Quantum Theoretical Chemistry, NWI-MOL112 (3EC)

Lecturer: Prof. Gerrit C. Groenenboom

In 2022-2023 this course will be replaced by two new courses:

Code	Name	Lecturer	quarter
NWI-MOL174	Computational and theoretical chemistry 1	Tijs Karman	3rd quarter
NWI-MOL176	Computational and theoretical chemistry 2	Gerrit C. Groenenboom	4rd quarter

Note: this website will be updated during the course:

Course guide
Schedule
The TAs are the PhD students: Kim Steenbakkers, Marijn Man, Etienne Walraven
There are three computer assigments, they should be turned in at the end of weeks 3, 5, and 7 on brightspace. If you cannot make let me know how much extra time you need.

Lecture notes (updated Feb 16, 2022)

Week 1
- Chapter 1, 2, and 3 of the Lecture notes
- Topics
  - Review of quantum mechanics for particle in one dimension
  - Hermitian operators
  - "Diatomic molecule" in one dimension
- Exercise
  - Set up variational calculation of anharmonic vibration in harmonic oscillator basis
- Computer assignment 1: variational calculation
Week 2, Chapter 4
- Diatomic molecules in three dimensions, classically
- Diatomic molecules in three dimensions, quantum mechanically
- Exercise
Week 3, Chapter 5
- Angular momentum theory
- Exercise
- Computer assignment 2: numerical solution of 1D problem, Chapter 6
Week 4, Chapter 7
- Atom-diatom system
- Angular momentum coupling
- Exercise
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
- Computer assignment 3: variational calculation atom-diatom system
Week 6, Chapter 9
- Two-fold symmetries
- Permutation symmetry, bosons & fermions
- Parity
- Symmetry adapted basis sets
- Selection rules
- Exercise
Week 7
- Finish computer assignments
- An example exam with answers is available on brightspace.

Computer assignment language

The computer assignments can be done in your favorite language, using your favorite operating system:

Matlab - make sure you get a license from C&CZ to work at home
Python - you'll need the numpy library
Octave - free software, mostly compatible with Matlab
Scilab - free software, syntax not quite the same as Matlab

Chemistry students probably want to use Matlab, physics students probably know python. Octave may be a bit slower than Matlab, but we won't need big calculations, so it should work, and you won't need a license. Scilab is used in the theoretical chemistry group for some projects, so this could be an opportunity to learn to use it if you consider a traineeship in the theoretical chemstry group. In the theoretical chemistry group we mostly use Linux, but Windows or Mac should be fine for this course.

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.

Aims

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 theory
Compute energy shifts due to external electric and magnetic fields

Content

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.

Topics

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

Additional comments

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: https://www.theochem.ru.nl/qtc

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" (NWI-MOL406).

HTML5-validator Last updated: 28-Mar-2023, by Gerrit C. Groenenboom.