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Computational studies of Polymorphs: Applications

Computational studies of Polymorphs: Applications. Sarah (Sally) L Price Department of Chemistry UCL. The aim of crystal structure prediction. A computational method to predict the crystal structure(s) for a molecule from the chemical diagram

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Computational studies of Polymorphs: Applications

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  1. Computational studies of Polymorphs: Applications Sarah (Sally) L Price Department of Chemistry UCL

  2. The aim of crystal structure prediction 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

  3. 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

  4. 1999, ~11 x 3 guesses(2000, Acta Cryst B56, 697) 2001 ~15 x 3 guesses (2002, Acta Cryst B58,647) 2004 ~18 x 3 guesses (2004, Acta Cryst B in preparation) Motherwell, Lommerse, Ammon, Dunitz, Gavezzotti, Hofmann, Leusen, Mooij, Price, Scheweizer, Schmidt, van Eijk, Verwer, Williams + Dzyabchenko, Scheraga + Facelli, Pantelides, DellaValle Rigid Polymorphic Stable 0 Metastable 4 Rigid 1 correct Flexible 1 correct Rigid 2 correct Rigid Pure enantiomer 2-4 correct Flexible 0 correct New polymorph found later Rigid Unfortunately not blind 6 correct Replacement Rigid 0 correct Rigid 1 correct Flexible 0 correct Results of CCDC Blind Tests – Limited Success?

  5. Why develop a computational method of 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)

  6. Zeroth Order Assumption For A • the experimental crystal structure will correspond to the global minimum in the static lattice energy • a crude 0K thermodynamic model X • any competitive local minima are possible polymorphs • within < 2 kcal/mol of global min. (Bernstein, Polymorphism in Molecular Crystals, OUP 2002)

  7. Requirements for finding low energy 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

  8. Model 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.

  9. Electrostatic model from r(r) • Analyse to give sets of atomic multipoles (DMA, A.J.Stone) • represents lone-pairs, p- electrons etc • electrostatic contribution to lattice energy ~ accuracy Y Cl2r - rspherical atoms

  10. Nyburg & Faerman 1984 C DMA + exp-6 potentialCoombes 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, CN, Br...

  11. Non-empirical repulsion models based on overlap of r(r) • Assume: repulsion  overlap of charge distributions Urep = KSr = K ò rA(r) rB (r) dr • r(r) divided into atoms => Sr in atom atom form. Can fit anisotropic Sr model. • Finally get the single proportionality parameter - K

  12. Develop anisotropic Cl repulsion model Atom-atom form Aexp(-a(R-r(W))) where r(W) = r0+r1(z1.R+z2.R) +r2(3 z1.r2+3z2.R2-2)/2 1990 Cl2 crystal reproduced by overlap repulsion model RJ Wheatley & SLP, Mol.Phys 71, 1381 2003 Extended to series of 12 chlorobenzene crystals & properties Anisotropy consistent “lone pair” density Towards nonempirical Y based potentials for organics - main problem dispersion ?Extend Williams & Stone 2003 JCP 119, 4620 GM Day & SLP, JACS, 125, 16434

  13. Simulation MethodJ Comput Chem 16 (1995) 628; J Phys Chem A 105(2001) 9961. -CN N  C- • 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

  14. Rel Growth Rate p-dichlorobenzene searchGMDay & SLP, J. Am. Chem. Soc. 125 (2003) 16434 2.4 a 1.7 b 2.1 g 1.0 ~a+ b

  15. Molecular 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?

  16. N-H angle bent by 17° limits reproduction of crystal (ExptMinOpt) Angle bending crucial to adoption of known crystal structure? Certainly to search! Uric acid - structure shows distortion of N-H (Ringertz 1966) Add molecular diagram Always contrast Expt, ExptMinExpt & ExptMinOpt prior to study

  17. The challenge of flexible molecules • 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 conformers

  18. Why aspirin?C. Ouvrard & SLP, Cryst. Growth Des, submitted. • 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]

  19. How much does the crystal packing 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?

  20. Consider 2 lowest of 9 minima + 2 best planar transition states DE /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

  21. 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

  22. More detail for lowest energy structures Known structure found ~ best for Z=1, but other rival structures 2a-P21/c 2a-C2/c 1a-P21/c 1a- . Corr. to Expt. COOH dimer Stable conformer C=O acetyl chains Similar Expt, but low shear resistance

  23. Model gives good reproduction of known crystal structure Room temperature crystal structure versus ExptMinOpt for B3LYP conformer 2a Note that ab initio conformer is very close to experimental molecule

  24. Lattice energy sensitive to exact molecular model Experimental vs gas phase molecule searches find mostly the same crystal structures BUT different energy gaps Lattice energy / kJ/mol Sensitivity of Ulatt to molecular structure + problems of evaluating DEintra make flexible molecules very challenging, even when crystal packing does not distort molecule from “gas phase” conformation. Can distinguish between packing ability of conformers

  25. Search Method for Starting Structures • 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

  26. Problem of distinct minimaE.g. Indigo Price & Beyer, Trans. ACA 33 (1998) 23. Known sheet structures lowest in energy Observed H-bonded sheet of two known polymorphs favored More hypothetical sheet stackings close in energy ?  polytypism

  27. Possible outcomes of searchesPrice, Adv. Drug Delivery Reviews (2004) Hypothetical structures 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

  28. Prediction of isomer crystals shows results depend on molecule not functional group Early study “Blind” Challenge Withnall & Palmer ?

  29. Contrasting set of lattice energy minima Sheet structures Min from Expt ~Global min Global min = min from expt Min using different H-bond donors & acceptors

  30. Lattice 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

  31. No hydrogen-bonds structure of alloxan is global minimum in lattice energy Shortest H…O 2.37Å but ExptMinOpt found as global minimum

  32. -34.8 kJ/mol -37 kJ/mol -36.2 kJ/mol Dimer energies also show molecule has unusual hydrogen bonding capabilities Hydrogen bonds weak CO…CO strong Electrostatic potential

  33. Variability of multiple minima problemSurvey of lattice energy min studies CrystEngComm 3 (2001) 178 (29 known to be polymorphic) Many structures found as local minima Errors in energies? Published are meta-stable? Other polymorphs possible? NB Perverse choice of difficult molecules

  34. Validity 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

  35. Reach for the stars, and you might 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?

  36. Workshop IV practice in computing 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

  37. To progress computational 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

  38. Some 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

  39. 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

  40. Grateful 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

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