Molecular crystal structure prediction with evolutionary algorithm

The layout of the thesis is as follow: In Chapter 1, we present the theoretical background of DFT, Projector-Augmented-Wave (PAW) and Gauge-Including Projector-Augmented-Wave (GIPAW) methods. In Chapter 2, we introduce the crystal structure prediction problem and present evolutionary algorithms as one solution to perform crystal structure search for molecular crystals. Chapter 3 and Chapter 4 are dedicated to the detailed results when using evolutionary algorithm in crystal structure search for the studies of glycine and cholesterol respectivel

An investigation into the crystallisation behaviour of glycine homopeptides

The combinations of amino acids into peptides and proteins, through peptide bonds, are the building blocks of life on earth. Their natural therapeutic properties has seen a significant increase in the application of these materials in the treatment of chronic diseases. The purest and most stable crystalline form provides structural information at the atomic level and is desirable for formulation into efficacious pharmaceutical products. Peptide crystallisation, as a good alternative to chromatographic purification, can also solve the shortcomings of traditional purification method, such as high cost, proteolytic degradation and physiochemical instability. However, peptide crystallisation still remains a major challenge due to highly flexible conformations especially in the case where water plays an integral role in the crystal structure. Glycine is the simplest amino acid and is known to play an important role in new biomimetic functional materials and biopharmaceutical research. Its hydrogen side chain makes the molecule an ideal candidate to study the effeect of chain length on the peptide solubility and crystallisation, without the effect of side chain. The glycine homopeptides crystallisation research in this thesis includes three parts: thermodynamic properties, kinetic properties, and the relationship between peptides conformation and crystallisation. Firstly, the solubility of glycine homopeptides (glycine, diglycine, triglycine, tetraglycine, pentaglycine, and hexaglycine), amino acids with different side chains (aspartic acid, phenylalanine, histidine, and tyrosine) and their dipeptides (asp-phe, gly-asp, gly-phe, phe-phe, gly-gly, tyr-phe, gly-tyr, gly-his) in water from 278.15K to 313.15K were measured using the UV-Vis spectroscopy method and dynamic method. The modified Apelblat equation is used to correlate the relationship between solubility in water and temperature. Molecular dynamic (MD) simulation was further employed to investigate the solute-solvent interactions behind the dissolution behaviors. Moreover, the group-group interaction matrix of the SAFT-γ Mie approach was extended for the prediction of the solubility of amino acids and peptides, exploring the application of SAFT-γ Mie to biomolecular thermodynamic properties. Secondly, the classical nucleation theory was applied to the short-chain glycine homopeptide crystallisation to explore the nucleation theory of macromolecules. The nucleation parameters (nucleation rate, growth rate, interfacial surface energy, and activation Gibbs energy) were calculated based on the classical nucleation theory to explore the chain length effect on the classical nucleation mechanism of peptides, providing kinetic data to the crystallisation conditions designed for industry and modeling tools, such as gPROMS. The evidence of the non-classical nucleation phenomenon was also observed and discussed. Finally, the interaction between water and peptide molecules which can stabilize the unfolded structure of peptides and proteins was revealed, the effect of temperature and salts on the transition between unfolded and folded structure was explored, giving an inspiration to the relationship between conformation and peptide crystallisation. The research presented in this thesis investigates the thermodynamic and kinetic properties of glycine homopeptides, as well as the flexible conformation of peptides during crystallisation, thereby providing a comprehensive strategy for designing and optimising the crystallisation process. Additionally, the research establishes a fundamental understanding of peptide crystallisation, which is extremely beneficial for future macromolecular crystallisation research.Open Acces

Isolation of enantiomers via diastereomer crystallisation

Enantiomer separation remains an important technique for obtaining optically active materials. Even though the enantiomers have identical physical properties, the difference in their biological activities make it important to separate them, in order to use single enantiomer products in the pharmaceutical and fine chemical industries. In this project, the separations of three pairs of diastereomer salts (Fig1) by crystallisation are studied, as examples of the ‘classical’ resolution of enantiomers via conversion to diastereomers. The lattice energies of these diastereomer compounds are calculated computationally (based on realistic potentials for the dominant electrostatic interactions and ab initio conformational energies). Then the experimental data are compared with the theoretical data to study the efficiency of the resolving agent. All three fractional crystallisations occurred relatively slowly, and appeared to be thermodynamically controlled. Separabilities by crystallisation have been compared with measured phase equilibrium data for the three systems studied. All crystallisations appear to be consistent with ternary phase diagrams. In the case of R = CH3, where the salt-solvent ternaries exhibited eutonic behaviour, the direction of isomeric enrichment changed abruptly on passing through the eutonic composition. In another example, R = OH, the ternaries indicated near-ideal solubility behaviour of the salt mixtures, and the separation by crystallisation again corresponded. Further, new polymorphic structures and generally better structure predictions have been obtained through out this study. In the case of R = CH3, an improved structure of the p-salt has been determined. In the case of R = C2H5, new polymorphic forms of the n-salts, II and III, have been both discovered and predicted. This work also demonstrates that chemically related organic molecules can exhibit different patterns of the relative energies of the theoretical low energy crystal structures, along with differences in the experimental polymorphic behaviour. This joint experimental and computational investigation provides a stringent test of the reliability of lattice modelling to explain the origins of chiral resolution via diastereomer formation. All the experimental and computational works investigated in this thesis are published (see APPENDIX 1)

Systematic Investigation of Intermolecular Interactions in NEXAFS Spectroscopy

Near Edge X-ray Absorption Fine Structure (NEXAFS) spectroscopy can be used to study molecular packing and order in organic materials, but only if the spectroscopic effects of intermolecular interactions are well understood. This work aims to contribute to an improved general understanding of the roles of intermolecular interactions on NEXAFS spectroscopy by studying the effects of Rydberg quenching on the degree of Rydberg-valence mixing in saturated molecules and π-π interactions of unsaturated molecules. The effects of π-π interactions were systematically studied by using paracyclophane (PCP) molecules, in which the benzene/benzene separation distance can be systematically varied through the length of the spacer between benzene rings. The effects of Rydberg quenching on the degree of Rydberg-valence mixing in saturated molecules were systematically studied as a function of different crystalline polymorphs (orthorhombic and monoclinic) and chain lengths of n-alkane single crystals. The effects of π-π interactions with varied spacing between co-facial benzene rings in PCPs are observed and these intermolecular effects can be used to study molecular packing and order in unsaturated materials. This work explores the strengths and significance of the effects of π-π interactions on NEXAFS spectroscopy as a function of benzene-benzene separation distances. The effects of Rydberg quenching on the degree of Rydberg-valence mixing to the NEXAFS spectra are not significant between different n-alkanes crystalline polymorphs. However, linear dichroism effects were observed for these different n-alkane crystalline polymorphs. For a given a crystal structure (orthorhombic or monoclinic), the relative intensities of the two C-H peaks (287-288 eV) and the energy of the C-H band (287-288 eV) changed when X-ray linear horizontal polarization was aligned along the principal axes (X,Y) of individual crystals. In addition to the observed linear dichroism, the room temperature NEXAFS spectra of orthorhombic alkanes becomes broader as the alkane chain length decreased. This broadening of NEXAFS spectra is believed to be the result of increased molecular disorder and nuclear motion at room temperature. Nuclear motion effects refers to the energetically accessible molecular conformations present at the experimental temperature. In summary, this work is a significant contribution to the development a more comprehensive understanding of the influences of intermolecular interactions on NEXAFS spectroscopy

Structural investigations with high pressure techniques and multicomponent systems

This thesis illustrates the use of high pressure crystallography techniques for the discovery and investigation of solid-state forms and probes the relationship between molecular structure and compression of both single and multicomponent systems. As well as investigating a data-driven approach to directing experimental co-crystallisation attempts.;Single crystal X-ray diffraction techniques are a highlight in all areas of this study, as well as computational approaches which were used in the evaluation of the interactions of small molecule systems. Data-mining of the Cambridge Structural Database made the comparison of the compression studies richer.;The pharmaceutical co-crystal, indomethacin and saccharin was analysed with respect to increasing pressure. The system is an example of a homomolecular synthon co-crystal allowing investigation of the component dimers free of strong interaction with surrounding molecules. The ambient pressure structure remains stable but investigation showed that the saccharin dimer sits in a pocket made by indomethacin allowing the dimer to lie further apart than in the pure compound.;To follow, a structural compression study of the single component saccharin using synchrotron radiation lead to the structural characterisation of the first new polymorph of saccharin. The hydrogen bonding pattern of the new phase remains consistent however Pixel calculations revealed that the biggest difference in packing arises due to the reduction of an interlayer distance.;To further explore multicomponent systems, two stoichiometric ratios of benzoic acid and isonicotinamide (2:1 & 1:1) were investigated. The rate of compression in these systems are almost identical despite the different molecular packing in each of the stoichiometric ratios. Through the investigation of materials in these initial chapters, the rate of compression in particular supramolecular synthons, e.g. amide-dimers, is demonstrated to be consistent despite the difference in the molecular make-up of the materials under study and their packing arrangements.;Lastly, a data-driven approach was applied in directing the discovery of a new solid-state entity. Following previous failed attempts, machine learning was employed to direct experimental co-crystallisations which led to a new co-crystal of Artemisinin and 1-Napthol. Pixel calculations revealed that the largest contribution to crystal stabilisation comes from dispersion energy and enabled the identification of dominant intermolecular interactions in the crystal structures.This thesis illustrates the use of high pressure crystallography techniques for the discovery and investigation of solid-state forms and probes the relationship between molecular structure and compression of both single and multicomponent systems. As well as investigating a data-driven approach to directing experimental co-crystallisation attempts.;Single crystal X-ray diffraction techniques are a highlight in all areas of this study, as well as computational approaches which were used in the evaluation of the interactions of small molecule systems. Data-mining of the Cambridge Structural Database made the comparison of the compression studies richer.;The pharmaceutical co-crystal, indomethacin and saccharin was analysed with respect to increasing pressure. The system is an example of a homomolecular synthon co-crystal allowing investigation of the component dimers free of strong interaction with surrounding molecules. The ambient pressure structure remains stable but investigation showed that the saccharin dimer sits in a pocket made by indomethacin allowing the dimer to lie further apart than in the pure compound.;To follow, a structural compression study of the single component saccharin using synchrotron radiation lead to the structural characterisation of the first new polymorph of saccharin. The hydrogen bonding pattern of the new phase remains consistent however Pixel calculations revealed that the biggest difference in packing arises due to the reduction of an interlayer distance.;To further explore multicomponent systems, two stoichiometric ratios of benzoic acid and isonicotinamide (2:1 & 1:1) were investigated. The rate of compression in these systems are almost identical despite the different molecular packing in each of the stoichiometric ratios. Through the investigation of materials in these initial chapters, the rate of compression in particular supramolecular synthons, e.g. amide-dimers, is demonstrated to be consistent despite the difference in the molecular make-up of the materials under study and their packing arrangements.;Lastly, a data-driven approach was applied in directing the discovery of a new solid-state entity. Following previous failed attempts, machine learning was employed to direct experimental co-crystallisations which led to a new co-crystal of Artemisinin and 1-Napthol. Pixel calculations revealed that the largest contribution to crystal stabilisation comes from dispersion energy and enabled the identification of dominant intermolecular interactions in the crystal structures

Calculation of the free energy of crystalline solids

The prediction of the packing of molecules into crystalline phases is a key step in understanding the properties of solids. Of particular interest is the phenomenon of polymorphism, which refers to the ability of one compound to form crystals with different structures, which have identical chemical properties, but whose physical properties may vary tremendously. Consequently the control of the polymorphic behavior of a compound is of scientific interest and also of immense industrial importance. Over the last decades there has been growing interest in the development of crystal structure prediction algorithms as a complement and guide to experimental screenings for polymorphs. The majority of existing crystal structure prediction methodologies is based on the minimization of the static lattice energy. Building on recent advances, such approaches have proved increasingly successful in identifying experimentally observed crystals of organic compounds. However, they do not always predict satisfactorily the relative stability among the many predicted structures they generate. This can partly be attributed to the fact that temperature effects are not accounted for in static calculations. Furthermore, existing approaches are not applicable to enantiotropic crystals, in which relative stability is a function of temperature. In this thesis, a method for the calculation of the free energy of crystals is developed with the aim to address these issues. To ensure reliable predictions, it is essential to adopt highly accurate molecular models and to carry out an exhaustive search for putative structures. In view of these requirements, the harmonic approximation in lattice dynamics offers a good balance between accuracy and efficiency. In the models adopted, the intra-molecular interactions are calculated using quantum mechanical techniques; the electrostatic inter-molecular interactions are modeled using an ab-initio derived multipole expansion; a semi-empirical potential is used for the repulsion/dispersion interactions. Rapidly convergent expressions for the calculation of the conditionally and poorly convergent series that arise in the electrostatic model are derived based on the Ewald summation method. Using the proposed approach, the phonon frequencies of argon are predicted successfully using a simple model. With a more detailed model, the effects of temperature on the predicted lattice energy landscapes of imidazole and tetracyanoethylene are investigated. The experimental structure of imidazole is Abstract | ii correctly predicted to be the most stable structure up to the melting point. The phase transition that has been reported between the two known polymorphs of tetracyanoethylene is also observed computationally. Furthermore, the predicted phonon frequencies of the monoclinic form of tetracyanoethylene are in good agreement with experimental data. The potential to extend the approach to predict the effect of temperature on crystal structure by minimizing the free energy is also investigated in the case of argon, with very encouraging results.Open Acces

Polymorphic Phase Transitions:Macroscopic Theory and Molecular Simulation

Transformations in the solid state are of considerable interest, both for fundamental reasons and because they underpin important technological applications. The interest spans a wide spectrum of disciplines and application domains. For pharmaceuticals, a common issue is unexpected polymorphic transformation of the drug or excipient during processing or on storage, which can result in product failure. A more ambitious goal is that of exploiting the advantages of metastable polymorphs (e.g. higher solubility and dissolution rate) while ensuring their stability with respect to solid state transformation. To address these issues and to advance technology, there is an urgent need for significant insights that can only come from a detailed molecular level understanding of the involved processes. Whilst experimental approaches at best yield time- and space-averaged structural information, molecular simulation offers unprecedented, time-resolved molecular-level resolution of the processes taking place. This review aims to provide a comprehensive and critical account of state-of-the-art methods for modelling polymorph stability and transitions between solid phases. This is flanked by revisiting the associated macroscopic theoretical framework for phase transitions, including their classification, proposed molecular mechanisms, and kinetics. The simulation methods are presented in tutorial form, focusing on their application to phase transition phenomena. We describe molecular simulation studies for crystal structure prediction and polymorph screening, phase coexistence and phase diagrams, simulations of crystal-crystal transitions of various types (displacive/martensitic, reconstructive and diffusive), effects of defects, and phase stability and transitions at the nanoscale. Our selection of literature is intended to illustrate significant insights, concepts and understanding, as well as the current scope of using molecular simulations for understanding polymorphic transitions in an accessible way, rather than claiming completeness. With exciting prospects in both simulation methods development and enhancements in computer hardware, we are on the verge of accessing an unprecedented capability for designing and developing dosage forms and drug delivery systems in silico, including tackling challenges in polymorph control on a rational basis

Behaviour of intermolecular interactions at extreme pressures

In organic solids, pressures of only a few gigapascals modify and rearrange intermolecular contacts such as H-bonds and van der Waals contacts leading to extensive phase diversity. Applications in this rich area of research include searches for new phases and solvates of pharmaceutical materials; modelling of detonation mechanisms of energetic materials, and modelling of the driving forces of phase transitions. The overarching theme of this PhD thesis is to obtain new, often difficult to isolate, high-pressure polymorphs of small molecules and elucidate the role of intermolecular interactions in their phase stabilities. The need to obtain precise structural information at atomic resolution demands the use of single crystal diffraction methods but scattering intensities are typically low, and the pressure apparatus used in these studies (the diamond anvil cell) results in incomplete data. This can make direct structure determinations for some materials difficult or even impossible. Third generation synchrotron X-ray sources are therefore used for their brightness, high energies, and small focused beams to extract as much structural information from samples as possible. The amino acid L-threonine, characterised by its hydrogen bond network, has been structurally characterised at 22 GPa which is an unusually high-pressure for a complex organic molecule. L-threonine undergoes two isosymmetric phase transitions at ca. 2 and ca. 9 GPa, and a phase transition at ca. 18 GPa that results in a loss of crystal symmetry. Structures of L-threonine were determined by single-crystal X-ray diffraction to 22 GPa; which is the highest-pressure structure ever reported for an amino acid. High-pressure polymorphism in pyridine was studied extensively by single-crystal X-ray diffraction, Raman spectroscopy and neutron powder diffraction. Pyridine has at least three polymorphs in the narrow pressure range of ca. 1 to ca. 2 GPa but the sluggish nature of the phase transitions has made isolating and characterising one of the phases difficult, until now. Here, we used in situ crystal growth in the diamond anvil cell to obtain a stable, diffraction quality single crystal of the elusive phase III and determined its crystal structure for the first time. A mechanism for the transformation is also proposed. The halogen bonded molecule, 4-iodobenzonitrile was studied experimentally by single-crystal X-ray diffraction and Raman spectroscopy up to 10 GPa. 4-iodobenzonitrile undergoes a reconstructive phase change above 5 GPa that results in crystals breaking apart, making it difficult to obtain meaningful diffraction data. Nevertheless, the structure of the new high-pressure phase was determined for the first time by rapidly pressurising a crystal grown in situ to 8 GPa. Crystal lattice and intermolecular PIXEL energy calculations have been validated for use with small organics to 22 GPa, as well as for halogen containing molecules at very high pressures; allowing the roles of stabilising, or destabilising, molecular interactions to be probed in high-pressure polymorphs for a range of organic molecules. Finally, a neon co-crystal was obtained on compression of a Cu2 Pacman complex. This single-crystal structure represents one of only a few published neon containing organometallic structures. Neon resides within the interstitial voids as a result of the Pacman complex reconfiguring to allow neon-uptake. The study shows the interplay between the pressure transmitting medium and crystal structure and we discuss the potential applications of pressure mediated guest-uptake in the Pacman complexes