational studies of Polymorphs: ApplicationsApplications
Sarah (Sally) L Price
Department of Chemistry
UCL
The aim of crystal structure predictionThe aim of crystal structure prediction
S NBr
OO
A computational method to predict the crystal structure(s) for a molecule from the chemical diagram
cell parameters, space group, fractional coordinates, prior to synthesis
Currently aim to predict common (simple) crystal structures of small organics
Are crystal structures predictable?Are crystal structures predictable?
No, but…. (Gavezzotti 1994)
Maybe, or even a conditional Yes” (Dunitz 2003)
Because of the many factors that are known experimentally to affect the polymorph
-disappearing & concomitant polymorphs
A reliable computational method would have to quantify the factors that determine the crystallisation process
Results of CCDC Blind Tests – Limited Success?Results of CCDC Blind Tests – Limited Success?
Rigid
Unfortunately not blind
6 correct
Replacement Rigid
0 correct
Rigid
1 correct
Flexible
0 correct
Rigid
2 correct
Rigid
Pure enantiomer
2-4 correct
Flexible
0 correct
New polymorph found later
Rigid
Polymorphic
Stable 0
Metastable 4
Rigid
1 correct
Flexible
1 correct
Motherwell, Lommerse, Ammon, Dunitz, Gavezzotti, Hofmann, Leusen, Mooij, Price, Scheweizer, Schmidt, van Motherwell, Lommerse, Ammon, Dunitz, Gavezzotti, Hofmann, Leusen, Mooij, Price, Scheweizer, Schmidt, van Eijk, Verwer, Williams + Dzyabchenko, Scheraga + Facelli, Pantelides, DellaValleEijk, Verwer, Williams + Dzyabchenko, Scheraga + Facelli, Pantelides, DellaValle
2004 ~18 x 3 guesses(2004, Acta Cryst B in preparation)
2001 ~15 x 3 guesses (2002, Acta Cryst B58,647)
1999, ~11 x 3 guesses(2000, Acta Cryst B56, 697)
O
SCN
OH
O
BO
NH
O
O
S NBr
OO
N
SNO
O
H
NH2
NH
NH
OO
NH
H
H
H
H H
H
O
O
I
I
O2N
O2N
CH3
NH
CH3
O
Why develop a computational method of Why develop a computational method of crystal structure prediction?crystal structure prediction?
To design new materials prior to synthesis energetic, non-linear optical,…
To aid the search for polymorphs as an aid quality control pharmaceutical industry
To aid structure characterisation from unindexable X-ray powder data
To help understand crystal structure(s)
Zeroth Order AssumptionZeroth Order Assumption the experimental crystal structure will
correspond to the global minimum in the static lattice energy a crude 0K thermodynamic model
any competitive local minima are possible polymorphs within < 2 kcal/mol of global
min. (Bernstein, Polymorphism in Molecular
Crystals, OUP 2002)
XFor A
Requirements for finding low Requirements for finding low energy structuresenergy structures
A model for the molecular structure A model for the intermolecular forces A method of simulating the crystal A search method to cover the range of possible
crystal structures
Many possibilities for each
Currently significant limitations on which molecules & structures can be studied
Model intermolecular potentialModel intermolecular potential must give a minimum in the lattice energy
reasonably close to expt (target) want relative lattice energies of known &
hypothetical structures accurately relative to differences in predicted Ulatt
need firm theoretical basis and tested to reproduce structures wide range of relative orientations of functional groups hydrogen bonds, interactions etc.
Electrostatic model from Electrostatic model from r)r)
Analyse to give sets of atomic multipoles (DMA, A.J.Stone)
represents lone-pairs, - electrons etc electrostatic contribution to lattice energy
~ accuracy Cl2 - spherical
atoms
DMA + DMA + exp-6 exp-6 potentialpotentialCoombes et al., J. Phys. Chem. 100 (1996) 7352Coombes et al., J. Phys. Chem. 100 (1996) 7352
All other terms in atom-atom potential
empirically fitted parameters, C, N, O, HC, HN (Williams + fitted)
need specific,
non-empirical anisotropic
repulsion for Cl, CN, Br...
U U A A B B R C C Riki k i k
ik ik 1 2 1 2
1 2 1 2 62, ,
/ /exp / /
CNyburg & Faerman 1984
Non-empirical repulsion models Non-empirical repulsion models based on overlap of based on overlap of (r)(r)
Assume: repulsion overlap of charge distributions
Urep = KS(r) (r) dr
(r) divided into atoms
=> S in atom atom form.
Can fit anisotropic S model.
Finally get the single proportionality parameter - K
Develop anisotropic Cl repulsion modelDevelop anisotropic Cl repulsion model
Cl Cl
C
C1 Å
z2z1
R
Atom-atom form
Aexp(-(R-())) where
() = 0+1(z1.R+z2.R)
+2(3 z1.r2+3z2.R2-2)/2
Anisotropy consistent “lone pair” density
GM Day & SLP, JACS, 125, 16434
1990 Cl2 crystal reproduced by overlap repulsion model RJ Wheatley & SLP, Mol.Phys 71, 1381
2003 Extended to series of 12 chlorobenzene crystals & properties
Towards nonempirical based potentials for organics - main problem dispersion ?Extend Williams & Stone 2003 JCP 119, 4620
Simulation MethodSimulation MethodJ Comput Chem 16 (1995) 628;J Comput Chem 16 (1995) 628; J Phys Chem A J Phys Chem A 105(2001) 9961.105(2001) 9961.
DMAREL to use anisotropic atom-atom potentials to minimize Ulattice w.r.t. cell & molecular translation & orientation. Uses symmetry + Hessian , 2U/p2, for true minimum + elastic constants+phonons N.B. Lattice energy minimization is 0K &
neglects thermal effects Limits accuracy to ~ thermal expansion, organics ~ -
2% to 4% in cell lengths
-CN N C-
2.4
p-dichlorobenzene searchp-dichlorobenzene search GMGM Day & SLP, J. Am. Chem. Soc. 125 (2003) 16434Day & SLP, J. Am. Chem. Soc. 125 (2003) 16434
-74
-73
-72
-71
-70
-69
149 150 151 152 153 154 155
Volume/molecule (Å3)
Lat
tice
En
ergy
(k
J/m
ol)
P1 P_1P21 P21/cCc C2C2/c PmP2/c P21/mP21212 PcP212121 Pca21Pna21 PbcnPbca Pmn21Pma21 ALPHABETA GAMMA
Rel Growth Rate
1.0
2.1
1.7
Molecular ModelMolecular Model
Influence of crystal structure on molecular structure - will differ between different polymorphs. Ideal accurate balanced inter/intramolecular
force-field Use rigid molecule - ab initio optimized
Are minor distortions in molecular geometry significant?
Uric acid - structure shows Uric acid - structure shows distortion of N-H distortion of N-H (Ringertz 1966)(Ringertz 1966)
N-H angle bent by 17° limits reproduction of crystal (ExptMinOpt)
Angle bending crucial to adoption of known crystal structure?
Certainly to search!
Add molecular diagram
Always contrast Expt, ExptMinExpt & ExptMinOpt prior to study
-169
-168
-167
-166
-165
-164
-163
-162
-161
-160
-159
140 142 144 146 148 150 152 154 156
Cell Volume per Molecule (Cubic Angstroms)
Lat
tice
En
erg
y (k
J/m
ol)
P-1
P21
P21/c
Cc
C2/c
P212121
Pca21
Pna21
Pbcn
Pbca
Exptminopt
-182
-181
-180
-179
-178
-177
-176
-175
-174
-173
138 140 142 144 146 148 150 152
Cell Volume per Molecule (cubic Angstrom)
Lat
tice
En
erg
y (k
J/m
ol)
P1
P-1
P21
P21/c
Cc
C2
C2/c
P21212
P212121
Pca21
Pna21
Pbcn
Pbca
Exptminexpt
The challenge of flexible The challenge of flexible moleculesmolecules
Consider Etot=Ulattice + Eintra
Atomistic force-fields for both terms not accurate enough [Brodersen et al, PCCP 5 (2003) 4923]
Detailed study for alcohols & sugars proceeded to very high level atomistic intermolecular force-field + ab initio conformational energies & forces for
[Mooij et al, J. Am. Chem. Soc. 122 (2000) 3500]
Consider rigid gas-phase conformersOH
OH
OH OH
OH
Suitably challenging degree of flexibility Very unlikely to be any polymorphs Study with rigid experimental structure of
molecule had found known structure as global min [Gavezzotti, J. Am. Chem. Soc. 117 (1995) 12299]
Force-field study had predicted that there could be a more stable polymorph with the molecule in a planar conformation [Payne et al., J. Comput. Chem. 20 (1999) 262]
Why aspirin?Why aspirin?C. Ouvrard & SLP, Cryst. Growth Des, submitted.C. Ouvrard & SLP, Cryst. Growth Des, submitted.
OH
O
O
O
C6
C5C4
C3
C2
C1
C7
O1O2
H8
O3C8
O4
C9H6H7
H5
How much does the crystal packing How much does the crystal packing affect the molecular structure?affect the molecular structure?
Difference between molecule in crystal 20K and room temperature black < difference “gas phase” B3LYP/6-31G** and MP2/ /6-31G** structures for local minimum in ab initio energy
?? Difference due to crystal packing
Is good agreement between B3LYP & experiment fortuitous?
Consider 2 lowest of 9 minima Consider 2 lowest of 9 minima + 2 best planar transition states+ 2 best planar transition states
E /kJ/mol 1a 2a~expt Planar A Planar B
MP2 0 2.86
B3LYP 0 3.47 11.94 12.12
HF 0 4.59
Other minima >12 kJ/mol above most stable, including one with weak internal hydrogen bond
Lattice energy search results Lattice energy search results
Metastable conformer 2a gives better lattice energies than global min 1a
Planar A and B cannot compensate for poor conformational energies
-108
-98
-88
-78
-68
-58
205 215 225 235 245 255 265
Cell Volume per Molecule / Å3
To
tal E
ne
rgy
/ kJ
mo
l-1
PlanarA
PlanarB
1a
2a (expt. conf.)
More detail for lowest energy More detail for lowest energy structuresstructures
Known structure found ~ best for Z=1,
but other rival structures
Corr. to Expt.
COOH dimerStable conformer
C=O acetyl chains Similar Expt, but low shear resistance
-103.0
-102.5
-102.0
-101.5
-101.0
-100.5
-100.0
205 210 215 220 225 230
Cell volume per molecule / Å3
Tota
l pa
ck
ing
en
erg
y /
kJ
mo
l-1
2a-P21/c
2a-C2/c
1a-P21/c
1a- . P 1
Model gives good reproduction of Model gives good reproduction of known crystal structureknown crystal structure
Room temperature crystal structure versus ExptMinOpt for B3LYP conformer 2a
Note that ab initio conformer is very close to experimental molecule
Lattice energy sensitive to exact molecular Lattice energy sensitive to exact molecular modelmodel
Sensitivity of Ulatt to molecular structure + problems of evaluating Eintra make flexible molecules very challenging, even when crystal packing does not distort molecule from “gas phase” conformation.
Can distinguish between packing ability of conformers
Experimental vs gas phase molecule
Latti
ce e
nerg
y / k
J/m
ol
-116
-114
-112
-110
-108
-106
-104
-102
-100
-98
Series1
searches find mostly the same crystal structures
BUT different energy gaps
Search Method for Starting Search Method for Starting StructuresStructures
MOLPAK Holden et al. J Comput Chem 14 (1993) 422
Systematic search for dense packings of pseudo hard-sphere molecule in 29+ common Z=1 co-ordination types
P21/c, P1,P21,P212121,P1, Pbca, C2/c, Pca21, Pna21,…,,
Generate ~1500 hypothetical structures as starting points for DMAREL minimisation of Ulattice
Most searches more thorough, producing even more minima
Problem of distinct minimaProblem of distinct minimaE.g. Indigo E.g. Indigo Price & Beyer, Trans. ACA 33 (1998) 23.Price & Beyer, Trans. ACA 33 (1998) 23. H
N
O
N
OH
Known sheet structures lowest in energy
Observed H-bonded sheet of two known polymorphs favored
More hypothetical sheet stackings close in energy ? polytypism
Possible outcomes of searchesPossible outcomes of searchesPrice, Adv. Drug Delivery Reviews (2004)Price, Adv. Drug Delivery Reviews (2004)
Expect a) no polymorphism e.g. Pigment Yellow 74 b) only meta-stable polymorphs (provided known remains most stable at T) - reassuring for
quality control. c) a more thermodynamically stable form might be found?? Nightmare for quality control BUT hydrogen bonding motifs of low energy structures might suggest easy transformations
OR solvents/additives to help find new polymorphs.
ExptMinOpt
Hypothetical structures
Prediction of isomer crystals Prediction of isomer crystals shows results depend on molecule shows results depend on molecule not functional groupnot functional group
?
NH
N
NH
O
O
NH
NH
O
N
O
Early study
“Blind” Challenge
Withnall & Palmer
Min from Expt
~Global min
Min using different H-bond donors & acceptors
Sheet structuresGlobal min
= min from expt
Contrasting set of lattice energy minima
NH
N
NH
O
O
NH
NH
O
N
O
Lattice energy searches shouldLattice energy searches should
Reveal IF there is a clearly preferred motif eg crystal, sheet structure, hydrogen-bonding motif
OR there is no good packing variety of equally good/bad packings linked to polymorphism/solvate formation generate ideas about range of energetically feasible
crystal structures and competition between steric/functional group interactions
No hydrogen-bonds structure of alloxan No hydrogen-bonds structure of alloxan is global minimum in lattice energyis global minimum in lattice energy
-125
-120
-115
-110
-105
-100
-95
-90
-85
120 125 130 135 140 145 150 155 160
Unit cell volume per molecule / A^3
La
ttic
e e
ne
rgy
/ k
J/M
ol
P1
P-1
P21
P21/c
P212121
Pna21
Pca21
Pbca
C2/c
MIN (P41212)
Shortest H…O 2.37Å but ExptMinOpt found as global minimum
Dimer energies also show molecule has Dimer energies also show molecule has unusual hydrogen bonding capabilitiesunusual hydrogen bonding capabilities
Hydrogen
bonds
weak
CO…CO strong
-37 kJ/mol-34.8 kJ/mol
-36.2 kJ/mol
Electrostatic
potential
Variability of multiple minima problemVariability of multiple minima problemSurvey of lattice energy min studies CrystEngComm 3 (2001) 178Survey of lattice energy min studies CrystEngComm 3 (2001) 178
0
10
20
30
40
50
60
70
Nu
mb
er o
f se
arch
es
253 searches 189 molecules
Not found
Minimum unspecified
Local Minimum
Global Minimum
Many structures found as local minima
Errors in energies?
Published are meta-stable?
Other polymorphs possible?
(29 known to be polymorphic)
NB Perverse choice of difficult molecules
Validity lattice energy criterionValidity lattice energy criterion Many searches report more energetically
feasible structures than known polymorphs Low energy minimum in lattice energy a
necessary but often not sufficient condition
Cannot evaluate results for a specific molecule without collaboration with careful experimental polymorph screening studies
Reach for the stars, and you Reach for the stars, and you might get to the moonmight get to the moon
Even when you cannot predict which hypothetical structures will be observed, they can be used in determining structures from poor powder data, etc.
Prediction of new polymorphs can inspire successful searches for new experimental polymorphs
Some crystal structures are easy to predict, problem is which?
Workshop IV practice in Workshop IV practice in computing crystal structurescomputing crystal structures
See for yourself what goes into, and what you can get out of, lattice energy minima searches for:
Simple case Suggested L. Yu - chiral lantone
To progress computational To progress computational prediction, we need:prediction, we need:
better thermodynamics - Temperature relative free energies
kinetics of relative nucleation rates of relative crystal growth rates of transformations to more stable structures
considering solvents, seeding etc. effects
in model to distinguish which structures are likely to be observed polymorphs
Some crude models for kinetic factorsSome crude models for kinetic factors Mechanically weak crystals unlikely to grow readily
eliminate structures with very low shear elastic constants
Structures will transform to more stable structure if there is a low energy barrier to the transformation
eliminate higher energy structures if closely related structures
Structures with very low growth rates are less likely to grow in competition
Use attachment energy (model for vapour growth morphology) to see if any structures have face(s) that are predicted grow very slowly and relative growth rates
Research Councils UK Basic Technology Program £2.4M + facilities funding started Oct. 2003
“Control & Prediction of the Organic Solid State”- robotic polymorph screening, neutron & nucleation expts
- develop models for kinetics nucleation & growth
- build database, over wide range of simple molecules, of hypothetical structures & their properties to data-mine against experimentally observed polymorphs
Looking for wider collaborations
Grateful Thanks toGrateful Thanks to
Programs M Leslie, AJ Stone, H Ammon Students: GM Day, HHY Tsui, T Beyer, DS
Coombes, PP Jethani Postdocs C Ouvrard, JBO Mitchell , KS Wibley, DJ
Willock Many, many other teachers, collaborators & co-
workers. Funding CCDC, Zeneca, EPSRC,
Basic Technology Program of RC UK