Syracuse University SURFACE Dissertations - ALL SURFACE December 2014 Evaluation of Non-Covalent Interaction Models in Molecular Crystals Using Terahertz Spectroscopy Thomas Juliano Syracuse University Follow this and additional works at: https://surface.syr.edu/etd Part of the Physical Sciences and Mathematics Commons Recommended Citation Juliano, Thomas, "Evaluation of Non-Covalent Interaction Models in Molecular Crystals Using Terahertz Spectroscopy" (2014). Dissertations - ALL. 168. https://surface.syr.edu/etd/168 This Dissertation is brought to you for free and open access by the SURFACE at SURFACE. It has been accepted for inclusion in Dissertations - ALL by an authorized administrator of SURFACE. For more information, please contact [email protected]. Abstract Density functional theory (DFT) is a powerful tool that can be used to evaluate the low- frequency vibrational spectra of solid-state crystalline materials. Since THz spectroscopy is sensitive to both the intermolecular and intramolecular forces that govern the formation of crystalline materials, it is an ideal tool to investigate the accuracy of calculated DFT crystal structures and their vibrational spectra. When using solid-state DFT, non-covalent dispersion interactions are not fully treated in typical approaches. In order to account for these interactions, the addition of dispersion force correction terms are necessary. A number of methods exist to correct for this deficiency of DFT, and this work investigates the use of semi-empirical London dispersion force correction models. Through the investigation of several small organic molecules, amino acids and related compounds, the standard implementation (referred to as DFT-D) is examined, and the need to alter this standard approach has been identified. Modifications of the scaling factor and atomic parameters within this method have led to more accurate simulations, termed the DFT-DX model. In addition to this work on improving London dispersion force corrections, solid-state DFT calculations with these enhancements can be used to predict the crystal structures of previously unknown or difficult to synthesize materials, such as amino acid hydrates, and achieve detailed information about the internal and external forces in molecular crystals. EVALUATION OF NON-COVALENT INTERACTION MODELS IN MOLECULAR CRYSTALS USING TERAHERTZ SPECTROSCOPY by Thomas R. Juliano Jr. B.S. University at Buffalo, 2011 M.Phil. Syracuse University, 2013 Dissertation Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemistry Syracuse University December 2014 Copyright © Thomas R. Juliano Jr. 2014 All Rights Reserved Acknowledgments This project would not have been possible without the help and support of a number of people. First and foremost, I would like to thank Dr. Timothy Korter. As my advisor, he assisted me through all of the work presented here. He worked with me daily, ensuring that everything was moving along smoothly, and when problems arose, he was there to help me figure them out. I would like to thank Dr. Ari Chakraborty and Dr. Joe Chaiken who have been my main two committee members since my second year research proposal. I would also like to thank the rest of my committee members, Dr. Lisa Manning, Dr. Bruce Hudson, and Dr. Tara Kahan, for taking the time to read my thesis and be a part of my defense. I also need to thank the Chemistry department office staff, who was very helpful throughout my time here, especially while getting ready for my defense. I also thank the friends that I have made here and especially the current and former members of the Korter group. Dr. Matt King, Dr. Ewelina Witko, and Dr. Sean Delaney assisted me when I joined the group and showed me what I would need to do to make it to this day, and Mike Ruggiero who is a current group member that played a large role in our international travels. My family has supported me throughout this entire process since day one, and for this I thank them. No matter how things were going, I could always count on them to be behind me. I also would like to thank my wife, Stephanie. She moved out here with me with no questions asked and has been the main force behind me when I was less-than-motivated. Finally I would like to thank the NSF and Syracuse University for their support which allows all of this research to take place. iv Table of Contents Acknowledgments.......................................................................................................................... iv List of Illustrative Materials......................................................................................................... viii CHAPTER 1: Introduction ............................................................................................................. 1 1.1 Research Objectives .............................................................................................................. 1 1.2 Terahertz Spectroscopy ......................................................................................................... 7 1.3 Solid-State Density Functional Theory ............................................................................... 14 1.3.1 Quantum Theory ........................................................................................................... 14 1.3.2 Density Functional Theory ........................................................................................... 16 1.3.2.1 Density Functionals ............................................................................................... 18 1.3.2.2 Local Density Approximations .............................................................................. 19 1.3.2.3 Generalized Gradient Approximations .................................................................. 19 1.3.2.4 Hybrid Functionals................................................................................................. 21 1.3.3 Basis Sets ...................................................................................................................... 22 1.3.3.1 Pople-style Basis Sets ............................................................................................ 23 1.3.3.2 Correlation-consistent Split-valence Basis Sets..................................................... 24 1.3.4 Density Functional Theory in the Solid State ............................................................... 25 1.3.4.1 Reciprocal Space, the Brillouin Zone, and Bloch Functions ................................. 25 1.3.4.2 Periodic Boundary Conditions ............................................................................... 28 1.3.4.3 Geometry Optimizations ........................................................................................ 31 1.3.4.4 Vibrational Mode Calculations .............................................................................. 32 1.3.4.4.1 Vibrational Frequencies .................................................................................. 32 1.3.4.4.2 Infrared Intensities........................................................................................... 34 1.3.4.5 Dispersion Forces................................................................................................... 34 1.4 References ........................................................................................................................... 41 CHAPTER 2: Terahertz Spectroscopy in the Korter Group ......................................................... 50 2.1 Time-Domain Terahertz Spectrometer................................................................................ 50 2.2 Terahertz Generation and Detection ................................................................................... 52 2.2.1 Optical Rectification ..................................................................................................... 52 2.2.2 Free-Space Electro-Optic Sampling ............................................................................. 54 2.3 Sample Preparation ............................................................................................................. 55 2.4 Data Acquisition and Processing......................................................................................... 56 2.5 References ........................................................................................................................... 59 CHAPTER 3. Use of Solid-State Density Functional Theory in the Korter Group ..................... 60 3.1 CRYSTAL Software Package ............................................................................................. 60 3.2 Unit Cell Optimizations ...................................................................................................... 62 3.3 Frequency Calculations ....................................................................................................... 64 3.4 Energy Calculations ............................................................................................................ 67 v 3.4.1 Total Electronic Energy ................................................................................................ 67 3.4.2 Conformational and Cohesive Energies ....................................................................... 67 3.4.3 Basis Set Superposition Error ....................................................................................... 69 3.6 References ..........................................................................................................................