GENERAL INFO

This course will survey the computational methods commonly used to calculate the electronic properties of materials. The emphasis will be on both understanding the limitations and approximations of the various techniques, and learning to apply them to obtain meaningful results. There will be considerable hands-on computing, both developing programs and using public-domain packages. Specific computational approaches which we will cover include the tight-binding method, the empirical pseudopotential method and density functional theory. Assesment will be based entirely on computing assignments. Prerequisites: 1 year of graduate level quantum mechanics and solid state, or consent of instructor. Familiarity with a programming language.

RECOMMENDED TEXTS

• Electronic structure and the properties of solids, W.A. Harrison (Dover)
• Planewaves, Pseudopotentials and the LAPW Method, David J Singh (Kluwer Academic Pub)
• Electronic Structure, Dynamics, and Quantum Structural Properties of Condensed Matter (NATO Asi Series B, Physics, Vol 121), Jozef T. Devreese (Editor) (Plenum Pub Corp)

DETAILED COURSE OUTLINE

Mon. March 30.

• Tight-binding method for bulk materials.
• HW - read Chadi and Cohen paper

Wed. April 1.

• review Chadi and Cohen paper, computer implementation of TB method
• HW - write TB code

Mon. April 6.

• No class. extra office hours to help with HW - Thursday April 9, 2-4pm.
• HW - read Harrison review paper

Wed. April 8.

• T.B. for finite sized materials, 2nd quantization, methods for diagonalizing large matrices
• HW - read literature article on valence band line-ups.

Mon. April 13.

• Review article on valence band line-ups, further selected topics in TB - interfaces between semiconductors, spin-orbit coupling, TB fitting to ab initio bands(?)
• HW - read Marvin Cohen's article on pseudopotentials (PPs)

Wed. April 15.

• Empirical PP method, Nearly Free Electron model, why do PPs work at all? Phillips-Kleinman Cancelation theorem, properties of PPs.
• HW - article on empirical pseudopotential method

Mon. April 20.

• The empirical pseudopotential method, how to do a EPP calculation, examples from the literature
• HW - read Schluter and Sham paper on intro to density functional theory
• **TURN IN TB HW**

Wed. April 22.

• The interacting electron gas, intro to density functional theory (DFT) - formalism
• HW - admire Hohenberg-Kohn and Kohn-Sham papers

Mon. April 27.

• More DFT fundamentals - Kohn-Sham equations, the local density approximation, total energy calculations, pseudopotentials with DFT, contrast with LAPW method
• HW - read Yin and Cohen paper.

Wed. April 29.

• Intro to the castep package - how to actually run a calculation.
• HW - calculate bond length and bulk modulus of silicon

Mon. May 4.

• More applications of DFT - phonons, phase transitions, Kohn-Sham band structures
• HW - read Steve Louie's article in NATO book.

Wed. May 6.

• Modern ab initio PPs for DFT calculations
• HW - read HSC and BHS papers

Mon. May 11.

• No class (me at UCI). Extra office hours to help with castep calculation - Thursday May 14, 2-4pm
• HW - catch up with your reading!

Wed. May 13.

• Optimized PPs, non-linear core corrections (NLCCs)
• HW - read Andrew Rappe's paper on optimized PPs, plus Steve Louie's paper on NLCCs.

Mon. May 18.

• How to actually calculate a pseudopotential
• HW - calculate a pseudopotential!
• **TURN IN DFT Si HW**

Wed. May 20.

• No class (me at UCSD). Extra office hours to help with pseudopotential calculation - Thursday May 21, 2-4pm.

Mon. May 25.

• Memorial Day - no class

Wed. May 27.

• Last class - review, questions, left-overs.

Mon. June 1.

• Student presentations - special topics - your choice

Wed. June 3

• Student presentations - special topics - your choice

Fri. June 12.

• **TURN IN PSEUDOPOTENTIAL HW**