Computational and Theoretical Chemistry 2, NWI-MOL176 (3EC)

Lecturer: Prof. Gerrit C. Groenenboom
It is assumed you participated in CTC1.

Lecture on Wednesday April 23, 13:30-15:15 is in HG02.802

Course description
Schedule
Lecture notes (last update 27-Apr-2025)

Computer assignments

Computer assignment 1 (report due Friday 25-April-2025) [r_e(HF) corrected on 20-April-2025]
Computer assignment 2 (report due Friday 23-May-2025)
Computer assignment 3 (report due Friday 13-June-2025)

Lectures

(Topics with section numbers in Lecture notes)

Week 1: Diatomic molecules
- Classical dynamics
  - 1.1 Newton's law
  - 1.2 Hamilton's classical equations of motion
  - 3.0 Diatomic, separation of center-of-mass
  - 4.1 Diatomic molecule in 3D
- Quantum: rotation-vibration of diatomic molecule
  - 3.1 One-dimensional model
  - 4.2 Angular momentum operator
  - 4.3 Kinetic energy operator (3D)
  - 4.4 Ro-vibrational wave functions
Week 2: Angular momentum theory I
- 5.1 Angular momentum states
- 5.2 Ladder operators
- 5.3 Matrix representation
- 5.4 Functions of operators
- 5.5 Functions of Hermitian matrices
- 5.6 Translation as a unitary operator
- 5.7 Rotation operator
Week 3: Angular momentum theory II
- 5.8 Rotations in R³
- 5.9 Wigner rotation matrices
- 5.10 Rotational wave functions
- 5.11 Euler angles
- 7.2 Atom-diatom Jacobi coordinates
- 7.3 Atom-diatom Hamiltonian
- 7.4 Atom-diatom uncoupled basis
Week 4: Atom-diatom system
- 7.5 Total angular momentum representation
- 7.6 Clebsch-Gordan coefficients
- 8.1 Expansion of potential
- 8.2 Gauss-Legendre quadrature
- 8.3 Spherical hamonics addition theorem
Week 5:
- 8.4 Clebsch-Gordan series
- Two-fold symmetries
- Permutation symmetry, bosons & fermions
- Parity
- Symmetry adapted basis sets
- Selection rules
Week 6:
- 10.1 Classical Hamiltonian rigid rotor, inertial tensor
- 10.2, 10.3 Body-fixed and principle-axis frames
- 10.4 Quantum rigid rotor
- 10.5, 10.6 Space-fixed and body-fixed angular momentum operators
Week 7:
- 10.7 Angular momentum eigenfunctions
- 10.8 Rotational wave functions, sperical top, symmetric top asymmetric top

Exercises

Practice exam

Download pdf. The answers will be made available on brightspace.

Instruction for computer assignment reports

The computer program must be handed in (in brightspace) 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.

HTML5-validator Last updated: 20-Apr-2025, by Gerrit C. Groenenboom.