DFT CALCULATIONS OF MAGNETIC SHIELDING AND QUADRUPOLAR COUPLING IN ORDERED SYSTEMS: METHODS AND APPLICATIONS TO NMR CRYSTALLOGRAPHY by Sean T. Holmes A dissertation submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemistry and Biochemistry Winter 2017 © 2017 Sean Holmes All Rights Reserved ProQuest Number:10256206 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest 10256206 Published by ProQuest LLC ( 2017). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 DFT CALCULATIONS OF MAGNETIC SHIELDING AND QUADRUPOLAR COUPLING IN ORDERED SYSTEMS: METHODS AND APPLICATIONS TO NMR CRYSTALLOGRAPHY by Sean T. Holmes Approved: __________________________________________________________ Murray V. Johnston, Ph.D. Chair of the Department of Chemistry and Biochemistry Approved: __________________________________________________________ George H. Watson, Ph.D. Dean of the College of Arts and Sciences Approved: __________________________________________________________ Ann L. Ardis, Ph.D. Senior Vice Provost for Graduate and Professional Education I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: __________________________________________________________ Cecil Dybowski, Ph.D. Professor in charge of dissertation I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: __________________________________________________________ Tatyana Polenova, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: __________________________________________________________ Shi Bai, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: __________________________________________________________ Robbie Iuliucci, Ph.D. Member of dissertation committee ACKNOWLEDGMENTS I would like to begin by expressing my sincerest gratitude to my advisor, Professor Cecil Dybowski, for his mentorship over the past five years. I would also like to thank the other members of our research group, Dr. Fahri Alkan, Anna Murphy, and Yao Yao. I thank the members of my dissertation committee, Prof. Tatyana Polenova, Prof. Shi Bai, and Prof. Robbie Iuliucci, for their continued input throughout the completion of this work. I also thank Prof. Cynthia Jameson for helpful discussions regarding this work. Several undergraduate students, namely John Lora, Shelby Chan, and Ashley Knoerdel, have worked with me on various projects, and I would like to thank them for their contributions. Computational resources necessary for the completion of this dissertation were generously provided by Prof. Karl Mueller and Pennsylvania State University Center for Nanoscale Science. This dissertation incorporates portions of my previously published work. Chapter 2 contains material from “Density functional investigation of intermolecular effects on 13C NMR chemical-shielding tensors modeled with molecular clusters”, adapted with permission from Journal of Chemical Physics, 2014, 141 (16), 164121. DOI: 10.1063/1.4900158. Copyright 2014 AIP Publishing. Chapter 3 is based on “Carbon-13 chemical-shift tensors in indigo: a two-dimensional NMR-ROCSA and DFT study”, and adapted with permission from Solid State Nuclear Magnetic Resonance, 2015, 72, 90-95. DOI: 10.1016/j.ssnmr.2015.08.004. Copyright 2015 Elsevier. Chapter 4 is based on “Critical analysis of cluster models and exchange- correlation functionals for calculating magnetic shielding in molecular solids”, and iv adapted with permission from Journal of Chemical Theory and Computation, 2015, 11 (11), 5229-5241. DOI: 10.1021/acs.jctc.5b00752. Copyright 2016 American Chemical Society. Chapter 5 is based on “Calculations of solid-state 43Ca NMR parameters: a comparison of periodic and cluster approaches and an evaluation of DFT functionals”, which is under review for publication by the Journal of Computational Chemistry. Chapter 6 is based on “Analysis of the bond-valence method for calculating 29Si and 31P magnetic shielding in covalent network solids”, and adapted with permission from Journal of Computational Chemistry, 2016, 37 (18), 1704-1710. DOI: 10.1002/jcc.24389. Copyright 2016 John Wiley and Sons. Chapter 7 is based on “Semi-empirical refinements of crystal structures using 17O quadrupolar-coupling tensors”, which is under review for publication by the Journal of Chemical Physics. v TABLE OF CONTENTS LIST OF TABLES ......................................................................................................... x LIST OF FIGURES ..................................................................................................... xiv ABSTRACT ................................................................................................................ xxi Chapter 1 INTRODUCTION .............................................................................................. 1 1.1 Motivation and Outline .............................................................................. 1 1.2 Introduction to Nuclear Magnetic Resonance Spectroscopy ..................... 4 1.3 Magnetic-Shielding Tensors ...................................................................... 6 1.4 Quadrupolar-Coupling Tensors ............................................................... 10 1.5 Overview of Electronic Structure Methods ............................................. 13 1.6 Exchange-Correlation Functionals .......................................................... 18 1.6.1 The Local-Density Approximation .............................................. 18 1.6.2 The Generalized-Gradient Approximation .................................. 19 1.6.3 The Meta-Generalized-Gradient Approximation ........................ 20 1.6.4 Hybrid Methods ........................................................................... 20 1.7 Theory and Calculation of Quadrupolar-Coupling Tensors .................... 21 1.8 Theory and Calculation of Magnetic-Shielding Tensors ......................... 22 REFERENCES ........................................................................................................ 28 2 THE SYMMETRY-ADAPTED CLUSTER ANSATZ: CALCULATIONS OF 13C MAGNETIC-SHIELDING TENSORS ............................................... 36 2.1 Introduction ............................................................................................. 36 2.1.1 Models for Computing Magnetic Shielding in Solids ................. 37 2.2 Materials, Computational Details, and Analysis ..................................... 46 2.3 Results and Discussion ............................................................................ 50 2.3.1 Size Requirements for Molecular Clusters .................................. 50 2.3.2 Symmetry Requirements for Molecular Clusters ........................ 52 2.3.3 Locally-Dense Basis Sets ............................................................ 55 2.3.4 Relationship between Calculated and Experimental Results ...... 56 2.3.5 Analysis of Magnetic Shielding Principal Components .............. 62 vi 2.3.6 Effects of Plane-Wave Structural Refinements on Calculated Shielding ...................................................................................... 69 2.4 Conclusions ............................................................................................. 71 REFERENCES ........................................................................................................ 73 3 CARBON-13 CHEMICAL-SHIFT TENSORS IN INDIGO: A TWO- DIMENSIONAL NMR-ROCSA AND DFT STUDY ..................................... 84 3.1 Introduction ............................................................................................. 84 3.2 Experimental Methods ............................................................................. 86 3.3 Computational Methods .......................................................................... 86 3.4 Results and Discussion ............................................................................ 88 3.4.1 NMR Measurements and Peak Assignments .............................. 88 3.4.2 Discussion of 13C Chemical-Shift Tensors of Indigo .................. 89 3.4.3 Assessment of Lattice Effects ..................................................... 96 3.5 Conclusion ............................................................................................... 99 REFERENCES .....................................................................................................