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Emerging Classifications of Polymorph Predictability

"Computed crystal energy landscapes for understanding and predicting organic crystal structures and polymorphism." Price SL 2009. Accounts Chem Res 42:117-126. summarises the evidence for the interpretation of energy landscapes.

Each computational study starts by generating a set of energetically feasible crystal structures for the molecule. We are currently limited in the molecules that can be studied, and the types of crystal structure that can be found in the search, as well as the accuracy of the relative energies. The resulting distributions of the lattice energies of the known and hypothetical crystal structures fall into different (overlapping) categories, which differ in the confidence with which the crystal structures can be predicted.

Let us assume that the following schematic diagrams give the relative energies for all different crystal structures, with open red shapes denoting the experimentally observed structures and shape of symbols depicting groups of similar structures. Such diagrams summarise the crystal energy landscape, the structures and relative energies of the thermodynamically plausible crystal packings of the molecule. The bar to the right of each plot indicates the energy range of potential polymorphism.

typical energy density plot(1)
  1. The only known crystal structure is found at the global minimum and there is a sufficient energy gap that no others are energetically plausible. Only in this case is the search for energetically feasible structures able to unambiguously predict the structure and rule out the possibility of polymorphism. Examples below show the gap to the next hypothetical structure found in the search:
    • 3-oxauracil (4 kJ mol-1)
    • 1,2-dichloro-3-nitrobenzene (1.7 kJ mol-1)
  1. There is a known crystal structure at the global minimum, and there are other structures close enough in energy that they could be potential polymorphs. Either:
  1. the other low energy crystal structures are closely related, and so it is unlikely that the nucleation pathway would produce a metastable structure, and even if it did it would be likely to transform to the more stable structure fairly easily. In this case polymorphism is unlikely.
    • Imidazole (same hydrogen bonded chain)
    • 5-azauracil (same hydrogen bonded sheet)
    • 5-hydroxyuracil
    • Coumarin
    • 1,3-dichloro-5-nitrobenzene
    • 7-hydroxycoumarin
typical energy density plot(2a)
  1. some of the other hypothetical structures are sufficiently different (e.g. in hydrogen bonding motif) that it is plausible that different crystallisation conditions might nucleate different structures and that transforming to the most stable structure would be difficult. Hence, we need to rationalise the kinetic factors that can lead to the observation of metastable polymorphs. This may be linked to the range of crystallisation conditions that can be used.
    • Polymorphic
    • No polymorphs observed so far, but very limited range of crystallisation conditions available.
      • uracil (no polymorphs observed so far, but limited solubility)
      • 6-azauracil (no polymorphs observed so far, but limited solubility)
      • alloxan (no polymorphs observed so far, but reacts readily)
      • parabanic acid
    • Some other rationalisation for kinetic effects preventing polymorphism
      • 3-azabicyclononane-2,4-dione
      • 5-fluoroisatin
typical energy density plot(2b)
  1. The known crystal structure is not the global minimum, i.e. there are other structures that are predicted to be more stable. This would be a valuable warning that there is potentially a more stable polymorph, and by having the predicted structure it may be possible to design methods of crystallisation to find the new polymorph.
typical energy density plot(3)
  1. Cases where new polymorphs have been found following the prediction:
  2. Cases where no new polymorphs have yet been found, and we need to understand why there appears to be no kinetic pathway to the most thermodynamically stable form. This again may reflect the variety of crystallisation conditions, for example
    • 2,6-diamino-3,5-dinitropyrazine (alternative hydrogen bonding patterns observed)
    • cyanuric acid (sheets preferred)
    • p-dichlorobenzene (growth rate favours known structures)
    • p-hydroxyuracil (alternative hydrogen bonding patterns)
    • adenine (poorly soluble)
    • guanine (poorly soluble)

Note that the cases 2b and 3 differ in whether it is easy to crystallise the most thermodynamically stable polymorph. In both cases, we need extensive experimental studies seeking to identify all long-lived polymorphs in order to understand the kinetic factors involved. Following extensive experimental studies (even those where reactions have been carried out with no new polymorphs being identified), it should be possible to develop a more quantitative and predictive computational model of the kinetic factors that determine polymorphism. This is a major aim of the CPOSS project.

  1. There are a multitude of hypothetical structures very close together near the energy minimum.
  1. The experimental structure is not the sort of simple structure that can be found in the theoretical search. However, there is a relationship between the hypothetical low energy structures that enables packing motifs to interchange, e.g. different stacking of sheets. In this case the predictions suggest that a specific type of disorder is likely in the crystal. For example:
    • cyclopentane (rotational disorder)
    • chlorothalonil (Form 2: disordered sheets; Form 3: Z'=3 - both closely related to pairs of structures found in the search)
    • 5-chlorouracil
    • 5-bromouracil
    • azetidine (the Z'=2 structure is probably a thermal average over Z'=4 lower symmetry structures)
    • aspirin (evidence of polymorphic domains of the 2 forms has been found)
    • carbonic acid (with 2 distinct amorphous phases linked to the two polymorphs of unknown structure)
typical energy density plot(4a)
  1. The poor lattice energy and multitude of equally poor compromises between close packing and the specific interactions show that the molecule has no good ways of packing with itself. The hydrogen bonding motifs seen in these low energy structures are observed in a range of polymorphs and solvates.
    • hydrochlorothiazide
    • 5-fluorocytosine
typical energy density plot(4b)

There are cases where we had hoped to be able to predict the crystal structure, but it became obvious during the course of the calculations that the accuracy in the relative energies was such that the assignment into one of the above categories would be very tentative. Possible reasons include:

  1. the relative energies of the low energy crystal structures are very sensitive to small changes in the molecular conformation, which may be induced by the packing forces, for example:
    • barbituric acid
    • 5-hydroxyuracil
    • hydantoin
    • uric acid
    • urazole
    In many of these cases the observed crystal structure is the global minimum structure when the experimental molecular conformation is used, but is significantly above the global minimum observed using the gas phase conformer.
  2. the intermolecular potential is not known sufficiently accurately so that different reasonable models produce qualitatively different energy diagrams, for example:
    • parabanic acid
    • 2,9-di-iodo-anthanthrone (tackled for the Blind Test)
  3. The calculation of the free energy, rather than the lattice energy, produces a significant reordering of the structures.

We are currently developing our method of crystal structure prediction and methods of modelling both intermolecular and intramolecular forces, to both model the above systems better, and progress to salts, hydrates, conformationally flexible molecules, and more complicated systems and more diverse molecules. The experimental studies being performed on such systems are essential to the development of predictive methods, as many screening studies are finding new forms.

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