Students are given an overview of quantum chemistry for the fundamentals of physical chemistry, and provided with the quantum-chemical basics for an idea on materials, from atoms and molecules to molecular aggregates.
Students will understand the principle of the indistinguishability of identical particles, which forms the foundation of physicochemical properties of materials, as well as Pauli's principle, which is derived from it. Students then learn about the electronic state, structure, dynamic properties of molecules and their interaction with light. Furthermore, based on statistical mechanics of molecular aggregates, students study the electronic state and electronic properties of molecular aggregates, and learn the concepts of metals, semiconductors, etc.
By the end of this course students will understand
1) the indistinguishability of identical particles and the Pauli principle
2) the hierarchy of energy in molecules and the corresponding spectroscopy
3) the electronic states and electronic properties of condensed matter and the behavior of metals and semiconductors
Indistinguishability of identical particles, the Pauli principle, Molecular structure, Molecular spectroscopy, Molecular partition function, Density of states, Fermi energy
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
The topic changes every 5 weeks.
|Course schedule||Required learning|
|Class 1||The Pauli principle, revisited (the two-body system)||Derive the property of the permutation symmetry of two identical particles from the indistinguishability of identical particles.|
|Class 2||The Pauli principle, revisited (the n-body system)||Derive the property of the permutation symmetry of n identical particles from the indistinguishability of identical particles.|
|Class 3||The Pauli principle, revisited (bosons and fermions)||Understand that the quantal particles are divided into two groups, the bosons and fermions.|
|Class 4||The system comprising n identical bosons||Understand the behavior of the system comprising n identical bosons.|
|Class 5||The system comprising n identical fermions and the Pauli principle||Understand the behavior of the system comprising n identical fermions and prove the Pauli principle.|
|Class 6||Introduction of energy levels of molecules||Explain the hierarchy of energy in molecules and the corresponding wave lengths of light.|
|Class 7||Rotational levels and microwave spectroscopy||Quantitatively describe the rotational energy level structure of linear molecules and show the relationship to molecular structure.|
|Class 8||Vibrational levels and IR/Raman spectroscopy||Quantitatively describe the energy level structure of harmonic oscillators and explain the selection rules for IR transitions.|
|Class 9||Electronic states and visible/UV spectroscopy||Describe the electronic states of molecules in terms of molecular orbitals and specify the symmetry of the electronic states by using group theory.|
|Class 10||Electron and Nuclear spins and magnetic resonances||Describe the quantum mechanics of spin angular momentum, and quantitatively show the interactions between the spin and the external magnetic field and between multiple spins.|
|Class 11||Fundamental of statistical physics||Explain molecular partition function.|
|Class 12||Application of statistical physics to ideal gas||Explain molecular partition function of ideal gas.|
|Class 13||Lattice specific heat||Explain lattice specific heat.|
|Class 14||Electronic structure of solids||Explain density of states of metal.|
|Class 15||Electronic specific heat||Explain temperature dependence of electronic specific heat.|
Course materials are provided during class if necessary.
Students’ course scores are based on understanding of basic concepts of atoms and molecules, condensed matter, and surfaces.
Activities in class 10%, Final examination 90%
Introductory quantum chemistry
Noriyuki Kouchi nkouchi[at]chem.titech.ac.jp
Yasuhiro Ohshima ohshima[at]chem.titech.ac.jp
Manabu Kiguti kiguti[at]chem.titech.ac.jp
Contact by email in advance to schedule an appointment.
Noriyuki Kouchi (West Building 4, Room 508)
Yasuhiro Ohshima (West Building 4, Room 105B)
Manabu Kiguti (West Building 4, Room 102B)