U of I

So Hirata

Marvin T. Schmidt Professor
Department of Chemistry

Noyes Laboratory 355F
600 S. Mathews Ave.
Urbana, IL 61801-3364

Tel: (217) 244-0629
Fax: (217) 244-3186
Email: sohirata@illinois.edu

CHEM 548 Advanced Electronic Structure
For Molecules and Solids
Spring 2021
Syllabus

Room: Zoom
Period: January 26 – May 4, TR 9:30 – 10:50 AM

Instructor: So Hirata
Email: sohirata@illinois.edu
Phone: 217-244-0629
Office: Zoom
Office hours: On appointment

Required text: A. Szabo and N. S. Ostlund, “Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory”

Recommended texts: B. O. Roos, “Lecture Notes in Quantum Chemistry” I and II
T. Helgaker, P. Jørgensen, and J. Olsen, “Molecular Electronic Structure Theory”
N. H. March, W. H. Young, and S. Sampanthar, “The Many-Body Problem in Quantum Mechanics”
I. Shavitt and R. J. Bartlett, “Many-Body Methods in Chemistry and Physics”
R. D. Mattuck, “A Guide to Feynman Diagrams in the Many-Body Problem”
J. J. Sakurai, “Advanced Quantum Mechanics”

Objectives: This course is intended for graduate students who specialize in computational or theoretical quantum chemistry. Its goal is to have students acquire skills essential for developing new computational methodologies broadly applicable to atomic, molecular, solid-state chemistry. This course does not teach how to run computational chemistry programs. Instead, it teaches how to write computational chemistry programs and to derive formulas of the underlying theories. This course interleaves lectures on theories and computer programming projects. The lectures encompass electronic structure methods, introductory band theory, and harmonic and anharmonic vibrational analyses. The programming projects are fun.

Exams: There will be no exams.

Programming reports: There will be three computer programming projects. One or two lectures will introduce each project and students are asked to work on them outside the lecture hours individually or in small groups. Students who are not familiar with programming are strongly encouraged to take advantage of the instructor’s office hours to seek hands-on assistance. Each student must write his/her own research-paper-style report and submit it to the instructor by the due date. Each student must have an access to a basic coding environment (a UNIX or LINUX computer or cluster with a C or Fortran compiler) and will be given one if he/she does not.

Grades: Attendance and class participation 50%. Programming reports 50%. In grading the reports, emphasis will not be placed on the correctness or completeness of the programs written. 

Online lecture notes

Miscellaneous

Project #1: Numerical methods for Schrödinger eq.

Optional Homework #1

Project #1: Time-dependent perturbation theory and spectroscopy

Project #1 (due on 2/18)

Slater determinants, Dirac bra-ket notations, orthogonal functions, unitary transformation, diagonalization, delta function

Optional Homework #2

Electronic structure theory overview, Hartree-Fock theory, full configuration-interaction theory

Optional Homework #3

Operators, molecular integrals, Slater-Condon rules

 

Second quantization

Optional Homework #4

Normal ordering, Wick’s theorem

 

Feynman diagrams

Quantum field theory (New)

Hartree-Fock theory

Optional Homework #5

Molecular integrals over Gaussians

Optional Homework #6

Pulay's analytical gradient method

Pulay's ACS Award citation

Project #2: Gaussian functions, Fourier transform, real and reciprocal spaces, correlation function

Optional Homework #7

Project #2: Wave packet propagation, phase and group velocities, Ehrenfest theorem, convolution theorem, path integrals

Project #2 (due on 3/25)

Configuration-interaction theory

Why is energy extensive?

Coupled-cluster theory

Bartlett's ACS Award citation

Many-body perturbation theory

Optional Homework #8

Finite-temperature many-body perturbation theory (New)

Lecture video slides (New)

Many-body Green's function theory (New)

Intro to MBGF (New)

Density-functional theory

Optional Homework #9

HF and DFT in density matrix form

 

Time-dependent HF and DFT for excited states

Optional Homework #10

Coupled-cluster and configuration-interaction theories for excited states

 

Project #3: Hückel and Su-Schrieffer-Heeger band structures for 1D and 2D solids

Project #3 (due on 5/4)

Crystal orbital theory and size consistency

 

Superconductivity (New)

 

Special theory of relativity

 

Relativisitic quantum mechanics and quantum electrodynamics