Physico-chemical principles augmented by ever-advancing computation technology have become a tool for explaining rich materials properties, designing nano-structures and their possible functionality. This course overviews basic quantum principles of materials structure, and a hierarchy of approximations broadly used in computational models. This includes classical many-body potentials, tight-binding approximations, electronic density functional theory methods, etc. Along with the basic theoretical concepts, students will acquire practical skills for using state-of-the-art software packages (*Mathematica*, codes for performing first-principles calculations) for solving real-life problems in materials science.
**Basic Theory…**
- Quantum mechanics refresher
- The Thomas–Fermi model: early density functionals
- N-particle systems, independent electrons
- The Hartree–Fock theory
- The Kohn–Sham theory
- Periodic systems and Bloch theorem
- The Born-Oppenheimer approximation
- The tight-binding method
- Molecular dynamics methods
- Beyond the independent particle approximation
- The cluster expansion method
**and Practice**
- Introduction to
*Mathematica*: syntax, concepts, examples
- Simple lattices
- Implicit lattices: a random walk example
- Solving the Thomas–Fermi equation
- Lower excited states of He from a variational principle: dissecting a Wolfram Demonstrations project
- Functional derivatives in DFT: symbolic calculations and Mathematica packages
- Tight-binding band structure with Mathematica: graphene
- Quantum Espresso: short intro
- Bulk properties of Si
- Band structure of Si
Textbooks:
R. Martin, *Electronic Structure: Basic Theory and Practical Methods *(Cambridge, 2004)
R. Parr, W. Yang, *Density-Functional Theory of Atoms and Molecules* (Oxford, 1989)
P. Welin, *Programming with Mathematica. An introduction* (Cambridge, 2013) |