This course is designed to provide students systematic understanding on quantum states of atoms and molecules and their interaction with optical fields, by extending the study on the microscopic fundamental laws, introduced in the preceding course: CHM.C201, “Introductory quantum chemistry.” The course is organized to develop students' abilities in the following two main subjects:
(A) Optical transition and quantum states in molecules: Utilizing the time-dependent perturbation theory and applying it to derive fundamental rules for optical transitions in atoms and molecules, and utilizing the aforementioned fundamental knowledge on quantum chemistry to understand the energy levels of molecules and molecular spectra,
(B) Angular momentum and quantum states in atoms: Understanding fundamentals of angular momentum in quantum mechanics and applying them to solve basic problems relating various angular momenta appearing in atoms, and utilizing the acquired knowledge to establish detailed description of quantum states in atoms.
By the end of this course, students will be able to:
1) Understand how to utilize the basic principles of quantum chemistry, such as angular-momentum and perturbation theories, and apply them appropriately to various problems relating microscopic behavior of atoms and molecules,
2) Find out by themselves the way to explore microscopic properties of atoms and molecules and their reactivity, on the basis of clear understanding on atomic and molecular quantum states and their response to external stimulation such as optical and magnetic fields.
Physical chemistry, Quantum mechanics, Anugular momentum, Optical transitions, Atomic and molecular spectra
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
(1) At the biginning of each class, subjects of the previous class are reviewed briefly.
(2) Towards the end of class, students are given excercise problems related to what is taught on that day to solve.
(3) Students must familiarize themselves with topics described in the required learning section before comming to class.
|Course schedule||Required learning|
|Class 1||(A) Optical transition and quantum states in molecules (1) Time-dependent perturbation theory||Describe the first-order correction for wave function by the perturbation theory. Calculate the change of eigen energy and wave function by the constant perturbation.|
|Class 2||(B) Angular momentum and quantum states in atoms (1) Angular momentum and its shift operators||Describe the commutation relation of angular momentum. Derive matrix elements for the shift operators.|
|Class 3||(A) Optical transition and quantum states in molecules (2) Field-matter interaction, derivation of optical transition rates||Describe the interaction term for optical transition. Explain what the Fermi’s golden rule is.|
|Class 4||(B) Angular momentum and quantum states in atoms (2) Coupling of two angular momenta||Derive the values of total angular momentum composed with two angular momenta. Explain what the vector model for angular momentum is.|
|Class 5||(A) Optical transition and quantum states in molecules (3) Stimulated absorption/emission and spontaneous emission||Explain what the Einstein’s A and B constants are. Explain the principle of LASER. Explain the wave-length dependence for spontaneous-emission probability.|
|Class 6||(B) Angular momentum and quantum states in atoms (3) Spin multiplicity and orbital and spin angular momenta||Describe the singlet and triplet spin functions. Explain the way for coupling of orbital and spin angular momenta.|
|Class 7||(A) Optical transition and quantum states in molecules (4) General remarks on molecular energy levels and spectra, molecular rotational spectrum||Explain the energy ordering for electronic, vibrational, and rotational motion. Explain the relation between rotational spectra and molecular structure.|
|Class 8||(B) Angular momentum and quantum states in atoms (4) Composite orbital/spin momenta and term symbols||Derive the commutation relation between two orbital angular momenta. Derive the term symbols for atoms in the first and the second rows.|
|Class 9||(A) Optical transition and quantum states in molecules (5) Molecular vibrational spectrum||Describe the selection rules for vibrational transitions. Explain what the Raman process is.|
|Class 10||(B) Angular momentum and quantum states in atoms (5) Stater determinants, LS coupling||Derive the Slater determinants of the excited states of He. Describe the operator for the spin-orbit interaction.|
|Class 11||(A) Optical transition and quantum states in molecules (6) Molecular electronic spectum||Describe the electronic states of nitrogen molecule. Explain what the Franck-Condon principle is.|
|Class 12||(B) Angular momentum and quantum states in atoms (6) Selection rules for atomic absorption/emission||Describe the optical selection rules for atomic hydrogen. Explain the splitting in the D lines of alkali atoms.|
|Class 13||(A) Optical transition and quantum states in molecules (7) Relaxation processes in electronic excited states||Explain the relation between fluorescence life times and non-radiative transitions. Explain what internal conversion (IC) and intersystem crossing (ISC) are.|
|Class 14||(B) Angular momentum and quantum states in atoms (7) Magnetic property of atoms and molecules||Explain the operation principle of electron spin resonance (ESR). Explain what the hyperfine splitting is.|
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.
Physical chemistry: A molecular approach, by D. A. McQuarrie and J. D. Simon, The University Science Books.
Physical chemistry, by P. W. Atkins, Oxford University Press.
Molecular Quantum Mechanics, by P. W. Atkins, Oxford University Press.
Students will be assessed on their understanding of fundamentals of quantum mechanics and their application to atomic/molecular systems.
Students' course scores are based on the final exam (60%) and exercise problems (40%).
No prerequisites are necessary, but enrollment in the related courses is desirable.
Yasuhiro Ohshima: ohshima[at]chem.titech.ac.jp
Masakazu Yamazaki: yamazaki[at]chem.titech.ac.jp
Contact by email in advance to schedule an appointment.
Yasuhiro Ohshima (West Building 4, Room 105B)
Masakazu Yamazaki (West Building 4, Roon 502)