A major advance in crystal structure prediction · A major advance in crystal structure prediction Frank Leusen. BCA meeting 5 November ... Crystal defects Surface interactions Diffusion

BCA meeting5 November 2008

A major advance incrystal structure prediction

Frank Leusen


Outline

• Crystal structure prediction• Blind tests in crystal structure prediction• 1999, 2001 and 2004 editions• The 2007 edition of the blind test• Methodology and results• Conclusions and outlook


Crystal structure prediction

• Find lowest lying minima on lattice energy hypersurface

• Function of– Space group– Lattice constants a, b, c, α, β, γ– Contents of asymmetric unit

?


Problems in CSP

• Mathematical problem– Number of degrees of freedom

• Unit cell, molecular flexibility, molecular orientation, number of molecules in asymmetric unit

• Physical problem– Accuracy of energy calculations

• ‘Exotic’ elements, intra-molecular energy, polarisation, ionic systems


Lattice energy

• Basic thermodynamics G = U + pV – TS

– Gibbs free energy G, enthalpy U, pressure p, volume V, temperature T and entropy S

– U is the most important contribution– pV is very small at normal pressure and can

be neglected– TS is not negligible at room temperature but

is difficult to calculate accurately


• Ultimately, the free energy should be calculated and kinetics should be considered

However:• Currently, the Model is often just not close enough to U (0)

Model The real world

U (0) G (T)E

1

23

TemperatureSolvent

ImpuritiesPressure

MorphologySupersaturationCrystal defects

Surface interactionsDiffusion

Stirrer


Available software

• Many programs for crystal structure prediction now exist– Large variation in methodology, both in search for candidate

crystal structures and in stability ranking

• Two commercial software packages– Polymorph Predictor (Accelrys)– GRACE (Avant-garde Materials Simulation)

• About a dozen academic programs– UPACK, FlexCryst, Promet, MolPak and others

• Reviews– Verwer and Leusen, Reviews in Computational Chemistry, 12:

327 – 365 (1998)– Price, Physical Chemistry Chemical Physics, 10: 1996 – 2009

(2008)


Cambridge CrystallographicData Centre

Blind Tests in

Crystal Structure Prediction


Background

• Organised and hosted by Cambridge University / CCDC– In 1999, 2001, 2004 and 2007

• Each test: three or four molecules– Experimentally observed crystal structures are kept

hidden

• Invited participants to predict crystal structures – Up to three predictions per molecule

• Time limit of six months


Motherw

ell

I (polymorph B)

XX1XXXVII (propane)

1III

2XXXII

1113I (polymorph A)

William

s

Verw

er &

Leusen

Schm

idt

Price

Mooij

Lomm

erse

Hofm

ann

Gavezzotti

&S

chweizer

van Eijck

Am

mon

CSP 1999

11 participants4 molecules

Lommerse et al., Acta Crystallographica B, 56: 697 – 714 (2000)


2

Mooij

X

Lomm

erse

X

X

Gavezzotti

Hofm

ann

3

Leusen

X

1

Price

IV

XX

VI

3X11

V

William

s

Verw

er

Schw

eizer

Schm

idt

Scheraga

Motherw

ell

Erk

van Eijck

Dzyabchenko

Am

mon

CSP 2001


Motherwell et al., Acta Crystallographica B, 58: 647 – 661 (2002)


X

Verw

er

X

Schw

eizer

X1X321X1

VIII (not blind!)

Hofm

annX

Facelli

Dzyabchenko

van Eijck

Erk

Liang

X1

IX

XI

XXX

Schm

idtS

cheragaP

riceP

antelidesM

otherwell

Leusen

Della V

alleD

ayB

oerrigterA

mm

on

CSP 2004


Day et al., Acta Crystallographica B, 61: 511 – 527 (2005)


Blind test 2007

• 15 participants• 4 molecules

:


Our approach

• Use AMS’ novel technology for crystal structure generation and lattice energy calculation

• Predictions in all 230 space groups• Crystal structure generation by random search

engine combined with lattice energy minimizer• Molecular flexibility probed automatically during

search• The two components of the co-crystal (molecule

XV) were treated independently


Methodology• Previously, all successful methods used molecular mechanics

approaches to generate structures and rank them by stability– Variety of potentials, e.g., point charges vs multipoles– Relatively fast, but inaccurate even with sophisticated potentials

• New approach uses tailor made force field to generate structuresand solid state hybrid MM / DFT for stability ranking– DFT calculations with VASP combined with molecular mechanics van

der Waals correction– Force field is fitted to hybrid MM / DFT results– Relatively slow, but very accurate– Requires significant expertise and significant CPU resources

• Hybrid MM / DFT method– Neumann and Perrin, Journal of Physical Chemistry B, 109: 15531 –

15541 (2005)• Force field fitting

– Neumann, Journal of Physical Chemistry B, 112: 9810 – 9829 (2008)


Computational strategy

Hybridmethod

Tailor-madeforce field

structuregeneration

final energyranking

parameterization

starting Hessian


Molecule XII

0.05900

0.03559

0.00000

Exp

Rel latt energy (kcal/mol atom)

90.090.090.09.759.516.9780.84PbcaExp

90.090.090.09.496.979.9882.44PbcaPred 1

γ (°)β (°)α (°)c (Å)b (Å)a (Å)Volume / as unit (Å3)

Space group

90.099.590.08.025.263.9381.75PcPred 3

90.0114.190.07.737.566.4185.36P21/cPred 2


-10

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Intensity

2-theta

MolXII (Sim) nlk_xii_0 (Sim) Observed Reflections

Molecule XII powder patterns

Simulated for experimental

structure

Simulated for predicted structure


Molecule XII

ExperimentalPredicted


Molecule XIII

0.02873

0.02676

0.00000

Exp


90.093.690.014.4313.513.89189.42P21/cExp

90.095.090.014.4713.463.87187.95P21/cPred 1


Space group

90.090.090.03.8528.8627.47190.88Fdd2Pred 3

90.090.090.03.8519.8419.84189.47P42/nPred 2


-10

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Intensity

2-theta

MolXIII (Sim) ms_xiii_1 (Sim) Observed Reflections

Molecule XIII powder patterns


structure



Molecule XIIIExperimental

Predicted


Molecule XIV

90.0105.890.09.349.7613.15288.510.00102P21/cPred *

0.04198

0.01890

0.00000

Exp


90.0105.890.09.349.7413.06285.59P21/cExp

90.074.290.09.319.8213.24291.37P21/cPred 1


Space group

90.094.790.09.239.8113.19297.54P21/cPred 3

90.090.090.025.619.489.77296.41PbcaPred 2


-10

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Intensity

2-theta

MolXIV (Sim) ms_xiv_1 (Sim) Observed Reflections

Molecule XIV powder patterns


structure



Molecule XIVExperimental

Predicted


Molecule XV

0.01796

0.01509

0.00000

Exp


90.096.690.012.6713.677.28313.07P21/nExp

90.065.690.013.6413.827.26311.56P21/cPred 1


Space group

90.058.190.08.2723.567.60314.22P21/cPred 3

112.591.699.912.267.687.36313.93P-1Pred 2

:


-10

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50

Intensity

2-theta

MolXV (Sim) ms_xv_1 (Sim) Observed Reflections

Molecule XV powder patterns


structure



Molecule XV dominant packing


Molecule XV

ExperimentalPredicted


Accuracy of tailor-made force fields

>968142Number of structures within 2x RMSD of the minimum

37121Rank of experimental structure according to tailor-made force field

0.0320.0240.0530.025RMS deviation (kcal/mol/atom) between tailor-made force field and hybrid method

963250100Number of structures optimised with hybrid method

XVXIVXIIIXIICompound


Summary

• Four out of four structures correct• All four structures were predicted as our top rank• Results could not have been better!

• Sanderson, Nature, 450: 771 (2007)• Neumann, Leusen and Kendrick, Angewandte Chemie

International Edition, 47: 2427 – 2430 (2008)• Day et al, Acta Crystallographica B, in preparation


Conclusions• Crystal structures of small organic molecules are

predictable– Use tailor made force field to generate limited set of

possible structures– Use solid state DFT with empirical van der Waals

correction to calculate accurate lattice energies– Requires significant compute power, time & expertise

• Accurate lattice energies are an appropriate selection criterion in crystal structure prediction

• Long way to go to make reliable CSP a standard tool– But a big leap forward has been made


Further work

• Further developments required to predict polymorphic stability– Consideration of zero point energies and entropic effects

• Run simulations on many more test systems to establish general accuracy and reliability– 100% success rate in blind test does not mean that the approach

always works– Larger sample required for meaningful statistics– Need to explore limitations– Progress is slow due to CPU requirements

• Extend parameterisation of hybrid method• Further improvements in force field accuracy required

– Focus on electrostatics


Challenges

More thanone molecule

per asymmetric unit

Solvates

Salts

Highly flexible molecules


Acknowledgements• Marcus Neumann (Avant-garde Materials Simulation)• John Kendrick (University of Bradford)• Sanofi-Aventis and Astra Zeneca for funding the

software development• Victoria Pennington (University of Bradford) for

keeping the hardware running• Ralf Siebrecht (Avant-garde Materials Simulation) and

Lionel Zaske (Sanofi-Aventis) for running some of the calculations

• Pascale Girard (Avant-garde Materials Simulation) and Marc-Antoine Perrin (Sanofi-Aventis) for general support

• Graeme Day (University of Cambridge) for organising and CCDC for hosting the blind test

• Other computational chemists at University of Bradford for allowing us to use so much CPU time

Documents

A major advance in crystal structure prediction · A major advance in crystal structure prediction Frank Leusen. BCA meeting 5 November ... Crystal defects Surface interactions Diffusion