QUANTITATIVE PREDICTION OF SPECTRAL PROPERTIES OF POLARITY SENSITIVE DYES USING A MD/QM APPROACH by Swapnil Baral 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 Physics Summer 2020 © 2020 Swapnil Baral All Rights Reserved QUANTITATIVE PREDICTION OF SPECTRAL PROPERTIES OF POLARITY SENSITIVE DYES USING A MD/QM APPROACH by Swapnil Baral Approved: Edmund Nowak, Ph.D. Chair of the Department of Physics and Astronomy Approved: John Pelesko, Ph.D. Dean of the College of Arts and Sciences Approved: Douglas J. Doren, Ph.D. Interim Vice Provost for Graduate and Professional Education and Dean of the Graduate College 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 dis- sertation for the degree of Doctor of Philosophy. Signed: Edward Lyman, 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 dis- sertation for the degree of Doctor of Philosophy. Signed: Björn Baumeier, 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 dis- sertation for the degree of Doctor of Philosophy. Signed: Sandeep Patel, 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 dis- sertation for the degree of Doctor of Philosophy. Signed: Lars Gundlach, 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 dis- sertation for the degree of Doctor of Philosophy. Signed: James MacDonald, Ph.D. Member of dissertation committee ACKNOWLEDGEMENTS I want to acknowledge the advice and support of many people and organiza- tions. This dissertation would not have been possible without my direct supervisor Dr. Edward R. Lyman, whose guidance and limitless patience have helped me de- velop professionally and become a critically thinking scientist. A huge thank you for mentoring and guiding me to complete this work. You have always encouraged me to focus on research and supported me to present my work at several conferences. I also want to thank all the group members (undergraduates, graduate students, and postdoctoral researchers) of our group (Lyman Group) from 2014 to 2020 for the engaging physics discussion on countless occasions. I want to thank Dr. Björn Baumeier (Eindhoven University of Technology (TU/e)), who taught me a lot about quantum mechanical calculations, especially the GW -BSE and its implementation in VOTCA-XTP. This work would not have been possible without the collaboration of Baumeier Research Group. I also thank you for generously covering a significant portion of my visit to TU/e. I want to express my gratitude towards Dr. Sandeep Patel for generously pro- viding about year-long financial support to me. You have also helped me understand the importance of Laurdan research and taught me how to get started with quantum calculations in Gaussian, especially during my early days in graduate school. I want to thank Dr. Lars Gundlach for raising profound discussions about my research and motivating me every time we met. Your group (Gundlach Group), v thorough our collaboration, has played a crucial role in testing the results of my calculations. I want to thank Dr. James MacDonald for supporting me throughout my stay at UD and agreeing to serve on my committee. You have been extremely helpful even before I joined UD during the application process. I want to thank Dr. Jeffrey R. Comer (Kansas State University) for helping me compute the Adaptive Biasing Force calculation and Dr. Alex MacKerell and Dr. Fang-Yu Lin (University of Maryland, Baltimore) for teaching me protocols of CHARMM Force Field parametrization. This work was supported by a National Institutes of Health grant NIH R01GM116961. Computations were performed on the Stampede supercomputer at the Texas Advanced Computing Center of the University of Texas at Austin (sup- ported through the XSEDE program of the NSF (TG-MCB170146)) which is sup- ported by National Science Foundation grant number ACI-1548562. I want to express my gratitude towards all the faculty, staff, and members in the Department of Physics and Astronomy (DPA) at the University of Delaware for continuously supporting me in times of need. Thanks to Physics and Astronomy Graduate Student Association for allowing me to serve as a vice-president (2015-2016), Graduate Student Government for al- lowing me to serve as a senator representing DPA (2016-2017), and Nepalese Student Association for allowing me to serve as the president (2017-2018). I want to thank all my teachers and mentors, from my first schools, River Valley and Pushpa Sadan Boarding High School, to the current school, the University of Delaware. I also want to remember the physics department at the National School of Sciences (Lainchaur, Kathmandu), the University of Texas at Arlington, and the Georgia Institute of Technology. vi I want to express my love to my mother, Dr. Sushma Banskota Baral, who was the first person to support me when I decided to study Physics in the United States. I want to thank my father, Dr. Krishnahari Baral, the hero of my life, for helping me pursue a career in Physics. I want to dedicate this work to both of you. I want to remember my siblings (Smriti Baral and Swikriti Baral), relatives, and friends who always stand by my side and continuously support me. I express my love to my wife, Aastha Dahal, for supporting me on my journey. Without your colorful smile, everything I achieve becomes colorless. vii TABLE OF CONTENTS LIST OF TABLES ::::::::::::::::::::::::::::::: xiii LIST OF FIGURES :::::::::::::::::::::::::::::: xv ABSTRACT :::::::::::::::::::::::::::::::::: xxii Chapter 1 BILAYERS AND CELL MEMBRANES: COMPOSITION, PHASES, AND PACKING ::::::::::::::::::::::: 1 1.1 Introduction ::::::::::::::::::::::::::::::: 1 1.2 Basic lipid chemistry :::::::::::::::::::::::::: 3 1.2.1 Membrane heterogeneity and lipid phases :::::::::: 6 2 INTRODUCTION TO FLUORESCENCE :::::::::::::: 9 2.1 Introduction ::::::::::::::::::::::::::::::: 9 2.2 Jablonski Diagram ::::::::::::::::::::::::::: 9 2.3 Stokes Shift ::::::::::::::::::::::::::::::: 12 2.4 Quantum Yield and Lifetime :::::::::::::::::::::: 12 2.5 Solvent effects and Polarity Sensitive Dyes :::::::::::::: 13 2.5.1 Solvent relaxation ::::::::::::::::::::::: 13 3 SPECTRAL PROPERTIES OF PRODAN AND LAURDAN :: 16 3.1 Introduction ::::::::::::::::::::::::::::::: 16 3.2 Prodan Structure :::::::::::::::::::::::::::: 16 viii 3.3 Nature of Prodan Emitting State ::::::::::::::::::: 17 3.4 Prodan Dipole Moment :::::::::::::::::::::::: 20 3.5 Prodan Absorption and Emission Spectra in Bulk Solvents ::::: 26 4 THEORETICAL BACKGROUND :::::::::::::::::: 28 4.1 Introduction ::::::::::::::::::::::::::::::: 28 4.2 Many-electron quantum mechanics :::::::::::::::::: 29 4.3 Wave-function :::::::::::::::::::::::::::::: 30 4.4 Born-Oppenheimer approximation ::::::::::::::::::: 32 4.5 Classical molecular dynamics simulation ::::::::::::::: 34 4.5.1 Force-Fields and potential energy function :::::::::: 35 4.5.1.1 Bonded terms :::::::::::::::::::: 36 4.5.1.2 Nonbonded terms :::::::::::::::::: 36 4.5.1.2.1 Lennard-Jones :::::::::::::: 36 4.5.1.2.2 Electrostatics :::::::::::::: 37 4.6 Solving electronic Schrödinger equation :::::::::::::::: 38 4.7 Density Functional Theory ::::::::::::::::::::::: 42 4.7.1 Exchange-Correlation Functional ::::::::::::::: 45 4.7.2 Basis sets :::::::::::::::::::::::::::: 46 4.8 Electronic excitations :::::::::::::::::::::::::: 47 4.8.1 General information about excited state calculations :::: 48 4.9 Electronically excited states calculation using Many-body Green’s Function: GW -BSE ::::::::::::::::::::::::::: 51 4.9.1 One particle excitation ::::::::::::::::::::: 51 4.9.2 Two-particle excitations :::::::::::::::::::: 59 4.10 GW -BSE/MM ::::::::::::::::::::::::::::: 65 ix 5 CHARMM GENERAL FORCE FIELD PARTIAL CHARGE PARAMETRIZATION OF PRODAN/LAURDAN :::::::: 67 5.1 Introduction ::::::::::::::::::::::::::::::: 67 5.2 Method ::::::::::::::::::::::::::::::::: 67 5.2.1 Results ::::::::::::::::::::::::::::: 72 6 MOLECULAR DYNAMICS SIMULATION OF LAURDAN IN LIPID MEMBRANES :::::::::::::::::::::::::: 77 6.1 Introduction ::::::::::::::::::::::::::::::: 77 6.2 MD Simulation ::::::::::::::::::::::::::::: 78 6.3 Simulation Results ::::::::::::::::::::::::::: 79 6.4 Discussion :::::::::::::::::::::::::::::::: 84 7 MD/QM CALCULATION OF PRODAN IN BULK SOLVENTS 86 7.1 Background Information :::::::::::::::::::::::: 87 7.2 Theory :::::::::::::::::::::::::::::::::: 89 7.2.1 Quasi-Particle Excitation ::::::::::::::::::: 89 7.2.2 Coupled Electron-Hole Excitations :::::::::::::: 90 7.2.3 Electrostatic embedding :::::::::::::::::::: 92 7.2.4 Transition probability and oscillator strength :::::::: 92 7.3 MD/GW -BSE: Excited state calculation and Iterative solvent relaxation :::::::::::::::::::::::::::::::: 93 7.3.1 Preparing MD trajectory for QM calculation :::::::: 93 7.3.2 MD/GW -BSE iterative protocol ::::::::::::::: 94 7.4 Prodan MD/GW -BSE calculation in bulk solvents :::::::::: 95 7.4.1