Syllabi of IPC courses

Brief description: The aim of this course is to introduce you to the field of quantum optics and to make contact with the recent developments in the field of vibrational strong coupling i.e., modulating chemistry using the quantum properties of light. More specifically, our interest is in finding out as to how quantised light interacts with matter in optical cavities and the potential change in reaction dynamics as a result of such confinement.

Prerequisites: Basic courses on quantum mechanics, statistical mechanics, rudimentary optics (not strictly necessary). Interested students are encouraged to discuss with the instructor if they have the necessary background.

Note: PhD students may credit this course as an elective. Int PhD and MSc students may also credit the course as an elective not earlier than their 3rd semester. UG students may credit the course not earlier than their 7th semester. In all cases, the requirement of the pre-requisites would apply.

Course outline and lecture schedule:

1. Quantum Electrodynamics (QED): Maxwell’s equations, gauges, quantisation of light, coherent states. [5]
2. Matter-radiation interaction: Dipole approximation. Atom-photon and molecule-photon interactions. Density matrix approach. [3]
3. Cavity QED: Hamiltonian, two level systems and treatment of the Rabi model, Jaynes- Cummings,Tavis-Cummings, and Dicke models, quantum coherence and decoherence, the quantum vaccuum, introduction to Fabry-Pérot cavity. [8]
4. Molecular polaritions: What is a polariton? Vibrational strong coupling, hybrid light- matter states, chemical reactions (does transition state theory work?) and control in optical cavities. Importance of dynamics, vibrational energy flow, cavity losses, decoherence and outstanding challenges. [12]

References:
Note that a large part of this course (particularly the second half) is mainly based on recent papers and reviews. I list some pertinent reviews here. There is no textbook yet. The first half of the course will follow some standard texts given below. There are many others that are not referenced, but during the course I will mention if a specific topic/idea/ thought has been taken from a specific book.

• J. J. Sakurai, Advanced Quantum Mechanics [Chapters 1 and 2], Addison-Wesley 1967.
• C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics, Wiley-VCH 1997.
• P. Meystre, M. Sargent, Elements of Quantum Optics, 3rd Ed, Springer 1999.
• Mandal et al, Theoretical advances in Polariton Chemistry and molecular cavity quantum electrodynamics, chemrxiv (2022).
• Campos-Gonzalez-Angulo et al, Swinging between shine and shadow: theoretical advances on thermally-activated vibropolaritonic chemistry, arXiv (2023).
• Sidler et al, A perspective on ab initio modeling of polaritonic chemistry: the role of non-equilibrium eûects and quantum collectivity, J. Chem. Phys. 156, 230901 (2022).
• Nagarajan et al, Chemistry under vibrational strong coupling, J. Am. Chem. Soc. 143, 16877 (2021).

Group theory: Symmetry elements, point groups, representation theory, great orthogonality theorem, SALCs. Time-dependent perturbation theory, light-matter interaction. H-like atoms, angular momenta and selection rules of transitions, multi-electon atoms, term symbols, spin-orbit coupling, Zeeman and linear Stark effects. Rotations and vibrations of diatoms, anharmonic effects, selection rules, electronic structure. Rotations and vibrations of polyatomic molecules, various tops and their properties, normal modes of vibration, selection rules, electronic states and transitions

References:

• I. N. Levine, Molecular Spectroscopy
• J. L. McHale, Molecular Spectroscopy
• P. F. Bernath, Spectra of Atoms and Molecules (2nd Ed.)
• F. A. Cotton, Chemical Applications of Group Theory

Principles of biochemistry and molecular biology, role of metal ions in biology, principles of coordination chemistry, amino acids and other bioligands, proteins – secondary and tertiary structure, nucleic acids, iron proteins, iron transport, role of zinc in biology – zinc enzymes, biological importance of nickel, copper proteins, redox reactions involving manganese, biological roles of vanadium, cobalt and molybdenum, basic concepts in drug design, metals and health - metal-based drugs and mechanism of their action, metalloproteins as drug targets.

References:

• S. J. Lippard and J. M. Berg, Principles of Bioinorganic Chemistry (University Science Books, California)

Structure and bonding in organometallic compounds – isolobal analogies, metal carbonyls, carbenes and NHC complexes, olefin and acetylene complexes, alkyls and allyl complexes, metallocenes. Major reaction types – oxidative addition, reductive elimination, insertion, isomerization and rearrangement reactions. Catalytic reactions: metathesis, hydrogenation, allylic activation, C-C coupling reactions, C-X coupling etc.

References:

• Ch. Elschenbroich, Organometallics (3rd edition, Wiley-VCH, Weinheim)

Concepts and terminology. Principles of polymerization – chain versus step growth process. Kinetics of chain polymerization process, estimation of various rate constants. Determination of molecular weight of polymers and their distribution.Solution properties and chain dimension. Characteristics and mechanisms of various chain polymerizations – radical, cationic, anionic, Ziegler-Natta and ring opening metathesis polymerizations. Living polymerizations – criteria for livingness, newer methods for living polymerizations – GTP, ATRP and TEMPO-mediated radical polymerizations. Copolymerization – random, alternating and block copolymers and kinetic schemes for analysis of copolymerization. Micro-structural analysis of polymers by NMR – estimation of regio- and stereo-regularity in polymers, sequence distribution in copolymers etc., and mechanisms for stereo-regulation.

References:

• P. J. Flory, Principles of Polymer Chemistry
• G. Odian, Principles of Polymerization
• P. C. Hiemenz and T. P. Lodge, Polymer Chemistry

Electrode kinetics and electrochemical techniques: polarizable and non-polarizable interfaces; current- potential relationship; methods of measurement of kinetic parameters; over potential; symmetry factor and transfer coefficient; mechanistic criteria; diffusion, activation phenomena. Steady state and potential step techniques; polarography; cyclic voltammetry; chrono- methods; convective diffusion systems: rotating disc and ring disc electrodes; microelectrodes; AC impedance techniques - concepts and applications. Applied topics: fundamentals of batteries: primary, secondary, reserve batteries; solid state and molten solvent- batteries; fuel cells. Photo-electrochemical solar cells and conversion of solar energy. Corrosion – fundamentals and applications.

References:

• A. J. Bard and L. R. Faulkner, Electrochemical methods: Principles and Applications (Wiley 1990)
• R. Greef, R. Peat, L. M. Peter, D. Pletcher and J. Robinson, Instrumental Methods in Electrochemistry (Ellis Harwood Ltd., 1985) • E. Gileadi, Electrode Kinetics for Chemists, Chemical Engineers and Material Scientists (VCH 1993)
• C. A. Vincent, Modern Batteries (Edward Arnold, UK 1984)
• A. J. Nozik, Photoeffects at semiconductor-electrolyte interfaces (ACS, Washington 1981)

[1] Phenomenology and Experiments: Elastic, Inelastic and reactive scattering; Potential Scattering; Newton Diagrams; Experiments; Physical Observables; Differential and total cross sections; Angular Distribution - Forward and Backward Scattering. [2] Potential Energy Surfaces: Diabatic and adiabatic representations - Born-Oppenheimer Approximation; Contour Diagrams; Reaction Dynamics as a Probe for Potential Energy Surfaces; Simple Classical Trajectory Calculations. [3] Transition from macroscopic to microscopic kinetics; thermal and energy dependent rate constants, k(T) and k(E); Dynamics of bimolecular collisions; simple collision model; Transition state theory (TST); variational TST; Roaming reactions and reactions with higher order saddle points. [4] Unimolecular reaction dynamics; Lindeman-Hinshelwood mechanism; Rice- Ramsperger-Kassel-Marcus (RRKM) theory; Statistical adiabatic channel model. [5] Experimental determinations of kinetic parameters: molecular beam scattering, state-resolved spectroscopic techniques.

References:

• R. B. Bernstein and R. D. Levine, Molecular Reaction Dynamics and Chemical Reactivity, Oxford University Press
• R. B. Bernstein, Chemical Dynamics via Molecular Beam and Laser Techniques, Oxford University Press
• N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, First, Second or Third Edition, Oxford University Press