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Computational Materials Science

Credits: 3

Lecturers: Jeng, Horng-Tay (¾G¥°®õ) and Takahashi, Kaito

Part I: Jeng, Horng-Tay (¾G¥°®õ)

Purpose of the course:

This lecture is designed to introduce the modern computational material science based on density functional theory (DFT). This lecture covers theoretical concept and practical applications using first-principles calculations within the local density approximation (LDA). The newly developed LDA+U method which takes the strong correlations U into consideration is also demonstrated to have insight into the localized systems. Also the surface and molecular systems are introduced.

Outline:

  1. Introduction to CMS and computational package VASP
  2. Electronic structure calculations of bulk systems
  3. Electronic structures of transition-metal oxides
  4. Strong correlations in localized systems
  5. LDA+U method and applications
  6. Band decomposed density of states and orbital ordering
  7. Surface calculations
  8. Molecular calculations

Evaluation: hands-on + final exam -- 50%

Useful books:

  • ¡§Local Density Theory of Polarizability¡¨, G. D. Mahan and K. R. Subbaswamy (1990).
  • ¡§Handbook of The Band Structure of Elemental Solids¡¨, D. A. Papaconstantopoulos (1986).
  • ¡§Strong Coulomb Correlations in Electronic Structure Calculations¡¨, V. I. Anisimov (2000)

Part II: Takahashi, Kaito

Purpose of the course:

The goal of this class is to understand what kind of calculation is done in package programs and to learn which method to use for the problem you want to solve! We will first learn the mathematical basics behind quantum chemistry calculations, the calculation on energies of electrons. Then we will study how these energies affect the motion of the nucleus, ie, understanding molecular structure and reaction. Next we will survey the methods used to simulate spectra that experimentalists take. Lastly methods used to model reactions in liquids will be presented.

Course schedule:

Week
Topics
  
1
Born Oppenheimer Approximation, LCAO H2+ calculation
2
H2, homonuclear and heteronuclear diatomic molecule, Restricted Hartree Fock
3
Unrestricted Hartree Fock, Roothan Equation, Basis Set Gaussian Calculation Input/structure optimization
4
Potential Energy Surface, Barrier Transition State
5
Electron correlation (DFT, MP2, QCISD, CCSD, CASSCF, MRCI, G2 G3)
6
Vibrational Spectroscopy, Electronic Spectroscopy
7
Force field parametrization, intermolecular potential
8
Molecular dynamics simulation of liquid, review for test
9
Test

Evaluation: Final test 50%, Oral Presentation 25%, Home Work 25%

Book: Modern Quantum Chemistry, Attila Szabo and Neil S. Ostlund