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

Lecturer: Prof. Gerrit C. Groenenboom

It is assumed you participated in CTC1.

This course replaces the "Quantum Theoretical Chemistry''
course that was taught until 2022.

#### Computer assignments

#### 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 R
^{3}
- 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 (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.

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*Last updated: 10-Apr-2024, by Gerrit C. Groenenboom.*