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Prediction of the Mechanical Deformation Properties of Organic Crystals Based upon their Crystallographic Structures: Case Studies of Pentaerythritol and Pentaerythritol Tetranitrate



Development of a quantitative model and associated workflow for predicting the mechanical deformation properties (plastic deformation or cleavage fracture) of organic single crystals from their crystallographic structures using molecular and crystallographic modelling.


Intermolecular synthons, hydrogen bonding, crystal morphology and surface chemistry are modelled using empirical force fields with the data integrated into the analysis of lattice deformation as computed using a statistical approach.


The approach developed comprises three main components. Firstly, the identification of the likely direction of deformation based on lattice unit cell geometry; secondly, the identification of likely lattice planes for deformation through the calculation of the strength and stereochemistry of interplanar intermolecular interactions, surface plane rugosity and surface energy; thirdly, identification of potential crystal planes for cleavage fracture by assessing intermolecular bonding anisotropy. Pentaerythritol is predicted to fracture by brittle cleavage on the {001} lattice planes by strong in-plane hydrogen-bond interactions in the <110>, whereas pentaerythritol tetranitrate is predicted to deform by plastic deformation through the slip system {110} < 001>, with both predictions being in excellent agreement with known experimental data.


A crystallographic framework and associated workflow for predicting the mechanical deformation of molecular crystals is developed through quantitative assessment of lattice energetics, crystal surface chemistry and crystal defects. The potential for the de novo prediction of the mechanical deformation of pharmaceutical materials using this approach is highlighted for its potential importance in the design of formulated drug products process as needed for manufacture by direct compression.

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Active Pharmaceutical Ingredients


Bravais, Friedel, Donnay, and Harker


Avogadro’s number




Pentaerythritol tetranitrate


Root means square




Dislocation constant


Burgers vector

dhkl :

Interplanar spacing

\({E}_{att}^{hkl}\) :

Attachment energy

\({E}_{sl}^{hkl}\) :

Slice energy

Ecore :

Dislocation core energy

Ecr :

Lattice energy

Edisloc :

Dislocation energy

Eline :

Dislocation line energy


Modulus of elasticity


Specific surface energy


Number of asymmetric units


Atomic pairwise intermolecular interactions


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Ibrahim, S.F., Pickering, J., Ramachandran, V. et al. Prediction of the Mechanical Deformation Properties of Organic Crystals Based upon their Crystallographic Structures: Case Studies of Pentaerythritol and Pentaerythritol Tetranitrate. Pharm Res 39, 3063–3078 (2022).

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  • crystallographic modelling
  • elastic anisotropy
  • mechanical properties
  • slip planes
  • synthonic engineering