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Computational Materials Science

Credits: 3

Lecturers: Hsu, Chao-Ping (許昭萍) and Jeng, Horng-Tay (鄭弘泰)

Part I: Hsu, Chao-Ping (許昭萍)

*course website:
http://idv.sinica.edu.tw/berrylab/courses/computationalmaterial2009/compmat97.html

Goals:

  1. Understand the fundamental theories behind modern quantum chemistry computation.
  2. Can use most quantum chemistry packages to obtained desired information. Know problems that computational quantum chemistry can offer.

Time: Wednesdays 9:10-12:00pm

Place: A508 Institute of Chemistry most of the times.
　　　For the last two lectures: Room 4011 (In the building of Central Office of Administration, 　　　4th floor)

Office hours: Thursdays 10-11 am, by appointment only. Please call or Email.

Grading: 50% Midterm + 50% Homeworks and Quizes

Textbook: [required]
        “Modern Quantum Chemistry” by A. Szabo and N. S. Ostlund.

Useful references are: [not required]

  1. I. N. Levin, Quantum Chemistry
  2. Mc Quarrie, Quantum Chemistry
  3. C. J. Cramer, Essentials of Computational Chemistry
  4. F. Jensen, Introduction to Computational Chemistry

Important policies:

  1. Homeworks are due one week after they are assigned, before the class starts. Late homeworks and term papers are NOT accepted.
  2. Discussion when working on homeworks is allowed. However, students are expected to write up their own solutions independently. Identical problem sets will not be graded, and will not receive any credit.

Weekly plan:

Week

Date

Topics

Links and files

1

2/18

Class setup
Background information

 2

2/25

Linear Algebra-Matrices and determinants
Eigenvalue problems
Determinants-many electron wave function

 

3

3/4

Spin, operators and matrix elements.
Born-Oppenheimer approximations
One and two-electron operators
Hartree-Fock Approximations

 

4

3/11

Hartree-Fock Theory
Semi-empirical methodologies

 

5

3/18

Basis sets, hand-on with Q-Chem
Examples of running jobs and obtaining scientific answers

 

6

3/25

Electron correlation

 

7

4/1

Structures and reactions
Introduction to simulations based on classical mechanics (1)

 

8

4/8

Introduction to simulations based on classical mechanics (2)
Review for mid term exam.

 

9

4/15

Mid-term exam

 

10

4/22

Part II-1: introduction

11
4/29
 CMS II-2: Density Functional Theory (DFT) and local-density approximation (LDA)
12
5/6
crystal structure, reciprocal lattice, and Brillouin zone
13
5/13
 band theory, band structure, k-point sampling, and density of state
14
5/20
plane wave, pseudopotential,
LDA, and LSDA
15
5/27
 Transition-metal oxides,
strong correlations, and LDA+U
16
6/3
 structure optimization
17
6/10
surface and molecule
18
6/17
 final exam  

Part II: Jeng, Horng-Tay (鄭弘泰)

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)