CHEM30060 Quantum Mechanics and Molecular Spectroscopy

Academic Year 2024/2025

This module aims to provide students with a critical understanding of the use of quantum mechanics in measuring and describing the nature of molecules. We will investigate the rotational, vibrational and electronic spectroscopy of molecules examining how changes in the energy, structure and motion of molecules affect their spectroscopic properties.

Conversely, careful analysis of molecular spectra will be shown to be an important way by which one may obtain critical information about the nature of molecules such as their electronic structure, the strengths, lengths and angles of bonds, and their dipole moments.

Also, we will survey the relaxation of electronically excited states by radiative and non-radiative decay processes: Fluorescence, intersystem crossing, phosphorescence, internal conversion, and dissociation. Finally, we will investigate electronically excited state relaxation by stimulated emission, how this process provides a basis for laser operation, and how lasers are now an indispensible element of the chemist’s spectroscopy tool kit.

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Curricular information is subject to change

Learning Outcomes:

By the end of this module it is to be expected that the students will have acquired an understanding of the following concepts and principles and that they will be able to:
Part 1: Quantum Mechanics Recap & Toolkit
• Articulate the postulates of quantum mechanics
• Describe eigenvalue equations, observables, operators, and Hermitian operators
• Recognise and describe orthogonal eigenfunctions (Dirac notation, Kronecker delta)
• Use Dirac notation to write matrix elements and to restate the definition of a Hermitian operator and of an expectation value
• Outline the use of time-independent perturbation theory as a method of approximation
• Apply time-dependent perturbation theory to the mechanism of interaction of light with quantum states and understand how transitions between states depend on the strength of the electromagnetic field and on the transition dipole moment
Part 2: Spectroscopy – Generalities
• Understand the use of the Born-Oppenheimer approximation in the estimation of the molecular potential energy curve
• Understand the general features of molecular spectroscopy including experimental measurement methods and the nature and impact of selection rules and transition moments
Part 3: Molecular Rotational Spectroscopy
• Understand pure rotation spectra of molecules
• Describe molecular moments of inertia, rotational energy levels and rotational transitions
Part 4: Molecular Vibrational Spectroscopy
• Understand the vibrations of diatomic molecules
• Describe the types of molecular vibrations, and the nature and impact of selection rules and anharmonicity on vibrational spectra
• Describe the vibrations of polyatomic molecules in terms of normal modes
• Describe the infrared absorption spectra of polyatomic molecules
Part 5: Aspects of Electron Spin
• Describe the property of electron spin
• Describe the Pauli principle and its implications for the Pauli exclusion principle, Hund’s rules, and the nature of singlet and triplet states
Part 6: Electronic Spectroscopy of Molecules
• Understand the characteristics of electronic transitions and their selection rules
• Describe the electronic spectra of diatomic molecules, and how the Franck-Condon principle leads to the vibrational structure of electronic spectra
• Describe the electronic transitions of representative organic chromophores
• Describe the electronic transitions of simple transition metal compounds
Part 7: Fates of Electronically Excited States
• Understand and illustrate possible fates of electronically excited states
• Describe the fluorescence lifetime and the fluorescence quantum yield
Part 8: Lasers
• Describe the operating principle of the laser
• Explain some uses of lasers in chemistry

Indicative Module Content:

Part 1: Quantum Mechanics Recap & Toolkit
• Postulates of Quantum Mechanics
• Eigenvalue Equations, Observables, Operators, Hermitian Operators
• Eigenfunctions are Orthogonal – Dirac Notation, Kronecker Delta
• Matrix Elements, Hermitian Operators Restated
• Eigenvalues are Real – Expectation Value
• Time-independent Perturbation Theory
• Time-dependent Perturbation Theory
• Transition Dipole Moment
Part 2: Spectroscopy – Generalities
• Emission, Absorption, Transitions
• Electromagnetic Radiation, Quantisation, Photons, Units
• Born-Oppenheimer Approximation
• Molecular Energy Levels, Their Quantisation, and Their Occupancy
• Spectrometers, Beer-Lambert Law, Absorption Coefficient
• Stimulated Absorption, Stimulated Emission, Spontaneous Emission
• Selection Rules and Transition Moments
• Linewidths of Spectral Lines
Part 3: Molecular Rotational Spectroscopy
• Rotations of Heteronuclear Diatomic Molecules – Rigid Rotor, Moment of Inertia, Particle-on-a-Sphere, Quantised Energy Levels, Selection Rules, Appearance of Spectra
• Rotations of Polyatomic Molecules – Linear, Symmetric, and Spherical Rotors, Quantised Energy & Angular Momentum, Degeneracy of Levels, Centrifugal Distortion, Selection Rules, Appearance of Spectra
Part 4: Molecular Vibrational Spectroscopy
• Vibrations of Heteronuclear Diatomic Molecules – Hooke’s Law, Parabolic Potential, Harmonic Oscillator, Quantised Energy Levels, Selection Rules, Appearance of Spectra, Anharmonicity, Convergence of Levels, Selection Rules, Spectra, Bond Dissociation Energy, Birge-Sponer Plot, Vibration-Rotation Spectra, Method of Combination Differences
• Vibrations of Polyatomic Molecules – Normal Modes, Harmonic Approximation, Selection Rules, Spectra, IR Spectroscopy in Chemistry
Part 5: Aspects of Electron Spin
• Spin Angular Momentum
• Orbital Approximation
• Pauli Exclusion Principle
• Pauli Principle
• Hund’s Rule & Spin Correlation
• Hartree-Fock Self-consistent Field Procedure
• Singlet & Triplet States
Part 6: Electronic Spectroscopy of Molecules
• Born-Oppenheimer Approximation, Molecular Energy Levels
• Selection Rules – Role of Electron Spin & Molecular Orbital Symmetry
• Vibrational Structure of Electronic Spectra – Franck-Condon Principle
• Electronic Absorption Spectrum of I2
• Polyatomic Molecules – Chromophores
• Organic Chromophores: Transitions (σ* ← σ; σ* ← n; π* ← π; π* ← n)
• Metal Complexes: Transitions (d – d; LMCT; MLCT)
Part 7: Fates of Electronically Excited States
• Excitation, Radiationless Relaxation, Fluorescence
• Solvent Effects on Fluorescence
• Intersystem Crossing, Phosphorescence
• Dissociation; Internal Conversion, Predissociation
• Jablonski Diagram
• Timescales of Photophysical Processes – Road to Photochemistry
• Primary Quantum Yield
• Decay of Excited Singlet States
• Fluorescence Lifetime & Fluorescence Quantum Yield
Part 8: Lasers
• Laser Action
• Population Inversion – Three-level Laser, Four-level Laser
• Cavity & Mode Characteristics
• Examples of Lasers
• Nonlinear Optics – Frequency Doubling
• Use of Lasers to Study Chemical Dynamics

Student Effort Hours: 
Student Effort Type Hours






Autonomous Student Learning




Approaches to Teaching and Learning:
In terms of teaching and learning methods, a combination of lecture-based teaching, laboratory-based practical experimentation, continuous assessment (problem-based learning), and self-study/reflective learning will be used. Key concepts and tools will be presented in lectures, while regular practical laboratories and tutorial workshops, as well as recommended informal self-study sessions, are intended to facilitate the students in applying this knowledge to real problems relevant to chemistry. 
Requirements, Exclusions and Recommendations
Learning Requirements:

CHEM20120 Physical Chemistry (Level 2) or equivalent

Module Requisites and Incompatibles
Not applicable to this module.
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Exam (In-person): End-of-trimester in-person written exam n/a Graded No


Practical Skills Assessment: Laboratory practical component based on specified experiments n/a Graded No


Assignment(Including Essay): Four homeworks/problem sheets n/a Graded No


Carry forward of passed components
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

There will be four assignments based on problem solving with a particular emphasis on numerical skills development Lecturer will provide in-person tutorials to describe aim of each question, relevance to lecture material, approach to solution, and worked solution Assignment questions will bridge between the in-class lecture material, the learning outcomes, and the end-of-trimester exam

Name Role
Mr Hans Eckhardt Tutor
Mr Karl Griffin Tutor
Chenxi Hao Tutor
Mr Shane O'Neill Tutor
Clara Zehe Tutor