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.