## COURSE DESCRIPTION

This course is aimed at introducing concepts and methods in modern electronic structure theory as applied to materials science. The course will begin with a review of one-electron theories and illustrate their usefulness through some common applications. An introduction to many electron problem along with a description of state of the art techniques, such as density functional theory, quantum Monte Carlo, many body perturbation theory, will follow. Practical aspects of the methods will be discussed in the context of problems of contemporary interest.

## COURSE CONTENTS

Revision of one electron theory: Periodic systems, Bloch theorem, Tight binding method, application to 1 dimensional crystals: chain of atoms, 2-dimensional systems (e.g. graphene), 3-dimensional systems (e.g. silicon).

Many electron systems: Crystal Hamiltonian, Born Oppenheimer approximation, Variational principle, brief introduction to Hartree-Fock theory.

Density Functional Theory: Fundamental theorems, Kohn-Sham formalism, practical aspects - basis sets, pseudopotential, Brillouin zone sampling, approximate exchange-correlation functionals.

Description of metals and insulators: Density of states, band dispersion, work function, smearing.

Spin density functional theory: magnetism, exchange interaction, strongly correlated materials and the DFT+U approach.

Advanced topics: Phonons, Berry phase approach to electric polarization, NEB, kinetic Monte Carlo, Ab initio MD, Quantum Monte Carlo, Perturbation theory methods - GW.

Nanomaterials, surfaces, interfaces.

**Prerequisites:**CHM 322/642 or PHY 303 or equivalent

**Text Books:**

- R. Martin, Electronic Structure: Basic Theory and Practical Methods
- A. P. Sutton, Electronic Structure of Materials
- D. Scholl, Density Functional Theory
- W. A. Harrison, Electronic Structure and the Properties of Solids
- D. Khomskii, Basic Aspects of Quantum Theory of Solids
- G. Grosso and G. PastoriParravicini, Solid State Physics
- J. Thijssen, Computational Physics
- M. C. Desjonqueres, Concepts in Surface Physics

## COURSE ASSESSMENT

This course will feature assignments (10%), a project/term paper (10%), a mid-semester exam (30%) and an end-semester exam (50%).

## TUTORIALS

None

## ANNOUNCEMENTS

**[03.01.2018]** Happy New Year and Welcome Back!

**[21.01.2018]** Lecture Notes uploaded.

**[21.02.2018]** Lecture Notes uploaded.