CH3304: Advanced Physical Chemistry
School | Cardiff School of Chemistry |
Department Code | CHEMY |
Module Code | CH3304 |
External Subject Code | 101050 |
Number of Credits | 20 |
Level | L6 |
Language of Delivery | English |
Module Leader | Dr James Platts |
Semester | Double Semester |
Academic Year | 2015/6 |
Outline Description of Module
The module describes the fundamental properties of common materials, in particular the solid state, polymeric materials and their underlying theoretical basis. Knowledge of the structure of the solid state will lay the basis for a discussion of band theory within a series of theoretical models. Finally, the fundamental concepts in quantum and statistical mechanics will be presented, starting from solution of the Schrödinger equation for model systems, quantum mechanical aspects of atomic and molecular electronic structure, with particular reference to the Pauli Principle and Variation theorem. Statistical mechanics will be based around the definition of partition functions, and will employ such definitions in discussion of thermodynamics and kinetics.
On completion of the module a student should be able to
- discuss the application of band structure to understand the electronic structure of solids;
- describe how the band structure is affected by the introduction of an interface;
- describe the basic ideas behind the periodic quantum chemistry approach to theoretical analysis of solid state structure;
- understand the application of Bloch functions to obtain wavefunctions for periodic systems;
- understand the concept of reciprocal space in describing wavefunctions and use of sampling to determine approximate band structures;
- understand how and why the electrical, magnetic and optical properties of a molecular solid depend crucially on the crystal structure of the solid.
- know the form of the Schrödinger equation for model systems, and requirements for acceptable solutions
- explain the Born-Oppenheimer approximation and its use in electronic structure calculations;
- appreciate how the Pauli principle is applied to quantum mechanical treatment of atoms and molecules;
- understand the use of the Variation theorem in finding approximate solutions to the Schrödinger equation;
- describe the essential features of the Hartree-Fock method for atoms and molecules;
- define electron correlation, appreciate its importance in chemical phenomena, and discuss methods for its calculation;
- discuss the difference between time and ensemble averages and the role of the ergodic hypothesis;
- give definitions of the partition function for translational, rotational and vibrational degrees of freedom;
- calculate thermodynamic quantities such as internal energy, entropy and heat capacity from partition functions;
- understand the role of potential energy surfaces and partition functions in determining rates of reaction;
- use transition state theory to predict reaction rates from relevant molecular properties;
- find exact solutions of the Schrödinger equation for model systems;
- use computational methods to construct approximate wavefunctions and energies for chemical phenomena;
- critically assess methods for calculation of molecular electronic structure for different classes of problem.
How the module will be delivered
The module will be delivered in 42 1-hour lectures, 8 1-hour workshops, and 4 1-hour tutorials.
Skills that will be practised and developed
On completion of the module a student will be able to:
- apply fundamental theory to explain structures, properties and behaviour of solid materials;
- discuss the factors that describe the electrical properties of polymers, and how these are harnessed in nanotechnology;
- critically assess the methods and algorithms used to simulate a range of chemical problem, and to extract the associated numerical and statistical data analysis.
How the module will be assessed
A written exam will test the student’s knowledge and understanding as elaborated under the learning outcomes. The coursework will allow the student to demonstrate his/her ability to judge and critically review relevant information.
Assessment Breakdown
Type | % | Title | Duration(hrs) |
---|---|---|---|
Exam - Spring Semester | 70 | Advanced Physical Chemistry | 3 |
Written Assessment | 12 | Autumn Semester Workshops | N/A |
Written Assessment | 3 | Autumn Semester Tutorials | N/A |
Written Assessment | 12 | Spring Semester Workshops | N/A |
Written Assessment | 3 | Spring Semester Tutorials | N/A |
Syllabus content
Band theory of solids
Band structure and its relationship to the electronic structure of solids
Band structure at interfaces
Periodic quantum chemistry approach for theoretical analysis of solid state structure
Bloch functions for wavefunctions for periodic systems
Reciprocal space and use of sampling to determine approximate band structures
Molecular Metals
Requirements for metallic conductivity
Band structure and rationalization of electrical conductivity in molecular solids
Examples of molecular metals
General considerations in the design of molecular metals
Molecular Superconductors
Fundamentals of superconductivity
BCS theory for Type I superconductors
Examples of molecular superconductors
Comparison with metallic and inorganic superconductors
Molecular Magnets
Fundamentals of magnetism
Intermolecular magnetic interactions
Examples of molecular magnets
Optical Properties of Molecular Solids
Fundamentals of linear optics
High refractive index materials
Applications of refraction and total internal reflection
Birefringent materials
Fundamentals of non-linear optics
Design and characterization of molecular non-linear optical materials
Examples of inorganic and molecular solids with applications in non-linear optics
Concepts in quantum mechanics
Review of basic concepts Hamiltonian, Schrödinger equation, operators and eigenvalues
Exact solutions for model problems: particle in 1D and 2D box, hydrogen atom
Approximate solutions for many-electron atoms: electron spin and the Pauli principle
Coulomb and exchange energies
Variation theorem and calculation of approximate wavefunctions and energies
Angular momentum, atomic quantum numbers and their interpretation
Approximate solutions for molecules: Born-Oppenheimer approximation
LCAO approximation, Slater determinants and basis sets
Hartree-Fock and self-consistent field approach
MO diagrams
Electron correlation: definition of static and dynamic correlation; relevance to chemical phenomena
Post-HF (configuration interaction) and density functional theory (DFT) methods
Concepts in statistical mechanics
Review of basic concepts: probability, kinetic theory of gases; microstates; Boltzmann distribution
Definition of partition functions for translational, rotational and vibrational degrees of freedom
Thermodynamics from partition functions: internal energy, entropy and heat capacity
Systems composed of interacting objects (e.g. Ising model, diluted ideal gases)
Essential Reading and Resource List
An indicative reading list will be included in the Course Handbook.
Background Reading and Resource List
An indicative reading list will be included in the Course Handbook.