EXPERIMENTAL AND COMPUTATIONAL ANALYSIS OF RELATIVE ENERGETIC STABILITIES OF CRYSTALLINE ANHYDROUS POLYMORPHS AND PSEUDOPOLYMORPHS

The stability of pharmaceutical solids is impacted by the properties of both active and inactive ingredients. Given that the aqueous solubility of solid-state medicinal products can be directly linked to the component properties, it is prudent to carefully study these materials to predict bioavailability and shelf stability. The relative energetic stabilities of the molecular crystals of interest are governed by both the intermolecular forces and the molecular conformations within the structure. In this research, the electronic origins of crystalline stability were investigated using a combination of solid-state density functional theory (ss-DFT) and terahertz time-domain spectroscopy (THz-TDS). Terahertz spectroscopy of the lattice vibrations offers a sensitive probe of solid-state interactions and serves as a rigorous benchmark for testing the quality of the applied theoretical methods. Vibrational simulations of different polymorphic forms are also useful for investigating the relative thermodynamic stabilities of these structures. Through the calculation of Gibbs free energy versus temperature trends, it was possible to not only identify enantiotropic or monotropic relationships between polymorphs, but also the precise transition temperature linking enantiotropic pairs. These combined experimental and computational methods were extended to analyzing the relative stabilities of not only pure solids, but also cocrystals. The successful use of DFT for identifying relative stabilities of known crystal structures led to its use for crystal structure prediction. Overall, this work has demonstrated the extensive applicability of ss-DFT in the analysis of electronic and thermodynamic relationships within polymorphic and pseudopolymorhic systems. Application of this methodology to pharmaceutical solids has provided new insights into the most important contributors to the stabilities of these materials

Molecular Flexibility in Crystal Structure Prediction

The packing of molecules in solids greatly affects the properties of the bulk materials. This is particularly important for the pharmaceutical industry, where the discovery of crystal forms at a late stage of process development can have disastrous consequences. As a result, the importance of polymorphism in crystal structures of organic molecules has been recognised for many years. This thesis presents computational developments that can complement experimental form screening of molecules for which conformational flexibility is significant. Current methods for crystal structure prediction are limited by the extent of molecular flexibility that can be practically handled due to the prohibitive computational cost associated with quantum mechanical calculations integrated in most of the successful approaches. In order to reduce the number of quantum mechanical evaluations, local approximate models can be defined for the estimation of the intramolecular energy, molecular geometry and the conformationally dependent intermolecular electrostatic model. A novel algorithm, CrystalOptimizer, for the accurate local minimisation of the lattice energy of crystals involving flexible organic molecules is presented. The main novelty of the algorithm is the use of dynamically constructed and updated local approximate models which essentially make available the full accuracy of quantum mechanical models at each and every iteration of the minimisation algorithm, requiring only a small number of explicit quantum mechanical calculations. This has made possible the accurate treatment of molecules involving a relatively large numbers of atoms with significant flexibility in torsional and bond angles and even bond lengths. The performance of the algorithm is critically assessed and demonstrated on a set of single and multi-component crystals. An extension of an existing algorithm for the identification of low energy crystal structures of flexible molecules, CrystalPredictor, is also described. In the proposed modification, the intramolecular energy and the molecular conformation are modelled using local approximate models. This provides a more realistic model for the effects of the flexible degrees of freedom on the molecular geometry and lattice energy. The use of deterministic low-discrepancy sequences ensures an extensive and uniform coverage of the multivariable search space. A parallelised implementation of the algorithm allows minimisations from several hundreds of thousands of initial guesses to be carried out in reasonable time. A further computational benefit is derived by the storage of the information used to construct the local approximate models in databases, which can be re-used in subsequent re-minimisation of structures with more accurate models for the lattice energy. The usefulness of these modifications is demonstrated on the ROY molecule, for which the structures of all experimentally known polymorphs are identified by the algorithm. By combining the above algorithms, a comprehensive multi-stage methodology for ab initio determination of the crystal structure of a given molecule based solely on its atomic connectivity is presented. The application of the methodology to two large and flexible molecules of pharmaceutical interest is also demonstrated

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

From small to big: understanding noncovalent interactions in chemical systems from quantum mechanical models

Noncovalent interactions in complex chemical systems are examined by considering model systems which capture the essential physics of the interactions and applying correlated electronic structure techniques to these systems. Noncovalent interactions are critical to understanding a host of energetic and structural properties in complex chemical systems, from base pair stacking in DNA to protein folding in organic solids. Complex chemical and biophysical systems, such as enzymes and proteins, are too large to be studied using computational techniques rigorous enough to capture the subtleties of noncovalent interactions. Thus, the larger chemical system must be truncated to a smaller model system to which rigorous methods can be applied in order to capture the essential physics of the interaction. Computational methodologies which can account for high levels of electron correlation, such as second-order perturbation theory and coupled-cluster theory, must be used. These computational techniques will be used to study several types (pi stacking, S/pi, and C-H/pi) of noncovalent interactions in two chemical contexts: biophysical systems and organic solids.Ph.D.Committee Chair: Sherrill, C. David; Committee Member: Bredas, Jean-Luc; Committee Member: El-Sayed, Mostafa A.; Committee Member: Harvey, Stephen C; Committee Member: Hernandez, Rigobert

Vibrational Anharmonicity in the Water-Nitrate Complex, Ice, and Gas Hydrates: Applications to Spectroscopy and Thermal Transport

Vibrational anharmonicity strongly influences the properties of gas-phase complexes and solids. Anharmonicity is responsible for the observation of “forbidden” vibrational transitions, thermal expansion, and phonon-phonon scattering. In the first portion of this dissertation the vibrational spectra of [(NO3-)(H2O)] and its isotopologues are examined through effective Hamiltonian and vibrational configuration interaction calculations employing ab initio force constants. While a harmonic treatment of the [(NO3-)(H2O)] infrared absorption spectrum predicts two OH stretch transitions, four strong peaks are experimentally observed. Anharmonic vibrational calculations confirm that the “extra” transitions are due to the rocking motion of the water molecule relative to the nitrate ion and a Fermi resonance between the OH stretch and water bend overtone. The second part of the dissertation explores the nature of the vibrational anharmonicity of gas hydrates and ice Ih as well as its effects on the structure and thermal conductivity. The arrangement of the hydrogen atoms in the solids and the gas-water interactions are found to have a strong influence on some of the properties of the crystals. Coarse-grained simulations and analytic scattering approximations qualitatively reproduce the observed behavior of the thermal conductivity of gas hydrates and ice. In addition, the calculations reveal that guest-host coupling cannot fully explain the differences in the thermal conductivity of gas hydrates and ice

Report on the sixth blind test of organic crystal structure prediction methods.

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.The organisers and participants are very grateful to the crystallographers who supplied the candidate structures: Dr. Peter Horton (XXII), Dr. Brian Samas (XXIII), Prof. Bruce Foxman (XXIV), and Prof. Kraig Wheeler (XXV and XXVI). We are also grateful to Dr. Emma Sharp and colleagues at Johnson Matthey (Pharmorphix) for the polymorph screening of XXVI, as well as numerous colleagues at the CCDC for assistance in organising the blind test. Submission 2: We acknowledge Dr. Oliver Korb for numerous useful discussions. Submission 3: The Day group acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. We acknowledge funding from the EPSRC (grants EP/J01110X/1 and EP/K018132/1) and the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC through grant agreements n. 307358 (ERC-stG- 2012-ANGLE) and n. 321156 (ERC-AG-PE5-ROBOT). Submission 4: I am grateful to Mikhail Kuzminskii for calculations of molecular structures on Gaussian 98 program in the Institute of Organic Chemistry RAS. The Russian Foundation for Basic Research is acknowledged for financial support (14-03-01091). Submission 5: Toine Schreurs provided computer facilities and assistance. I am grateful to Matthew Habgood at AWE company for providing a travel grant. Submission 6: We would like to acknowledge support of this work by GlaxoSmithKline, Merck, and Vertex. Submission 7: The research was financially supported by the VIDI Research Program 700.10.427, which is financed by The Netherlands Organisation for Scientific Research (NWO), and the European Research Council (ERC-2010-StG, grant agreement n. 259510-KISMOL). We acknowledge the support of the Foundation for Fundamental Research on Matter (FOM). Supercomputer facilities were provided by the National Computing Facilities Foundation (NCF). Submission 8: Computer resources were provided by the Center for High Performance Computing at the University of Utah and the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF grant number ACI-1053575. MBF and GIP acknowledge the support from the University of Buenos Aires and the Argentinian Research Council. Submission 9: We thank Dr. Bouke van Eijck for his valuable advice on our predicted structure of XXV. We thank the promotion office for TUT programs on advanced simulation engineering (ADSIM), the leading program for training brain information architects (BRAIN), and the information and media center (IMC) at Toyohashi University of Technology for the use of the TUT supercomputer systems and application software. We also thank the ACCMS at Kyoto University for the use of their supercomputer. In addition, we wish to thank financial supports from Conflex Corp. and Ministry of Education, Culture, Sports, Science and Technology. Submission 12: We thank Leslie Leiserowitz from the Weizmann Institute of Science and Geoffrey Hutchinson from the University of Pittsburgh for helpful discussions. We thank Adam Scovel at the Argonne Leadership Computing Facility (ALCF) for technical support. Work at Tulane University was funded by the Louisiana Board of Regents Award # LEQSF(2014-17)-RD-A-10 “Toward Crystal Engineering from First Principles”, by the NSF award # EPS-1003897 “The Louisiana Alliance for Simulation-Guided Materials Applications (LA-SiGMA)”, and by the Tulane Committee on Research Summer Fellowship. Work at the Technical University of Munich was supported by the Solar Technologies Go Hybrid initiative of the State of Bavaria, Germany. Computer time was provided by the Argonne Leadership Computing Facility (ALCF), which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357. Submission 13: This work would not have been possible without funding from Khalifa University’s College of Engineering. I would like to acknowledge Prof. Robert Bennell and Prof. Bayan Sharif for supporting me in acquiring the resources needed to carry out this research. Dr. Louise Price is thanked for her guidance on the use of DMACRYS and NEIGHCRYS during the course of this research. She is also thanked for useful discussions and numerous e-mail exchanges concerning the blind test. Prof. Sarah Price is acknowledged for her support and guidance over many years and for providing access to DMACRYS and NEIGHCRYS. Submission 15: The work was supported by the United Kingdom’s Engineering and Physical Sciences Research Council (EPSRC) (EP/J003840/1, EP/J014958/1) and was made possible through access to computational resources and support from the High Performance Computing Cluster at Imperial College London. We are grateful to Professor Sarah L. Price for supplying the DMACRYS code for use within CrystalOptimizer, and to her and her research group for support with DMACRYS and feedback on CrystalPredictor and CrystalOptimizer. Submission 16: R. J. N. acknowledges financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. [EP/J017639/1]. R. J. N. and C. J. P. acknowledge use of the Archer facilities of the U.K.’s national high-performance computing service (for which access was obtained via the UKCP consortium [EP/K014560/1]). C. J. P. also acknowledges a Leadership Fellowship Grant [EP/K013688/1]. B. M. acknowledges Robinson College, Cambridge, and the Cambridge Philosophical Society for a Henslow Research Fellowship. Submission 17: The work at the University of Delaware was supported by the Army Research Office under Grant W911NF-13-1- 0387 and by the National Science Foundation Grant CHE-1152899. The work at the University of Silesia was supported by the Polish National Science Centre Grant No. DEC-2012/05/B/ST4/00086. Submission 18: We would like to thank Constantinos Pantelides, Claire Adjiman and Isaac Sugden of Imperial College for their support of our use of CrystalPredictor and CrystalOptimizer in this and Submission 19. The CSP work of the group is supported by EPSRC, though grant ESPRC EP/K039229/1, and Eli Lilly. The PhD students support: RKH by a joint UCL Max-Planck Society Magdeburg Impact studentship, REW by a UCL Impact studentship; LI by the Cambridge Crystallographic Data Centre and the M3S Centre for Doctoral Training (EPSRC EP/G036675/1). Submission 19: The potential generation work at the University of Delaware was supported by the Army Research Office under Grant W911NF-13-1-0387 and by the National Science Foundation Grant CHE-1152899. Submission 20: The work at New York University was supported, in part, by the U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF-13-1-0387 (MET and LV) and, in part, by the Materials Research Science and Engineering Center (MRSEC) program of the National Science Foundation under Award Number DMR-1420073 (MET and ES). The work at the University of Delaware was supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF-13-1- 0387 and by the National Science Foundation Grant CHE-1152899. Submission 21: We thank the National Science Foundation (DMR-1231586), the Government of Russian Federation (Grant No. 14.A12.31.0003), the Foreign Talents Introduction and Academic Exchange Program (No. B08040) and the Russian Science Foundation, project no. 14-43-00052, base organization Photochemistry Center of the Russian Academy of Sciences. Calculations were performed on the Rurik supercomputer at Moscow Institute of Physics and Technology. Submission 22: The computational results presented have been achieved in part using the Vienna Scientific Cluster (VSC). Submission 24: The potential generation work at the University of Delaware was supported by the Army Research Office under Grant W911NF-13-1-0387 and by the National Science Foundation Grant CHE-1152899. Submission 25: J.H. and A.T. acknowledge the support from the Deutsche Forschungsgemeinschaft under the program DFG-SPP 1807. H-Y.K., R.A.D., and R.C. acknowledge support from the Department of Energy (DOE) under Grant Nos. DE-SC0008626. This research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC02-05CH11231. Additional computational resources were provided by the Terascale Infrastructure for Groundbreaking Research in Science and Engineering (TIGRESS) High Performance Computing Center and Visualization Laboratory at Princeton University.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1107/S2052520616007447