HERIOT-WATT UNIVERSITY Advances in the Theoretical Determination of Molecular Structure with Applications to Anion Photoelectron Spectroscopy by Zibo G. Keolopile A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in the School of Engineering and Physical Sciences Institute of Chemical Sciences December 2013 The copyright in this thesis is owned by the author. Any quotation from the thesis or use of any information contained in it must acknowledge this thesis as the source of the quotation or information. ACADEMIC REGISTRY Research Thesis Submission Name: Zibo Goabaone Keolopile School/PGI: Engineering and Physical Sciences Version: (i.e, Frst, First Degree Sought PhD Theoretical and Computational Resubmission, Final) (Award and Chemistry Subject area) I, ZIBO G. KEOLOPILE, declare that this thesis titled, `ADVANCES IN THE THEO- RETICAL DETERMINATION OF MOLECULAR STRUCTURES WITH APPLICA- TION TO ANION PHOTOELECTRON SPECTROSCOPY' and the work presented in it are my own. I confirm that: This work was done wholly or mainly while in candidature for a research degree at this University. Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated. Where I have consulted the published work of others, this is always clearly at- tributed. Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. I have acknowledged all main sources of help. Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself. Signed: Date: i \Quantum mechanics describes nature as absurd from the point of view of common sense. And yet it fully agrees with experiment. So I hope you can accept nature as She is - absurd." Richard P. Feynman HERIOT-WATT UNIVERSITY Abstract School of Engineering and Physical Sciences Institute of Chemical Sciences Doctor of Philosophy by Zibo G. Keolopile This Dissertation is focussed primarily on development of methods aiming at the deter- mination of molecular structures with application to systems with intra and intermolec- ular hydrogen bonds. I have developed and demonstrated usefulness of Potential Energy Surface Scanning Tool (PESST) by performing a systematic search for the most stable structures of neutral and anionic phenylalanine and tyrosine molecules using electronic structure methods. I have found out that tautomers resulting from the proton transfer from the carboxylic OH to phenyl ring determine the structure of the most stable anions of phenylalanine, but double proton transfer from the carboxylic and hydroxyl groups determine structures of the most stable anions of tyrosine. The most stable conformer of these valence anions remained adiabatically unbound with respect to the canonical neutral in case of phenylalanine but bound in case of tyrosine. Valence anions identified in this report have recently been observed experimentally. Acetoacetic acid (AA), equipped with neighbouring carboxylic and keto groups, is a promising system for studies of intramolecular proton transfer. The results of my com- putational search for the most stable tautomers and conformers of the neutral and anionic AA were used to interpret anion photoelectron and electron energy-loss spec- troscopy measurements. The valence anion was identified in photoelectron spectroscopy experiments and the measured electron vertical detachment energy is in good agreement with my computational predictions. My computational results allow rationalizing these experimental findings in terms of the co-existence of various conformers of AA. I considered stability of dimers formed by molecules that can exist in different con- formational states. I have developed a protocol that allows the dissection of the total stabilisation energy into one-body conformational and deformational components and the two-body interaction energy term. Interplay between these components determines the overall stability of the dimer. The protocol has been tested on the dimers of oxalic acid. The global minimum stability results from a balancing act between a moderately attractive two-body interaction energy and small repulsive one-body terms. I have anal- ysed zero-point vibrational corrections to the stability of various conformers of oxalic acid and their dimers. I have found that minimum energy structures with the most sta- bilising sets of hydrogen bonds have the largest zero-point vibrational energy, contrary to a naive anticipation based on red shifts of OH stretching modes involved in hydrogen bonds. My computational results demonstrated an unusual electrophilicity of oxalic acid (OA), the simplest dicarboxylic acid. The electrophilicity results primarily from the bonding carbon-carbon interaction in the SOMO orbital of the anion, but it is further enhanced by intramolecular hydrogen bonds. The well-resolved structure in the photoelectron spectrum has been reproduced theoretically, based on Franck-Condon factors for the vibronic anion!neutral transitions. The excess electron binding energies in the dimer and trimer of OA become very significant due to intermolecular proton transfer, with the corresponding vertical detachment energy (VDE) values of approximately 3.3 and 4.6 eV. I have postulated a mechanism of excess electron mobility along molecular linear chains supported by cyclic hydrogen bonds. Searches for the most stable molecular conformer are frustrated by energy barriers sepa- rating minima on the potential energy surface (PES). I have suggested that the barriers might be suppressed by subtracting selected force field terms from the original PES. The resulting deformed PES can be used in standard molecular dynamics (MD) or Monte Carlo simulations. The MD trajectories on the original and deformed PESs of ethanolamine differ markedly. The former gets stuck in a local minimum basin while the latter moves quickly to the global minimum basin. Acknowledgements I gratefully acknowledges the financial support and fellowship from the University of Botswana (UB). 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. DE-AC02-05CH11231. Computer resources were also provided by Heriot-Watt University. This material is based (in part) on experimental work which was supported by the (US) National Science Foundation through grant number, CHE-1111693. I gratefully acknowledge the support of my supervisor Prof. Maciej Stephan Gutowski through out my PhD study. His excellent guidance and generous support brought me this far. I would also like to thank my collaborator Dr. Maciej Haranczyk at Lawrence Berkeley National Laboratory for his support, guidance and most importantly to work in his team. My experimental collaborators at Johns Hopkins University lead by Dr. Kit H. Bowen are also gratefully acknowledged. My colleagues in the Gutowski, Paterson and Macgregor groups at Heriot-Watt, and our past PhD and project students, in partic- ular (but not limited to) Alexander V. Abramov, Sanliang Ling, Alexander Whiteside, Matthew R. Ryder, Brian Cox, David Grist, Calum Sloan and Benjamin Calzada. I would like to express my gratitude to my family and friends for their companionship, support and patience over the past years of study. vi Contents Declaration of Authorshipi Abstract iii Acknowledgements vi List of Figures xi List of Tables xviii Abbreviations xxi Physical Constants xxiii Symbols xxiv List of Papers xxvi 1 Introduction1 1.1 Molecular Structure Models..........................2 1.1.1 Lewis structures Model........................2 1.2 Mathematical Models.............................4 1.3 The Potential Energy Surface..........................5 1.4 Deterministic Models for molecular structures................ 12 1.5 Stochastic Methods for molecular structures................. 13 1.6 Experimental Determination of Molecular Structures............ 15 2 Classical Methods 22 2.1 Force Fields................................... 22 2.1.1 The stretch energy........................... 23 2.1.2 The bending energy.......................... 24 2.1.3 The torsional energy.......................... 25 2.1.4 Cross terms: Class 1, 2 and 3 Force Fields.............. 26 2.1.5 The van der Waals energy....................... 26 2.1.6 The electrostatic energy........................ 29 vii Contents viii 2.2 Geometry Optimization, (Mathematical methods of)............ 30 2.2.1 The Steepest Descent Method..................... 31 2.2.2 The Newton-Raphson Method.................... 32 2.3 Molecular Dynamics Algorithms/Schemes.................. 37 2.3.1 The Verlet algorithm.......................... 39 2.3.2 Leapfrog algorithm........................... 40 2.3.3 The velocity Verlet scheme...................... 41 2.3.4 The Beeman Scheme.......................... 41 2.4 Explicit Models for Tautomeric/Conformational Search.......... 42 2.4.1 Stochastic Search Methods...................... 43 3 Molecular Orbital Theory 45 3.1 Fundamental Aproximations.......................... 45 3.1.1 The Schr¨odingerEquation....................... 45 3.1.2 The Born-Oppenheimer approximation................ 51 3.1.3 Trial Wave Functions (Variational Principle)............ 52 3.2 The Hartree-Fock Theory (Principles of)................... 52 3.2.1 The Roothan equations.......................