Interfacial Potentials in Ion Solvation A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics of the McMicken College of Arts and Sciences by Carrie Conor Doyle B.S. in Physics, Rutgers, the State University of New Jersey, 2013 June 2020 supervised by Dr. Thomas L. Beck Committee Co-Chair: Dr. Carlos Bolech, Physics Committee Member: Dr. Rohana Wiedjewardhana, Physics Committee Member: Dr. Leigh Smith, Physics Abstract Solvation science is an integral part of many fields across physics, chemistry, and biology. Liquids, interfaces, and the ions that populate them are responsible for many poorly understood natural phenomena such as ion specific effects. Establishing a single-ion solvation free energy thermodynamic scale is a necessary component to unraveling ion-specific effects. This task is made difficult by the experimental immeasurability of quantities such as the interfacial potential between two media, which sets the scale. Computer simulations provide a necessary bridge between experimental and theoretical results. However, computer models are limited by the accuracy-efficiency dilemma, and results are misinterpreted when the underlying physics is overlooked. Classical molecular dynamic techniques, while efficient, lack transferability. Quantum-based ab initio techniques are accurate and transferable, but their inefficiency limits the accessible simulation size and time. This thesis seeks to determine the physical origin of the interfacial potential at the liquid-vapor interface using classical models. Additionally, I assess the ability of Neural Network Potential (NNP) simulation methods to produce electrostatic properties of bulk liquids and interfaces. Complicating factors are minimized through a simple water model (SPC/E) free of experimental parametrization and a finite droplet simulation free of Ewald effects. Multipolar decomposition of the potential in the region of zero charge density provides a direct method for determining the potential felt by ions near interfaces. Non-aqueous solvents are studied through an OPLS-AA based model of the organic liquid ethylene carbonate (EC) using the same approach to compare aqueous and non-aqueous solvents. Neural network potentials may be a step towards the higher-level 1 need for predictive models, but they require further testing. Using an existing NNP framework, I train models for dynamics, as well as multipole electrostatics. Combining the two in both a bulk and interfacial system allows for the calculation of interfacial electrostatic properties. My results for water elucidate the reason for widely varying net potentials calculated for various models with similar dipole but differing quadrupole moments. Near-cancelling dipole contributions between the droplet interface and the cavity interface of a solvated ion leaves the quadrupole as the dominant contribution to the net potential. Molecular density profiles and potential profiles show that a length scale of 5 Å from cavity boundary is needed for a convergent potential. A theoretical argument for the radial dependence of each contribution is made, which supports my results. EC also has this radial dependence but has a different length scale of convergence. Differences in the molecular size, orientation, hydrogen-bonding capabilities, and multipole moments results in solvent-specific net potential contributions. This is evidenced by the results for charged cavities and an orientational analysis of EC. NNPs are shown to provide excellent agreement with ab initio electrostatic properties. This is encouraging evidence for the use of NNPs in the calculation of thermodynamic properties and in force field development. 2 Acknowledgements I would like to express my gratitude to all those who were a part of my PhD studies. The guidance and support of my advisor Dr. Thomas L. Beck was an essential part of my thesis work. His vast interdisciplinary knowledge and encouragement of independent research was a constant source of motivation. I thank Dr. Bolech, Dr. Wiedjewardhana, and Dr. Smith for their contributions as my committee members, and as professors, along with others at the University of Cincinnati and Rutgers University who prepared me for rigorous scientific investigations. Lab group members Zohre Gorunmez, Mimi Liu, and Andrew Eisenhardt were always there to commiserate and grow with. Extensive discussions and collaboration with Yu Shi were an important part of the evolution of my research and a fond memory. I am forever grateful for the friends I met along the way. Finally, I thank my family, Lorraine, William, and Jessie Doyle for the constant support and encouragement, no matter the distance between us. 4 Yes, as everyone knows, meditation and water are wedded for ever. —Herman Melville Dedicated to William Doyle 5 Contents 1 Introduction 13 1.1 Preface......................................... 13 1.2 Evolution of the Computer Simulation of Liquids................. 16 1.2.1 History..................................... 17 1.2.2 Connection with Theory and Experiment.................. 18 1.3 Solvation Science................................... 20 1.3.1 Mixtures and Phase Separation....................... 20 1.3.2 Proteins and Membranes........................... 22 1.3.3 Specific Ion Solvation: Hofmeister Series.................. 24 1.4 Theories and Simulation of Ion Solvation...................... 27 1.4.1 Past...................................... 27 1.4.2 Present.................................... 30 Classical Simulation............................. 30 Ab Initio Simulation............................. 32 Neural Network Potentials.......................... 33 1.5 Interfacial Potential Effects............................. 35 1.5.1 Thermodynamic Scale............................ 35 1.5.2 Are they measurable?............................. 38 6 CONTENTS 1.5.3 What are we measuring?........................... 41 1.6 Summary....................................... 45 2 Theory 48 2.1 Preface......................................... 48 2.2 Classical Molecular Dynamics............................ 48 2.2.1 Equations of Motion............................. 49 2.2.2 Thermodynamic Ensembles and Equilibration............... 50 2.2.3 Classical Force Fields............................. 50 2.2.4 SPC/E Force Field.............................. 52 2.2.5 OPLS-AA................................... 53 2.2.6 Boundary Conditions............................. 53 2.3 Ab Initio Molecular Dynamics............................ 54 2.4 Neural Network Potentials.............................. 56 2.5 Thermodynamics of Ion Solvation.......................... 59 2.5.1 The Potential Distribution Theorem.................... 60 2.5.2 Quasichemical Theory............................ 61 2.5.3 Interfacial Potentials............................. 63 2.6 Macroscopic Interfacial Electrostatics........................ 65 2.6.1 Multipole Expansion of a Charge Distribution............... 66 2.6.2 Coordinate Systems: Cartesian and Spherical............... 67 2.6.3 Molecular Multipole Expansion of Electrostatic Potential......... 70 3 Water Liquid-Vapor Interfacial Potential Shifts 71 3.1 Preface......................................... 71 7 CONTENTS 3.2 Computational Methods............................... 73 3.3 Results and Discussion................................ 74 3.4 Conclusion....................................... 84 4 Ethylene Carbonate Liquid-Vapor Interfacial Potential Shifts 87 4.1 Preface......................................... 87 4.2 Computational Methods............................... 90 4.3 Results and Discussion................................ 91 4.3.1 Multipole moments of EC and Water.................... 91 4.3.2 Electrostatic Potential Analysis: Neutral Cavity.............. 92 4.3.3 Electrostatic Potential and Molecular Orientation............. 97 4.3.4 Electrostatic Potential Analysis: Charged Cavities............. 103 4.4 Conclusion....................................... 108 5 Electrostatic Properties from Neural Network Potentials 112 5.1 Preface......................................... 112 5.2 Computational Methods............................... 114 5.2.1 Ab Initio Simulation............................. 114 5.2.2 DeepMD reconstruction of the PES..................... 117 5.2.3 DNN for determination of Multipole Moments: DeePD, DeePM, DeePPM 119 5.2.4 DNN for determination of DeePMD multipole moments......... 120 5.3 Results and Discussion................................ 120 5.4 Conclusion....................................... 129 6 Conclusions 131 8 CONTENTS A Appendix 153 A.1 Molecular Multipole Definition............................ 153 A.2 Supporting Information: Chapter 3......................... 155 A.3 Supporting Information: Chapter 4......................... 159 9 List of Figures 1.1 Diagram of computational simulations, theory, and experiment.......... 19 1.2 Schematic of boundary conditions and interfacial potential shifts......... 45 2.1 Schematic of basic neural network.......................... 57 2.2 Schematic of studied system- a liquid solvent droplet and interfacial potential shifts.......................................... 64 3.1 SPC/E electrostatic potential profile for different cavity sizes........... 76 3.2 SPC/E electrostatic poential multipole expansion and RDF for differnet cavity sizes.......................................... 78 3.3 SPC/E net potential dependence on cavity size: multipole decomposition.... 83