The University of Southampton
Courses

# CHEM3045 Atoms, Molecules and Spins: Quantum Mechanics in Chemistry and Spectroscopy

## Module Overview

This module aims to develop an intermediate-level understanding of quantum mechanics, including familiarity with its mathematical formulation. It is intended to bridge the gap between the qualitative, pictorial approach used in the core modules of the first two years and a rigorous mathematical formulation of both time-independent and time-dependent quantum mechanics. A combination of lecture-based teaching, self-study, and problem-based learning will be used. Key concepts and tools will be presented in lectures, while regular workshops and informal self-study sessions will lead the students to applying them to real problems relevant to chemistry and to modern spectroscopic techniques such as magnetic resonance and magnetic resonance imaging.

### Aims and Objectives

#### Module Aims

1. To provide critical understanding of the fundamentals and mathematical formulation of quantum mechanics 2. To provide conversant knowledge of the quantum mechanical nature of atoms and molecules, building on basic material from Y1 (CHEM1013) and Y2 (CHEM2013) 3. To provide understanding of quantum dynamics - how spins, atoms, and molecules move, and how this affects chemistry

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• understand the fundamentals of quantum mechanics
• understand their formulation in mathematical terms
• understand the quantum mechanical treatment of angular momentum
• predict atomic and molecular spectra taking electron and nuclear spin into account
• understand how quantum states of multiple identical particles combine and how spin isomers arise.
• understand the role of time in quantum mechanics
• use time-dependent quantum mechanics to predict the outcome of simple experiments
• use time-dependent quantum mechanics to understand magnetic resonance and magnetic resonance imaging.

### Syllabus

Part A: The Quantum World Time independent quantum mechanics 1. Operators, momentum, commutators, expectation values 2. Heisenberg’s uncertainty principle, Schrödinger equation 3. Angular momentum, commutation, raising and lowering operators, quantisation of angular momentum 4. Spin 5. Fine structure and hyperfine structure 6. Coupling of angular momenta. Singlet and triplet states 7. Two particles in a box: The Pauli principle and the Pauli exclusion principle. 8. Multielectron atoms. 9. The allotropes of H2: Ortho and parahydrogen Part B: How Spins, Atoms, and Molecules Move Quantum Dynamics 10. Time-dependent quantum mechanics: Schrödinger equation 11. Time evolution of stationary states. 12. Superposition states. Quantum paradoxes - Schrödinger’s cat & friends 13. Spin state precession, magnetic resonance, and magnetic resonance imaging.

### Learning and Teaching

#### Teaching and learning methods

Study time allocation [Contact time includes: Lectures, seminars, tutorials, project supervision, demonstration, practicals/workshops/fieldwork/external visits/work based learning] Teaching and Learning Methods Formal lectures will provide an introduction to each of the topics covered by the syllabus and will include worked examples and illustrations of applications of the concepts. Workshops will provide students with guided practice in application of the concepts covered by the syllabus that exemplify the theories covered and will allow students to deepen their understanding. Self-study will enable students to consolidate their knowledge of the subject matter and to explore the application of the concepts to additional problems.

TypeHours
Practical classes and workshops8
Preparation for scheduled sessions32
Revision10
Follow-up work76
Lecture24
Total study time150

M. H. Levitt (2007). Spin Dynamics.

C. Cohen-Tannoudji, B. Diu, F. Laloe (1977). Quantum Mechanics.

P. W. Atkins and R. S. Friedman (2011). Molecular Quantum Mechanics.

### Assessment

#### Summative

MethodPercentage contribution
Assessment  (2 hours) 100%
In-class Test %

#### Referral

MethodPercentage contribution
Assessment  (2 hours) 100%
In-class Test %