University of California Santa Barbara Microwave Spectroscopy Algorithms for Context-Free Molecular Structure Determination A dissertation submitted in partial satisfaction of the requirements for the degree Bachelor of Science in Physics by Lia Yeh Committee in charge: Professor David Patterson, Chair Professor Sathya Guruswamy June 2020 The Dissertation of Lia Yeh is approved. Professor Sathya Guruswamy Professor David Patterson, Committee Chair June 2020 Should this text outlive me, so shall this dedication: To the best family I have ever had, the friends from my teenage years who spiced up my writing, and the friends I have made at UC Santa Barbara. iii Acknowledgements I could not have gotten anywhere near who I’ve become through this journey if not for the following persons. First and foremost, thanks to my physics academic advisor and teacher Professor Sathya Guruswamy, who first believed that I could be a physicist and a researcher. Thanks to my computer science academic advisors Professor Phill Conrad and Professor Richert Wang for all they’ve done so that Room 143 is home to some of my most cherished memories. Thanks to my research advisor Professor David Patterson, who is all in one person, creative and curious and thoughtful, and who I used to think was crazy for telling me two years ago that he thought I would come up with a solution to the spectral line assignment problem. I stand corrected and present this thesis as proof. I will sorely miss our lab (wow, has our group grown!) — for being people who learn from and support each other, and who endure Dave’s analogies and my antics. Special thanks to Lincoln Sattherthwaite and Greta Koumarianou for mentoring me; I will pass it forward. Lastly, tongue in cheek, I thank you, the reader, in advance because your plausible existence stirs me to write this. iv Abstract Microwave Spectroscopy Algorithms for Context-Free Molecular Structure Determination by Lia Yeh Modern microwave spectrometers, including the ones in our lab, can quickly and accurately measure thousands of frequencies which are absorbed by a given molecule. Our goal is to develop a black box methodology to infer molecular structure from these frequencies. The catch is that we aim for a context-free approach; in other words, we know nothing about the molecules we want to analyze except that we can take a microwave spectrum of it. The process of extracting information about the molecules present in our spectra is an inverse problem – you don’t know what you are looking for until you’ve found it. It has been a decades-long goal of the spectroscopy community to procedurally assign even theoretical spectra efficiently. Our algorithm, Robust Automated Assignment of Rigid Rotors (RAARR), is the first to analyze experimental spectra of complex mixtures, successfully assigning rotational constants in seconds for dozens of experimental spectra. We outperform prior brute-force automated approaches utilizing the fact that the rotational physics of most molecules at 6 Kelvin are well-approximated by simple patterns, such as quantization and conservation of energy. v Contents Abstract v Introduction 1 0.1 Outline of This Thesis ............................ 2 1 Rotational Physics of Molecules 4 1.1 The Rigid Rotor Hamiltonian ........................ 4 1.2 Kraitchman’s Equations ........................... 11 2 Microwave Spectroscopy 13 2.1 CP-FTMW Spectrometer of the Patterson Group ............. 14 2.2 Interpreting Spectra ............................. 16 2.3 Software Tooling ............................... 25 2.4 All RAARR’s Context-Free Assignments .................. 28 3 Robust Automated Assignment of Rigid Rotors (RAARR) 32 3.1 The RAARR Algorithm ........................... 33 3.2 Patterns in Rotational Spectra ....................... 35 3.3 a-type Series Algorithm ........................... 36 3.4 b-type Series Algorithm ........................... 42 3.5 Mixture Component Analysis ........................ 49 3.6 Limitations and Ongoing Work ....................... 52 3.7 Downloading and Running RAARR ..................... 54 4 Predicting Atom Positions from Rotational Constant Analysis (PA- PRCA) 56 4.1 Problem Statement .............................. 56 4.2 Unambiguous Atom Positions From Doubly-Substituted Isotopologues .. 58 4.3 Unambiguous Atom Positions From g-factor Measurements ........ 61 Conclusion 68 vi A Background on Physics of Rotations 69 Bibliography 74 vii Introduction Almost everything you can name is made of molecules; therefore, if we better under- stand molecules, we can better understand everything. This thesis presents my research in developing a methodology for determining the chemical composition and molecular structures of an unknown mixture, as long as we can take a microwave spectrum of it. After all, for measuring molecular structure parameters, microwave spectroscopy is arguably the most accurate tool available. There are too many applications to count motivating this work. To name a few po- tential uses of a molecular structure detector, we might want to reverse-engineer or detect counterfeit pharmaceuticals; probe molecules of atmospheric, extraterrestrial, or existen- tial interest; or perform molecular diagnostics to analyze biological markers. While not explored in this work, a central focus of our lab’s research is experimentally differenti- ating between different enantiomers (e.g. left-handedness versus right-handedness) ofa molecule utilizing microwave spectroscopy, for which in general spectral assignment is a prerequisite. Figure 0.1 gives a high level overview of our efforts. To determine molecular structure, first, we assign rotational constants to species in a microwave spectrum of an unknown mixture. Second, we determine positions of atoms in the molecule given many sets of rotational constants. 1 Introduction Figure 0.1: My research is on building methodologies and software to analyze chemical composition of an unknown mixture, concerning all but the very left of this figure. 0.1 Outline of This Thesis The body of this thesis is divided into four chapters. The first chapter, the background, is a theoretical foundation of the rotational physics of molecules. We discuss: • linear, symmetric, and asymmetric rigid rotor Hamiltonians • rotational constants and centrifugal distortion constants • Ray’s asymmetry parameter and the prolate and oblate rigid rotor limits • rotational quantum numbers Ka, Kc, and J • a-type, b-type, and c-type; and P-, Q-, and R-branch transitions • Kraitchman’s equations and Costain’s rule The second chapter focuses on microwave spectroscopy: how we take spectra, simulate them, and visualize them. We inspect our assigned spectra and their features, discuss limitations at three levels of abstraction, and comment on useful software tools. The third chapter is on the microwave spectral line assignment problem, which is a prerequisite task for analyzing molecular structure. Under a dozen experts in the world are capable of doing this task by hand, typically taking several hours. In the past two decades, many groups have attempted to automate this task. Our algorithm, 2 Introduction Robust Automated Assignment of Rigid Rotors (RAARR), is context-free, works on a broad range of molecules, and is by our estimate up to 40,000 times faster than the leading comparable automated solution. We make the daunting task of assigning the spectrum, without a clue what is in it, simpler by reducing the task to that of pattern- finding. These patterns which we call loops, series, and scaffolds, arise from conservation of energy, quantization of energy, and other features of the underlying physics. We discuss four variants of RAARR: 2 variants which work for most species with strong a-type and b-type transitions (a very common case in the real world), 1 variant which works for most species with strong a-type transitions, and 1 variant on which we have made progress targeting species with strong b-type transitions. The fourth chapter is on Predicting Atom Positions from Rotational Constant Anal- ysis (PAPRCA). In essence, this project is to deduce molecular structure from sets of rotational constants obtainable from a spectrum. Using Kraitchman’s equations, for any atom that undergoes isotopic substitution such that we can assign the isotopologue’s rotational constants, we can get the unsigned position of the atom in molecular axes coordinates. What we would like to know is the signed x, y, and z position of each atom in the molecule. What we get from Kraitchman’s equations is the unsigned x, y, and z position of each atom in the molecule for which we can assign rotational constants to the isotopologue of. Guessing is computationally not an option: since each atom could be in eight possible octants, for N atoms there are 8N−1 possible configurations. We investigate two methodologies to resolve sign ambiguities of Kraitchman’s substitution coordinates: assignment of doubly-substituted isotopologues, and precision measurement of the electric dipole moment and magnetic g-factor of singly-substituted isotopologues. We conclude that we require more precise instrumentation to realize these methodologies for any experimental spectrum, and give our results for the precision that if achieved, would enable context-free molecular structure determination. 3 Chapter 1 Rotational Physics of Molecules Our central question is: Given the rotational spectrum of a molecule and no other knowledge of the molecule, how well can we guess the structure of the molecule? 1.1 The Rigid