The attachment energy model takes the energetics of a crystal into account by calculating the attachment energy, i.e. the energy per molecule released on the attachment of a growth layer to a growing crystal surface. The attachment energy is the difference between the lattice energy of a crystal and the energy o f the growth slice of thickness dhki-'^^ Hartman and Perdok 29-32 observed that the growth rate of a face is directly proportional to its attachment energy. Therefore faces with a high attachment energy grow relatively fast and have a low morphological importance. The list of possible faces for which the attachment energies are calculated is usually generated by the BFDH model. As the attachment energy model is based on energetical criteria, it is more reliable for predicting the relative sizes and shapes o f the different surfaces. Hartman and Bennema 23 observed that for crystals grown from low supersaturations, the assumed proportionality between the growth rate of a face and the attachment energy is a valid approximation for the flat F-faces (morphologically dominant faces) and further work confirming this observation has been published. 24-36
Both methods, the BFDH and the attachment energy model do not take any temperature, solvent or impurity effects into account which can have a fundamental influence on the morphology of the experimental crystal. Therefore calculated morphologies are by these methods most likely to predict vapour grown crystals.
Several hypotheses of the influence of the solvent on crystal growth have been proposed and the ‘true’ mechanism of solvent interaction is still a m atter of debate.
_______________________Chapter 4. Calculation o f crystal structures and their properties
37-40 The growth rates and crystal habits can already be modified by a very small quantity of solvent or impurity by either inhibition or increase in the growth rate, 42 Therefore, in cases where the attachement energy calculated and the observed habit forms differ, this is often attributed to solvent and impurity effects. 43, 44
In this thesis the BFDH and the attachment energy model, as implemented in the MSI Cerius software, have been used to estimate the morphological properties of the hypothetical structures generated in the prediction search procedures (chapter
6
and 7). This estimate has been employed to discuss the growth rates of the lowest energy crystal structures and to link this to their likelihood of being observed experimentally as possible polymorphs.The morphologies for the paracetamol structures were calculated using the program Cerius^3.5 with the Dreiding-2.21 force field 45 with equilibrium charges, 46 following the reasonable success of this method in predicting the experimental morphologies grown from supersaturated IMS solution. 47
For the carboxylic acids morphology calculations, the empirically derived force field by Hagler et al. 48-50 has been applied.
_______________________Chapter 4.Calculation o f crystal structures and their properties
References fo r c h ap te r 4
(1) Dunitz, J.D. in Implications o f Molecular and Materials Structure fo r New Technologies, J.A.K. Howard, F.H. Allen, and G.P. Shields, Kluwer Academic Publishers, Dordrecht, 1999, 175-184. W eak interactions in molecular crystals. (2) Willock, D.J.; Price, S.L.; Leslie, M.; Catlow, C.R., J. Comp. Chem., 1995, 16,
628-647. The relaxation of molecular crystal structures using a distributed multipole electrostatic model.
(3) Amos, R.D.; Alberts, I.L.; Andrews, J.S.; Colwell, S.M.; Handy, N.C.; Jayatilaka, D.; Knowles, P.J.; Kobayashi, R.; Laidig, K.E.; Laming, G.; Lee, A.M.; Maslen, P.E.; Murray, C.W.; Rice, J.E.; Simandiras, E.D.; Stone, A.J.; Su, M.D.; Tozer, D.J., CADPAC6: The Cambridge Analytic Derivatives Package, Issue
6
: Cambridge University, 1995.(4) Allen, F.H.; Kennard, O.; Watson, D.G.; Brammer, L.; Orpen, A.G.R., J. Chem. Soc., Perkin Trans., 1987, 2, SI - S9. Tables of bond lengths determined by X- ray and neutron diffraction. Part 1. Bond lengths in organic compounds.
(5) Ewald, P.P., Ann. Physik, 1921, 64, 253-265. Die Berechnung optischer und elektrostatischer Gitterpotentiale.
(
6
) Payne, R.S.; Roberts, R.J.; Rowe, R.C.; McPartlin, M.; Bashal, A., Int. J. Pharm., 1996, 145, 165-173. The mechanical properties of the two forms of primidone predicted from their crystal structures.(7) Roberts, R.J.; Payne, R.S.; Rowe, R.C., Eur. J. Pharm. S e t, 2000, 9, 277-283. Mechanical property predictions for polymorphs of sulphathiazole and carbamazepine.
(
8
) Boldyreva, E. in Implications o f molecular and materials structure fo r new technologies, J.A.K. Howard, F.H. Allen, and G.P. Shields, Kluwer, Dordrecht, 1999, 151-174. Solid-state reactivity and implications for catalytic processes. (9) Drabble, J.R.; Husain, A.H.M., J. Phys. C.: Solid State Phys., 1 9 8 0 ,13, 1377. (10) Brose, K.-H.; Eckhardt, C., J. Chem. Phys. Lett., 1986, 125, 235-240.Calculation of elastic constants of TCNQ crystals using atom-atom potentials. (11) He, H.X.; Welberry, T.R., J. Phys. Chem. Solids, 1988, 49, 421-424. Calculation
of elastic constants for crystalline acenaphthylene, C i
2
H§, using semiempirical atom-atom potentials._______________________Chapter 4.Calculation o f crystal structures and their properties
(12) Michalski, D.; Swanson, D R.; Eckhardt, C.J., J. Phys. Chem., 1996, 100, 9506- 9511. Elasticity, bulk modulus, and mode Gruneisen parameters of the HPTB molecular crystal: Computational investigation of a clathrate precursor.
(13) Michalski, D.; Eckhardt, C.J., J. Phys. Chem. B, 1997, 101, 9690-9694. Computational determination of the elastic properties o f the alpha-phenazine crystal.
(14) Pavlides, P.; Pugh, D.; Roberts, K.J., Acta Cryst., 1991, A47, 846-850. Elastic- tensor atom-atom potential calculations for molecular crystals C
5
H5
AND C0
(NH2
)2
-(15) Walmsley, S.H., J. Chem. Phys., 1968, 48, 1438.
(16) Walmsley, S.H. in Lattice dynamics and intermolecular forces, L.V. Corso, Academic Press, New York, 1975, Basic theory of lattice dynamics of molecular crystals.
(17) Sharp, N.D.; Walmsley, S.H., Chem. Phys. Lett., 1994, 222, 546-550. The method of homogeneous deformations of atomic and molecular crystals. General formulation and rotational invariances.
(18) Day, G.M.; Price, S.L.; Leslie, M., Crystal Growth & Design, 2001, 7, 13-27. Elastic constant calculations for molecular organic crystals.
(19) Day, G.M.; Price, S.L. in Handbook o f elastic properties o f solids, liquids and gases. Levy, Bass, and Stern, Academic Press, 2001, 3-50. Properties of crystalline organic molecules.
(20) Voigt, W., Lehrbuch der Kristallphysik, 1928, Leipzig: Teubner. (21) Reuss, A., Z. Angew. Math. Mech., 1929, 9, 55.
(22) Berkovitch-Yellin, Z., J. Am. Chem. Soc., 1985, 107, 8239-8253. Toward an ab initio derivation of crystal morphology.
(23) Miller, W.H., A treatise on crystallography, 1839, Cambridge: Pitt Press. (24) Bravais, A., Etudes crystallographiques, 1866, Paris: Gauthier-Villars.
(25) Friedel, G., Bull. Soc. Fr. M ineral, 1907, 30, 326. Etudes sur la loi de Bravais. (26) Donnay, J.D.H.; Harker, D., Am. M ineral, 1937, 22, 446-467. A new law of
crystal morphology extending the law of Bravais.
(27) Donnay, J.D.H.; Donnay, G.C.R., Acad. S c l Paris, 1961, 252, 908.
(28) Docherty, R.; Clydesdale, G.; Roberts, K.J.; Bennema, P., J. Phys. D: Appl. Phys., 1991, 24, 89-99. Application o f Bravais-Friedel-Donnay-Harker,
_______________________Chapter 4. Calculation o f crystal structures and their properties
attachment energy and Ising models to predicting and understanding the morphology of molecular crystals.
(29) Hartman, P.; Perdok, W.G., Acta Cryst., 1955, 8, 49-52. On the relations between structure and morphology of crystals. I.
(30) Hartman, P.; Perdok, W.G., Acta Cryst., 1955, 8, 521-524. On the relations between structure and morphology of crystals. II.
(31) Hartman, P.; Perdok, W.G., Acta Cryst., 1955, 8, 525-529. On the relations between structure and morphology of crystals. III.
(32) Hartman, P. in Crystal Growth: An Introduction, P. Hartman, North Holland, Amsterdam, 1975, 367-402.
(33) Hartman, P.; Bennema, P., Journal o f Crystal Growth, 1980, 49, 145-156. The attachment energy as a habit controlling factor.
(34) Tassoni, D.; Riquet, J.P.; Durand, P., Acta Cryst., 1980, A 36, 420-428. Morphologie théorique du composé AlgNi et comparaison avec les formes observées.
(35) Hartman, P., J. Cryst. Growth, 1980, 49, 157-165.
(36) Hamer, R.; Tassoni, D.; Riquet, J.P.; Durand, F., J. Cryst. Growth, 1981, 51, 493-501. Morphology of the intermetallic compound AI
2
CU.(37) Wells, A.F., Philos. Mag., 1946, 37, 184.
(38) Bennema, P. in Crystal Growth: An Introduction, P. Hartman, North-Holland, Amsterdam, 1973, 274.
(39) Davey, R.J.; Milisavljevic, B.; Bourne, J.R., J. Phys. Chem., 1988, 92, 2032- 2036. Solvent interactions at crystal-surfaces-the kinetic story of alpha- resorcinol.
(40) Weissbuch, I.; Popovitibiro, R.; Lahav, M.; Leiserowitz, L., Acta Cryst., 1995, B 51, 115-148. Understanding and control o f nucléation, growth, habit, dissolution and structure of 2-dimensional and 3-dimensional crystals using tailor-made auxiliaries.
(41) Davey, R.J., J. Cryst. Growth, 1976, 34, 109-119. (42) Gilmer, G.H., Science, 1980, 208, 355-363. (43) Hartman, P., J. Cryst. Growth, 1980,49, 166-170.
(44) Visser, R.A.; Bennema, P., Neth. M ilk Dairy J., 1983, 37, 109-137. Interpretation of the morphology of alpha-lactose hydrate.
_______________________Chapter 4. Calculation o f crystal structures and their properties
(45) Mayo, S.L.; Olafson, B.D.; Goddard III, W.A., J. Phys. Chem., 1990, 94, 8897- 8909. DREIDING: A generic force field for molecular simulations.
(46) Rappe, A.K.; Goddard III, W.A., J. Phys. Chem., 1991, 95, 3358-3363. Charge equilibration for molecular-dynamics simulations.
(47) Nichols, G.; Frampton, C.S., Journal o f Pharmaceutical Sciences, 1998, 87, 684-693. Physicochemical Characterization of the orthorhombic polymorph of paracetamol crystallized from solution. Atomic coordinates by private communication.
(48) Lifson, S.; Hagler, A.T.; Dauber, P., J. Am. Chem. Soc., 1979, 101, 5111-5121. Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 1. Carboxylic acids, amides, and the C=O...H-hydrogen bonds.
(49) Hagler, A.T.; Lifson, S.; Dauber, P., J. Am. Chem. Soc., 1 9 7 9 ,101, 5122-5130. (50) Lifson, S.; Hagler, A.T.; Dauber, P., J. Am. Chem. Soc., 1979, 101, 5131-5141.
Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 2. A benchmark for the objective comparison of alternative force fields.
Chapter 5. CCDC crystal structure prediction workshop 1999
Chapter 5.
Cambridge Crystallographic
Dote Centre (CCDC) crystal
structure prediction workstiop
1999
A comprehensive and unified test run using a convenient molecule and comparing the performances o f all these packages would be desirable, but is very difficult to organize (ideally, this would be a good task fo r some committee o f the
International Union o f Crystallography).’ ^
In this chapter the international crystal structure prediction workshop 1999 for small organic molecules organised by the Cambridge Crystallographic Data Centre (CCDC) will be introduced and the study of blindtest compound I, 3-oxabicyclo(3.2.0)hepta-l,4-diene, will be discussed in detail. The studies for compound II and III have been carried out by SL Price and HHY Tsui / SL Price respectively and only the geometry optimisations and general conclusions for these two structures will be presented here. It has been the first workshop of this kind for molecular crystals and the results of it have been published. ^
_________________________Chapter 5. CCDC crystal structure prediction workshop 1999