Undergraduate Course: Electronic Structure Theory (PHYS11061)
|School||School of Physics and Astronomy
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Year 5 Undergraduate)
||Availability||Available to all students
|Summary||This course will introduce the methods and approaches used in parameter-free descriptions of the electronic structure of materials, which aim to solve the quantum mechanical many-electron problem. We will discuss underlying ground state theories, such as wave-function based correlation methods and density functional theory, and their implementations in high-performance computing environments. We will study how to use the linear response ansatz and many-body perturbation theory to extract excited state information from those calculations, and thus accurately simulate spectroscopic and inelastic scattering experiments.
Assignments will involve calculations on realistic materials on the UK's national supercomputer.
* The many-electron problem, Born-Oppenheimer approximation.
* Wave-function based approaches: Hartree, Hartree-Fock, self-consistent field method, correlation corrections.
* Density based approaches: Slater Xa method, Kato's cusp theorem, Hohenberg-Kohn theorems, Kohn-Sham equations, exchange-correlation functionals.
* Numerical implementations: basis sets, atomic pseudopotentials, Brillouin zone sampling, iterative diagonalization methods, software packages.
* Ground state properties of materials: Hellmann-Feynman theorem, stress tensor, geometry optimisations, electronic band structures, Fermi surfaces.
* Lattice dynamics: quasi-harmonic approximation, phonons, density functional perturbation theory, vibrational spectroscopy, electron-phonon coupling, BCS superconductivity.
* Electronic excitations: time-dependent density functional theory, many-body perturbation theory, Hedin's equations, Bethe-Salpeter equation, optical spectroscopy.
* Finite temperature effects: free energies, anharmonic phonons, first-principles molecular dynamics.
* Relativistic effects in materials, spin-orbit coupling.
* Nuclear quantum effects, path-integral molecular dynamics.
* Quantum chemistry methods in solids, quantum Monte Carlo methods.
* Molecular mechanics: chemical force fields, atomic many-body potentials, classical molecular dynamics, modelling of liquids and interfaces.
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 2,
Revision Session Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||60% coursework, 40% project.
|No Exam Information
On completion of this course, the student will be able to:
- State the many-electron problem and describe in precise terms commonly made approximations to make it tractable in simulations.
- Understand the numerical approximations underlying modern first-principles electronic structure implementations and deduce their limitations.
- Efficiently use scientific open-source software packages in a parallelised high-performance computing environment and analyse large-volume data sets from numerical simulations.
- Obtain ground and excited state properties of materials from atomistic modelling and be able to choose the appropriate level of theory for the simulations.
- Resolve conceptual and technical difficulties by locating and integrating relevant information from a variety of sources.
|Graduate Attributes and Skills
|Course organiser||Dr Elton Santos
|Course secretary||Miss Rachel Ord
Tel: (0131 6)50 9110