Quantum Theoretical Chemistry, NWI-MOL112 (3EC)
Note: this website will be updated during the course:
I will decide on how to organize the exam by Friday March 27, 2020 at the latest.
Answers in LaTeX for
the exercises of week 1, 2, 3, 4, 5, and 6, including questions in the corresponding Chapters are available below.
At the bottom of the page there are instructions for the computer assignment reports.
Hints and intermediate results for the computer assignments are available:
March 29, 2020: bug fixed in clebsch_gordan.m
Lecturer: Prof. Gerrit C. Groenenboom
- Week 1
- Week 2
- Week 3
- Week 4, Chapter 7
- Week 5, Chapter 8
- Atom-diatom: potential energy matrix elements
- Legendre expansion of potential
- Gauss-Legendre quadrature
- Spherical harmonics addition theorem
- Clebsch-Gordan series of Wigner D-matrices
- (Exercises in text chapter 8)
- Exercise (version April 7, 2020) (Answers-wk5.pdf [Eqs. (3), (4), fixed April 7, 2020])
- Week 6, Chapter 9
- Two-fold symmetries
- Permutation symmetry, bosons & fermions
- Symmetry adapted basis sets
- Selection rules
- Exercise (version Mar 11, 2020) (Answers-wk6.pdf)
Instruction for computer assignment reports
The computer program must be handed in (by e-mail to gerritg at theochem.ru.nl),
together with a brief report.
The report should contain enough detail so that
someone who has not seen the assignment can read the report and
understand which equations are solved by the computer program, and
how. All the parameters that were used must be given, so that it
would be possible to reproduce the results, without looking at the
program. There is no need, however, to include derivations and
general theory that can be found in the lecture notes. An
example of such a report (without the code though), is this
report on a particle-in-a-box time-dependent wave packet.
There are more hints for writing reports here. In particular, read
the "checklist for report". The abstract/introduction/conclusions etc
is not necessary for the computerassignment report.
After following this course, the student is able to:
- Write down the Hamiltonian of a small molecule
or a molecular complex in a suitable coordinate system
to describe rotation and vibration
- Use angular momentum theory and group theory to
setup suitable basis functions for a variational
calculation of molecular energy levels
- Write small computer programs to solve the
time-independent and time-dependent Schroedinger
equation to compute rotational and vibrational states
and compute spectra an other properties of these systems.
- Derive the proper functional form for intermolecular
interactions using first and second order perturbation
- Compute energy shifts due to external electric and magnetic fields
The focus of this course is the molecular quantum mechanics required to
describe the nuclear dynamics of gas phase molecules and clusters of
molecules, and to compute their spectra and physical properties. Most
principles will first be applied to diatomic molecules, but the
approach will be mathematical and form the basis of the quantum
mechanical study of molecules in general.
- Coordinate systems, in particular Jacobi coordinates
- The nuclear kinetic energy operator in internal coordinates
- Angular momentum operators and states
- Wigner rotation matrices
- Angular momentum coupling and Clesch-Gordan coefficients
- Integrals over Wigner rotation matrices
- Elementary group theory and the use of symmetry
- The use of discretization to solve the
anharmonic vibrational oscillator
During the "responsiecollege"
(Q&A session) each week a chapter will be discussed.
The student is expected to prepare for the lecture
by studying the material before the lecture.
The lecture notes, computerassignments, and topics of each
week are available on the website:
This course focuses on bound states of molecules. Collisions
of molecules or "quantum scattering" is the topic of
the master course on Quantum Dynamics (NWI-SM295).
The study of nuclear dynamics requires potential energy surfaces,
which are found by solving of the electronic Schrödinger equation.
This is the topic of the master course "Quantum Chemistry"
Last updated: 29-Mar-2020, by Gerrit C. Groenenboom.