The module describes the fundamental concepts in quantum and statistical mechanical description of molecules and solids. Starting from solution of the Schrödinger equation for model systems, quantum mechanical methods for approximate description of molecular electronic structure, and their applications, will be discussed. Statistical mechanics will be based around the definition of partition functions, and will employ such definitions in discussion of thermodynamics and kinetics. Extension of quantum mechanics to the solid state will lay the basis for of band theory description of the electronic structure of metals, semi-conductors and insulators.

Knowing(these are things that all students will need to be able to do to pass the module):

• Demonstrate awareness of methods for description of electronic structure of molecules and solids.
• Describe means to relate molecular to macroscopic properties using the techniques of statistical mechanics.

Acting(Performance in this area will enable students to achieve more than a basic pass):

• Evaluate results of electronic structure calculations, critically assess their performance and extract chemically relevant properties.
• Calculate thermodynamic and kinetic properties of molecular systems from knowledge of molecular properties.
• Understand and predict key properties of materials based on a band structure description of their electronic structure.

Being(Performance in this area will enable students to achieve more than a basic pass):

Retrieve and communicate data, findings and procedures from a variety of sources (literature, electronic databases, experiments/calculations).

Content will be delivered primarily using lectures (22 h across one semester, equating to two lectures per week). In addition, lectures will include worked problems and informal ad hocformative tests. This will address the learning outcomes under the ‘Knowing’ heading, while examples presented will show students how they may also demonstrate their achievement of the ‘Acting’ learning outcomes.

Workshops (3 x 1 h, two formative, one summative) will be used to enhance and assess problem-solving skills related to the retrieval and analysis of data.

Tutorials (2 x 1 h, formative) will allow tutors to monitor and guide the progress of students in meeting all learning outcomes.

Chemistry-specific skills will be focused on applying ideas from fundamental physical chemistry to understand how modern descriptions of the electronic structure of molecules and solids are constructed and applied to reach a unified picture of molecular properties. Students will develop a detailed understanding of how properties of molecules and materials are related to their electronic structure, and how these properties are related to observed macroscopic behaviour. The module will also involve a large element of problem solving using both numerical and algebraic techniques, based around real examples of theoretical methods.

The module is summatively assessed via in course assessments.

There is no examination for this module.

Quantum mechanics: Schrödinger equation, Born-Oppenheimer approximation; Exact solutions for model problems; electron spin and the Pauli principle; Coulomb and exchange energies; Variation theorem, approximate wavefunctions and energies; LCAO approximation, Slater determinants and basis sets; Hartree-Fock and self-consistent field approach; Electron correlation: Post-HF and density functional theory methods; potential energy surfaces and chemical properties.

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; role of partition functions in rate constants derived from transition state theory.

Band theory: 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.