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