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
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 Clebsch-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
|Three computer assignments (Pass/Not pass) and written exam.|
|Lecture notes will be available. 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"