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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Chemistry
- Instructor(s)
- Ohshima Yasuhiro Ishiuchi Shun-Ichi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- -
- Group
- -
- Course number
- CHM.C434
- Credits
- 1
- Academic year
- 2024
- Offered quarter
- 3Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
This course is designed to provide students the ability for systematic understanding on various chemical phenomena in terms of microscopic point of view, as well as present status of research in the fields. In this course, students will learn in particular about angular momentum algebra and its application to intermolecular interactions.
Student learning outcomes
By taking this course, students will acquire the ability to apply angular momentum algebra to molecular interactions.
Keywords
Clebsch-Gordan coefficient, rotation matrix, multipole expansion, intermolecular interatction
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Towards the end of class, students are given exercise problems related to what is taught on that day to solve.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Legendre polynomial and associate Legendre function | Derive low-order Legendre polynomials and associate Legendre functions. Derive the orthogonality. |
| Class 2 | Spherical harmonic | Derive low-order spherical harmonic functions. Derive the orthogonality. |
| Class 3 | Clebsch-Gordan coefficient and 3j-symbol | Explain the properties of the Clebsch-Gordan coefficient. Derive the coupled state of two 1/2 spin states. |
| Class 4 | Rotation matrics | Explain what a rotation matrix is. Convert a rotation matrix to Eular angular representation. Explain the relationship between rotation matrix and spherical harmonic functions. |
| Class 5 | Spherical tensor operator | Explain what a spherical tensor is. Derive the spherical tensor representation of a vector operator. |
| Class 6 | Multipole expansion | Explain what multipole expansion is. Derive the multipole expansion of the electrostatic potential. |
| Class 7 | Application to intermolecular interactions | Derive the multipole expansion of the electrostatic interactions between two molecules. Explain the distance dependence of multipole interactions. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None
Reference books, course materials, etc.
R. N. Zare: Angular Momentum - Understanding Spatial Aspects in Chemistry and Physics, Wiley
A. J. Stone: The Theory of Intermolecular Forces, Oxford
Assessment criteria and methods
Evaluated by repot.
Related courses
- CHM.C401 ： Basic Concepts of Physical Chemistry I
- CHM.C402 ： Basic Concepts of Physical Chemistry II
- CHM.C532 ： Advanced Quantum Chemistry
- CHM.C201 ： Introductory Quantum Chemistry
- CHM.C332 ： Quantum Chemistry
- CHM.A211 ： Mathematics for Chemistry I
- CHM.A212 ： Mathematics for Chemistry II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None
Other
See “Other” section in Japanese syllabus.
