U of I

So Hirata

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 Molecular Electronic Structure
Advanced Quantum Chemistry & Numerical Methods
Spring 2017

Room: Noyes Laboratory 162
Period: January 17 – May 2, TR 9:30 – 10:50 AM

Instructor: So Hirata
Email: sohirata@illinois.edu
Phone: 217-244-0629
Office: CLSL A520
Office hours: 10:50 – 11:50 AM after class

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”

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


Project #1: Numerical methods for Schrödinger eq.

Homework #1

Project #1: Time-dependent perturbation theory and spectroscopy

Project #1

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

Homework #2

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

Homework #3

Operators, molecular integrals, Slater-Condon rules


Second quantization

Homework #4

Normal ordering, Wick’s theorem




Hartree-Fock theory

Homework #5

Molecular integrals over Gaussians

Homework #6

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

Homework #7

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

Project #2

Configuration-interaction theory

Why is energy extensive?

Coupled-cluster theory

Homework #8

Many-body perturbation theory


Density-functional theory

Homework #9

HF and DFT in density matrix form


Time-dependent HF and DFT for excited states

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

Crystal orbital theory and size consistency