Undergraduate Course: Electronic Structure Theory (PHYS11061)
Course Outline
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 
SCQF Credits  10 
ECTS Credits  5 
Summary  This course will introduce the methods and approaches used in parameterfree descriptions of the electronic structure of materials, which aim to solve the quantum mechanical manyelectron problem. We will discuss underlying ground state theories, such as wavefunction based correlation methods and density functional theory, and their implementations in highperformance computing environments. We will study how to use the linear response ansatz and manybody 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. 
Course description 
* The manyelectron problem, BornOppenheimer approximation.
* Wavefunction based approaches: Hartree, HartreeFock, selfconsistent field method, correlation corrections.
* Density based approaches: Slater Xa method, Kato's cusp theorem, HohenbergKohn theorems, KohnSham equations, exchangecorrelation functionals.
* Numerical implementations: basis sets, atomic pseudopotentials, Brillouin zone sampling, iterative diagonalization methods, software packages.
* Ground state properties of materials: HellmannFeynman theorem, stress tensor, geometry optimisations, electronic band structures, Fermi surfaces.
* Lattice dynamics: quasiharmonic approximation, phonons, density functional perturbation theory, vibrational spectroscopy, electronphonon coupling, BCS superconductivity.
* Electronic excitations: timedependent density functional theory, manybody perturbation theory, Hedin's equations, BetheSalpeter equation, optical spectroscopy.
* Finite temperature effects: free energies, anharmonic phonons, firstprinciples molecular dynamics.
* Relativistic effects in materials, spinorbit coupling.
* Nuclear quantum effects, pathintegral molecular dynamics.
* Quantum chemistry methods in solids, quantum Monte Carlo methods.
* Molecular mechanics: chemical force fields, atomic manybody potentials, classical molecular dynamics, modelling of liquids and interfaces.

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 State the manyelectron problem and describe in precise terms commonly made approximations to make it tractable in simulations.
 Understand the numerical approximations underlying modern firstprinciples electronic structure implementations and deduce their limitations.
 Efficiently use scientific opensource software packages in a parallelised highperformance computing environment and analyse largevolume 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.

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  Not entered 
Contacts
Course organiser  Dr Andreas Hermann
Tel: (0131 6)50 5824
Email: a.hermann@ed.ac.uk 
Course secretary  Ms Grace Wilson
Tel: (0131 6)50 5310
Email: Grace.Wilson@ed.ac.uk 

