Modelling Molecular Flexibility for Crystal Structure Prediction Ogaga Glory Uzoh 14-01-2015 Submitted in partial fulfilment of the requirements for the degree of Doctor of Engineering to University College London Department of Chemistry University College London 20 Gordon Street London WC1H 0AJ United Kingdom 1 Declaration Declaration I, Ogaga Glory Uzoh, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. _______________ Ogaga Glory Uzoh January 2015 2 Abstract Abstract In the crystal packing of molecules wherein a single bond links aromatic groups, a change in the torsion angle can optimise close packing of the molecule. The improved intermolecular interactions, Uinter, outweigh the conformational energy penalty, Eintra, to give a more stable lattice energy, Elatt = Uinter +Eintra. This thesis uses this lattice energy model hierarchically in a new Crystal Structure Prediction (CSP) algorithm, CrystalPredictor version 1.6, which varies the low-barrier torsion angles at the start of generating hypothetical crystal structures. The crystal structure of 1-benzyl-1H-tetrazole was successfully predicted in an informal ‘blind test’ when given the chemical diagram and the number of molecules in the asymmetric unit cell. Then, the concept of whether specific molecular fragments favour polymorphism (i.e. polymorphophore) was investigated by analysing the crystal energy landscapes of the monomorphic fenamic acid and the polymorphic derivative tolfenamic acid. The CSP results show that the polymorphophore promotes but does not guarantee polymorphism and that the substituents on the polymorphophore fragment decide the relative energies of the crystal structures. Molecular Dynamics (MD) cannot use this lattice energy model because many ab initio calculations of Eintra on a single molecule are expensive. However, the examination of the physical origin of the torsional barrier in fenamates aided the derivation of an analytical model forEintra. This thesis develops codes for fitting analytical intramolecular force fields to ab initio conformational profiles of fenamates. An intramolecular exp-6 atom-atom term (for the non-bonded repulsion-dispersion contributions) plus a cosine term (that represents the changes to the Molecular Orbitals) accurately model the ab initio conformational energy surfaces of fenamic and tolfenamic acids. This thesis provides a first step in extendingEintra data generated from CSP studies to help MD on condensed phases of pharmaceutical-like organic molecules. 3 Dedication Dedication I dedicate this thesis to my wife, Jodi Uzoh, my mother, Felicia Uzoh, and my father, Emmanuel Uzoh. For their endless love, support, and encouragement. 4 Acknowledgments Acknowledgments Foremost, I would like to thank my supervisor, Professor Sally Price, for her support and direction throughout my time at UCL. Her encouragement and wise words at the start of my doctorate program were vital. My sincere gratitude to Louise Price for helping me to understand the practical aspects of the computational methods of Crystal Structure Prediction (CSP) and for the interesting and insightful discussions about research and life. My colleagues in Room G18 and friends at UCL made my time there fun, inspiring, and exciting. I would like to thank Rex Palmer for setting the informal blind test of Chapter 3 and for the subsequent collaborative paper. Many thanks to the Centre for Doctoral Training in Molecular Modelling and Materials Science (CDTM3S) at UCL for the rigorous training they gave me during the first year, and the yearly industrial day invitation to present my research. The opportunity to work with sixth form students in the third year, sponsored by CDTM3S, was one of the most rewarding experiences I had at UCL. My industrial sponsor, Cambridge Crystallographic Data Centre (CCDC), has been instrumental at every research stage. The encouragement received after presenting my work at the annual CCDC student day was invaluable. My industrial supervisors at CCDC––Aurora J. Cruz-Cabeza (a year and a half) and Peter Galek (two and a half years) ––have been instrumental in collaborative research and publications. I appreciate their insight, energy, time, and encouragement during our many meetings. Finally, this work would not be possible without the financial support from the CCDC and the Engineering and Physical Science Research Council (EPSRC) under the CDTM3S grant EP/G036675/1. 5 List of Publications List of Publications 1. Uzoh, O. G.; Cruz-Cabeza, A. J.; Price, S. L. Is the Fenamate Group a Polymorphophore? Contrasting the Crystal Energy Landscapes of Fenamic and Tolfenamic Acids. Cryst. Growth Des. 2012, 12 (8), 4230-4239. 2. Spencer, J.; Patel, H.; Deadman, J. J.; Palmer, R. A.; Male, L.; Coles, S. J.; Uzoh, O. G.; Price, S. L. The Unexpected but Predictable Tetrazole Packing in Flexible 1-Benzyl-1H-Tetrazole. CrystEngComm 2012, 14 (20), 6441-6446. I carried out all the computational work and prepared the manuscript. 3. Uzoh, O. G.; Galek, P. T. A; Price, S. L. Towards more Accurate Force Fields for pharmaceutical molecules – Analysing the Conformational Energy Profiles of Fenamates. 2014, (Submitted). 6 Table of Contents Table of Contents Modelling Molecular Flexibility for Crystal Structure Prediction .................... 1 Declaration .............................................................................................................. 2 Abstract ................................................................................................................... 3 Dedication ............................................................................................................... 4 Acknowledgments .................................................................................................. 5 List of Publications ................................................................................................. 6 Table of Contents .................................................................................................... 7 List of Figures ....................................................................................................... 11 List of Tables ........................................................................................................ 18 List of Abbreviations ............................................................................................ 20 List of Symbols ..................................................................................................... 21 Chapter 1. Introduction .................................................................................... 22 1.1. Background .......................................................................................................... 22 1.2. Scope and Outline of Thesis ................................................................................ 26 Chapter 2. Theoretical Background ................................................................. 27 2.1. Overview .............................................................................................................. 27 2.2. Intermolecular Forces ........................................................................................... 27 2.2.1. Pairwise Additivity ................................................................................................... 28 2.2.2. Physical Origin of Intermolecular Force .................................................................. 29 2.2.3. Long-range Interactions ........................................................................................... 30 2.2.4. Short-range Interactions ........................................................................................... 31 2.2.5. Penetration Energy and Charge Transfer ................................................................. 32 2.3. Modelling the Intermolecular Forces for Organic Molecules .............................. 32 2.3.1. Repulsion-Dispersion Potentials .............................................................................. 33 2.3.2. Electrostatics Potential ............................................................................................. 34 2.4. Intramolecular Energy .......................................................................................... 36 2.5. Force Fields (Atomistic Modelling) ..................................................................... 38 2.5.1. AMBER .................................................................................................................... 41 2.5.2. CHARMM ................................................................................................................ 42 2.5.3. Other Force Fields .................................................................................................... 42 2.5.4. The Limits of Current Force Fields .......................................................................... 43 7 Table of Contents 2.6. The Fitting Routine .............................................................................................. 44 2.6.1. Linear Least Square Method ..................................................................................... 44 2.6.2. Subroutine for Solving Least Squares....................................................................... 46 2.7. Electronic Structure Methods ............................................................................... 47 2.7.1. Hartree Fock Theory ................................................................................................