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 2025
Syllabus

Room: Literatures, Cultures & Linguistics G18
Period: January 21 – May 7, TR 9:30 – 10:50 AM

Instructor: So Hirata
Email: sohirata@illinois.edu
Phone: 217-244-0629
Office: Noyes Laboratory 355F
Office hours: On appointment

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

Recommended texts:  I. Shavitt and R. J. Bartlett, “Many-Body Methods in Chemistry and Physics”
B. O. Roos, “Lecture Notes in Quantum Chemistry” I and II
R. D. Mattuck, “A Guide to Feynman Diagrams in the Many-Body Problem”
N. H. March, W. H. Young, and S. Sampanthar, “The Many-Body Problem in Quantum Mechanics”
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: Weekly homework assignments 50%. Programming reports 50%. In grading these, emphasis will not be placed on the correctness or completeness. 

Date

Online lecture notes

Miscellaneous

1/23

Project #1: Time-independent Schrödinger equation solver

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

(Additional Materials: Dirac bra-ket notations, orthogonal functions, unitary transformation, diagonalization, delta function)

Project #1 (due on 2/25)

Project #1 (alternate) (due on 2/25)

Homework #1 (due 1/28)

1/28

Slater determinants, operators, molecular integrals, Slater-Condon rules

Homework #2 (due 1/30)

1/30

Second quantization

Homework #3 (due 2/4)

2/4

Normal-ordered second quantization

Homework #4 (due 2/6)

2/6

Wick’s theorem

(Additional Materials: Quantum field theory)

Homework #5 (due 2/11)

2/11

Feynman diagrams

2/13

Hartree-Fock theory (part I)

2/18

Hartree-Fock theory (part II)

2/20

Density-functional theory

(Additional Materials: Homogeneous electron gas)

2/25

Molecular integrals over Gaussians

(Additional Materials: Pople's memoirs on S.F.Boys)

Homework #6 (due 2/25)

2/27

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

Project #2 (due on 4/1)

Project #2 (alternate) (due on 4/1)

3/4

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

3/6

Configuration-interaction theory (part I)

Homework #7 (due 3/11)

3/11

Configuration-interaction theory (part II)

3/13

Coupled-cluster theory

(Additional Materials: Bartlett's ACS Award citation)

Homework #8 (due 3/13)

3/25

Many-body perturbation theory

Homework #9 (due 3/25)

3/27

Density matrix formulation

4/1

Time-dependent HF and DFT for excited states

(Additional Materials: Time-dependent perturbation theory and spectroscopy)

4/3

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

Project #3 (due on 5/6)

Project #3 (alternate) (due on 5/6)

4/8

Equation-of-motion coupled-cluster theory for excited states

4/10

Many-body Green's function theory (part I)

(Additional Materials: Intro to MBGF; Failures of MBGF; Summary)

4/15

Many-body Green's function theory (part II)

4/17

Crystal orbital theory (part I)

4/22

Crystal orbital theory (part II)

4/24

Size consistency and linked-diagram theorem

(Additional Materials: Why is energy extensive?; Summary)

4/29

Finite-temperature many-body perturbation theory

(Additional Materials: Lecture video; slides)

5/1

Finite-temperature HF theory

5/6

Superconductivity

 

N/A

Pulay's analytical gradient method

(Additional Materials: Pulay's ACS Award citation)