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UNIVERSITY of CALIFORNIA SAN DIEGO Effects of Vibrational Strong UNIVERSITY OF CALIFORNIA SAN DIEGO Effects of vibrational strong coupling on ground-state chemical kinetics A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Chemistry by Jorge Arturo Campos Gonzalez Angulo Committee in charge: Professor Joel Yuen-Zhou, Chair Professor Richard Averitt Professor Patricia Jennings Professor Katja Lindenberg Professor Francesco Paesani 2021 Copyright Jorge Arturo Campos Gonzalez Angulo, 2021 All rights reserved. The dissertation of Jorge Arturo Campos Gonzalez Angulo is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California San Diego 2021 iii EPIGRAPH Clarity is a fair distribution of light and shadow. —Johann Georg Hamann iv TABLE OF CONTENTS Signature Page . iii Epigraph . iv Table of Contents . .v List of Figures . vii List of Tables . viii Acknowledgements . ix Vita ............................................. xi Abstract of the Dissertation . xiii Chapter 1 Introduction . .1 1.1 Cavity-induced modifications of ground-state chemical kinetics: Ex- perimental observations . .5 1.2 Theoretical approaches to VSC modified chemical kinetics. 10 1.3 Summary of contents . 14 Chapter 2 Theoretical background . 16 2.1 Fundamentals of microcavities . 16 2.2 Normal modes of vibration . 21 2.3 Molecules in cavities . 25 2.3.1 The Cavity Born-Oppenheimer approximation . 25 2.3.2 Regimes of coupling intensity . 30 2.3.3 Many molecules inside the cavity . 34 2.4 Notions of cavity-modified chemical kinetics . 39 Chapter 3 Effects of vibrational strong coupling on adiabatic reactions . 43 3.1 Introduction . 43 3.2 Theory . 45 3.2.1 Single-molecule case . 51 3.3 Conclusions . 53 Chapter 4 Effects of vibrational strong coupling on non-adiabatic processes . 54 4.1 Introduction . 54 4.2 Theoretical framework . 56 4.2.1 Relation between reactant and product harmonic oscillator operators. 58 v 4.2.2 Rate in terms of polariton moldes . 60 4.2.3 Initial and final many-body vibronic states. 64 4.2.4 Dimensionally reduced Franck-Condon factor. 66 4.2.5 Conditions for rate enhancement . 68 4.2.6 Simulation of modified kinetics . 70 4.2.7 Numerical simulation . 75 4.2.8 Integration of the rate law. 76 4.3 Discussion . 78 Chapter 5 Vibrational strong coupling of anharmonic oscillators . 80 5.1 Introduction . 80 5.2 Description of the model . 83 5.3 Permutational symmetry . 86 5.4 Collective couplings. 98 5.4.1 Schur-Weyl basis. 102 !¹,º 5.4.2 Efficient calculation of `~0,`~ ................. 106 5.5 Algorithm for Hamiltonian separation . 111 5.6 Worked examples . 114 5.6.1 The triply excited manifold . 114 5.6.2 Matrices for lower manifolds . 118 5.7 Properties of eigenstates. 119 5.8 Conclusions. 124 Chapter 6 Conclusions and outlook. 126 Bibliography . 129 vi LIST OF FIGURES Figure 1.1: Fabry Perot resonator hosting organic molecules. .3 Figure 1.2: Correlation diagram of polaritonic energy levels. 11 Figure 2.1: Cavity modes in cartesian space. 17 Figure 2.2: Contour plot around the minimum of the PES for a single vibrational mode coupled to a single EM mode. 30 Figure 2.3: Frequencies of LP and UP as a function of the coupling constant between the vibration of CO and a resonant cavity. 31 Figure 2.4: Frequencies of LP and UP as a function of the coupling constant for a Hamiltonian with counter-rotating terms and one under the RWA. 33 Figure 2.5: Absorption signal of the polariton modes as a function of the intensity of light-matter coupling. 34 Figure 2.6: Cavity angular dispersion spanning modes 1 ≤ < ≤ 3............ 35 Figure 3.1: Effect of VSC on a reactive potential energy surface. 46 Figure 3.2: Ratio of rate constants as a function of the permanent dipole in the TS, and the collective light-matter coupling. 52 Figure 4.1: Depiction of a microcavity. 56 Figure 4.2: Probability coefficients for each molecular mode in the quasi-localized basis of dark modes. 62 Figure 4.3: Electron transfer parameters for catalytic behavior. 69 Figure 4.4: Potential energy surfaces under VSC along the slow coordinate . 71 Figure 4.5: Amplification of Fig. 4.4. 72 Figure 4.6: Ratio between rate coefficients inside and outside the cavity. 73 Figure 4.7: Evolution of reactant consumption. 75 Figure 5.1: Diagram of the relations between SABEs in the doubly excited manifold. 95 Figure 5.2: Energy spectra of emitters with various anharmonicities coupled to a harmonic EM mode as a function of coupling intensity in the weak-to-strong regime. 122 Figure 5.3: Energy spectra of anharmonic emitters coupled to a harmonic EM mode with illustrated degeneracies. 123 Figure 5.4: Photon content of harmonic eigenstates as a function of detuning. 124 vii LIST OF TABLES Table 1.1: Chemical reactions modulated by vibrational strong coupling. .7 Table 4.1: Correlation between methods of reaction time calculation . 78 Table 5.1: Examples of spectral configurations, partitions, and Young diagrams corre- sponding to selected PBEs. 87 Table 5.2: Spectral configurations, EM mode excitations and degeneracies for the first five excitation manifolds. 88 Table 5.3: Examples of standard Young tableaux and their associated indices for # = 6. 93 Table 5.4: Examples of semistandard Young tableaux and their associated indices for # = 6 and `~ = 031221.............................. 94 Table 5.5: Coefficients of projected couplings involving `~0 = 0#−21121 for repeated irreps with , = »# − 1, 1¼............................ 102 Table 5.6: SABEs in terms of PBEs for spectral configurations with at most three excitations in the emitters. 108 Table 5.7: SABEs in terms of PBEs with `~ = 0#−21121.................. 109 Table 5.8: Contribution of transitions in emitter space to the coupling coefficients between `~ = 0#−212 and `~0 = 0#−313.......................... 110 Table 5.9: Relevant partitions, spectral configurations, excitations in the EM mode, bare energies, and module dimensions calculated in the block diagonalization of 퐻^3¹#º..................................... 114 Table 5.10: Kostka numbers, ,-, relating the permutation and Specht modules that appear in the triply excited manifold. 115 Table 5.11: Energy levels involved and contributions from transitions in the EM and emitter modes to the couplings between spectral configurations in the triply excited manifold. 116 viii ACKNOWLEDGEMENTS In first place, I thank my advisor, Professor Joel Yuen-Zhou. Your leadership, support and generosity have been essential throughout these years. Thank you for your drive and ambition that helped me find a voice and a place as a scientist. I would also like to thank Dr. Raphael Florentino Ribeiro for his invaluable mentorship. Thank you for sharing your knowledge and talent that led me to many of the accomplishments evidenced in this dissertation. I am also grateful for Luis Ángel Martínez-Martínez, and Matthew Du. Thank you for your continuous and always helpful insights and feedback. I am thankful to the Air Force Office of Scientific Research for their sponsorship through the award FA9550-18-1-0289. I also acknowledge the financial support from the Consejo Nacional de Ciencia y Tecnología and the University of California Institute for Mexico and the United States through scholarship with reference number 235273/472318. Chapter 1, in part is currently being prepared for submission for publication of the material. “Thermally-activated vibro-polaritonic chemistry: theoretical perspectives.” Campos-Gonzalez- Angulo, Jorge A.; Du, Matthew; Yuen-Zhou, Joel. The dissertation author was the primary investigator and author of this material. Chapter 3, in full, is adapted from the material as it appears in “Polaritonic normal modes in transition state theory.” Campos-Gonzalez-Angulo, Jorge A.; Yuen-Zhou, Joel. The Journal of Chemical Physics, 152, 161101 (2020). The dissertation author was the primary investigator and author of this paper. Chapter 4, in full, is adapted from the material as it appears in “Resonant catalysis of thermally activated chemical reactions with vibrational polaritons.” Campos-Gonzalez-Angulo, Jorge A.; Ribeiro, Raphael F.; Yuen-Zhou, Joel. Nature Communications, 10, 4685 (2019). The dissertation author was the primary investigator and author of this paper. ix Chapter 5, in full is currently being prepared for submission for publication of the material. “Generalization of the Tavis-Cummings model for multi-level anharmonic systems”. Campos- Gonzalez-Angulo, Jorge A.; Ribeiro, Raphael F.; Yuen-Zhou, Joel. The dissertation author was the primary investigator and author of this material. x VITA 2009 B. Sc. in Chemistry Mención Honorífica, Universidad Nacional Autónoma de México 2011-2014 Lecturer, Universidad Nacional Autónoma de México 2012 M. Sc. in Chemical Sciences Mención Honorífica, Universidad Nacional Autónoma de México 2014-2015 Graduate Student Instructor, University of California Berkeley 2016 Main Instructor, Colegio Internacional de Líderes 2016-2017 Graduate Teaching Assistant, University of California San Diego 2019-2020 Graduate Writing Consultant, University of California San Diego 2021 Ph. D. in Chemistry, University of California San Diego PUBLICATIONS Campos-Gonzalez-Angulo, J. A., Wiesehan G., Ribeiro, R. F. & Yuen-Zhou, J. (2020)“Com- putational method for highly-constrained molecular dynamics of rigid bodies: coarse-grained simulation of auxetic two-dimensional protein crystals.”, The Journal of Chemical Physics, 152(23), 244102. Campos-Gonzalez-Angulo, J. A., & Yuen-Zhou, J. (2020)“Polaritonic normal modes in transition state theory.”, The Journal of Chemical Physics, 152(16), 161101. Campos-Gonzalez-Angulo, J. A., Ribeiro, R. F., & Yuen-Zhou, J. (2019). “Resonant catalysis of thermally activated chemical reactions with vibrational polaritons.” Nature communications, 10(1), 1-8. Ribeiro, R. F., Martínez-Martínez, L. A., Du, M., Campos-Gonzalez-Angulo, J., & Yuen-Zhou, J. (2018). “Polariton chemistry: controlling molecular dynamics with optical cavities.” Chemical science, 9(30), 6325-6339. Martínez-Martínez, L. A., Ribeiro, R. F., Campos-González-Angulo, J., & Yuen-Zhou, J. (2017). “Can ultrastrong coupling change ground-state chemical reactions?” ACS Photonics, 5(1), 167-176.
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