Teaching

MSNE 433/533 – COMPUTATIONAL MATERIALS MODELING
Credits: 3
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, exampleswolframlogo
  • 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 introQuantum_espresso_logo
  • 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)
MSCI 506 – PHYSICAL PROPERTIES OF SOLIDS
Credits: 3
Survey of the electrical, magnetic, and optical properties of metals, semiconductors, and dielectrics based upon elementary band theory concepts. Required for materials science and engineering majors. Not offered every year.
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