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. Polymeric materials will be discussed in terms of the nanotechnology revolution and modern day applications. 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.

1. discuss the application of band structure to understand the electronic structure of solids;
2. describe how the band structure is affected by the introduction of an interface;
3. describe the basic ideas behind the periodic quantum chemistry approach to theoretical analysis of solid state structure;
4. understand the application of Bloch functions to obtain wavefunctions for periodic systems;
5. understand the concept of reciprocal space in describing wavefunctions and use of sampling to determine approximate band structures;
6. understand how and why the electrical, magnetic and optical properties of a molecular solid depend crucially on the crystal structure of the solid.
7. appreciate that polymers exhibit quite different properties to ‘small’ molecules;
8. understand the role of polymers in many technological applications;
9. describe how physical properties (e.g. Tg, solubility, adsorption) may be controlled via modification to molecular structure;
10. know the form of the Schrödinger equation for model systems, and requirements for acceptable solutions
11. explain the Born-Oppenheimer approximation and its use in electronic structure calculations;
12. appreciate how the Pauli principle is applied to quantum mechanical treatment of atoms and molecules;
13. understand the use of the Variation theorem in finding approximate solutions to the Schrödinger equation;
14. describe the essential features of the Hartree-Fock method for atoms and molecules;
15. define electron correlation, appreciate its importance in chemical phenomena, and discuss methods for its calculation;
16. discuss the difference between time and ensemble averages and the role of the ergodic hypothesis;
17. give definitions of the partition function for translational, rotational and vibrational degrees of freedom;
18. calculate thermodynamic quantities such as internal energy, entropy and heat capacity from partition functions;
19. understand the role of potential energy surfaces and partition functions in determining rates of reaction;
20. use transition state theory to predict reaction rates from relevant molecular properties;
21. find exact solutions of the Schrödinger equation for model systems;
22. use computational methods to construct approximate wavefunctions and energies for chemical phenomena;
23. critically assess methods for calculation of molecular electronic structure for different classes of problem.

The module will be delivered in 42 1-hour lectures, 8 1-hour workshops, and 4 1-hour tutorials.

On completion of the module a student will be able to:

1. apply fundamental theory to explain structures, properties and behaviour of solid materials;
2. discuss the factors that describe the electrical properties of polymers, and how these are harnessed in nanotechnology;
3. critically assess the methods and algorithms used to simulate a range of chemical problem, and to extract the associated numerical and statistical data analysis.

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.

Properties of solids

Molecular Solids with High Electrical Conductivity ("Molecular Metals")

Preliminaries

Example of a Highly Conducting Molecular Solid: TTF/TCNQ

The Band Structure of TTF/TCNQ and Rationalization of Electrical Conductivity

Other Examples of Molecular Metals

General Considerations in the Design of Molecular Metals

Molecular Superconductors

Non-Linear Optical Properties of Molecular Solids

Introduction

Fundamentals of Non-Linear Optics

Design and Characterization of Molecular Solids for Applications in Non-Linear Optics

Examples of Molecular Solids with Applications in Non-Linear Optics

Molecular Magnets

Introduction

Intermolecular Magnetic Interactions

Examples of Molecular Magnets

Essential theory of the solid state

       Models of bonding in the solid state based on band theory, including tight-binding and nearly free electron models

       Fermi levels and density of states

       Conduction in polymers; doping; band-bending at semiconductor-electrolyte interfaces and photon capture

Applications

The electronic structure of interfaces will be used to illustrate practical applications of theoretical concepts: band bending and electrosynthesis, energy conversion (solar cells), surface science aspects of catalysis. Theoretical analysis of conducting polymer systems, metals and oxides will be used to illustrate the application of solid state theory in practice.

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, particle on a ring, 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; methods for calculation including post-HF and density functional theory 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)

An indicative reading list will be included in the Course Handbook.