Physical Chemistry II  Quantum Chemistry
Physical Chemistry II: Quantum Chemistry
物理化學二：量子化學 ( Lectured in Chinese)
30 units
This course aims to provide an introduction to the fundamental concepts in timeindependent quantum mechanics and approximation methods useful in physical chemistry, with an emphasis on the descriptions of manyelectron systems and spectroscopy. The lectures will be divided into three parts: 1/3 with focus on basics of timeindependent quantum mechanics and using quantum mechanics on simple systems, 1/3 with focus on electronic structures of atoms and molecules and the molecular orbital theory, and the last 1/3 with applications of quantum mechanics to spectroscopy.
This course aims to provide an introduction to the fundamental concepts in timeindependent quantum mechanics and approximation methods useful in physical chemistry, with an emphasis on the descriptions of manyelectron systems and spectroscopy. The lectures will be divided into three parts: 1/3 with focus on basics of timeindependent quantum mechanics and using quantum mechanics on simple systems, 1/3 with focus on electronic structures of atoms and molecules and the molecular orbital theory, and the last 1/3
Learning basic concepts of the quantum mechanic and its applications on the microscopic chemical system as the foundation of more advanced courses in chemistry.
General chemistry, basic calculus. ( A little bit of linear algebra will be better.)
wavefunction, timeindependent Schrödinger equation, quantum mechanical operators, particle in a box, harmonic oscillator, Hydrogenlike atoms, nondegenerate perturbation theory, variational theory, electronic structure of manyelectron atoms, electronic structure of molecules, molecular spectroscopy.
Physical Chemistry, 4^{th} Edition by Robert J. Silbey, Robert A. Alberty, and Moungi G. Bawendi, Wiley [SAB].
Week  Topics  Reference 

1  Why Quantum Mechanics? The Heisenberg Uncertainty Principle, The Timeindependent Schrödinger Equation, Operators  SAB 9.19.3 
2  The Superposition Principle & Expectation Values, Measurement  SAB 9.49.5 Lv Ch. 3 
3  Particle in a OneDimensional Box, Tunneling, Particle in a ThreeDimensional Box  SAB 9.6, 9.7, 9.15 
4  Quantum Harmonic Oscillator  SAB 9.9, 9.10, 9.17 
5  Postulates of Quantum Mechanics, Dirac Notation, Harmonic Oscillator Revisited, Direct Numerical Solution to the Schrödinger Eq.  SAB 9.13, 9.14 Lv 4.4, Ch. 7 
6  Angular Momentum & The Rigid Rotor, The Heisenberg Uncertainty Principle Revisited  SAB 9.11, 9.12 
7  No class  
8  Review Session  
9  Midterm Exam (Tuesday)  
9  The Schrödinger Equation for Hydrogenlike Atoms, Hydrogenlike Orbitals, Orbital Angular Momentum & Electron Spin  SAB 10.110.2, 10.4, 10.5 Lv 6.16.6, 6.8 
10  Electronic Structures of Hydrogenlike Atoms, Atomic Terms, Variational Method  SAB 10.6 Lv Ch. 8, Ch. 9 
11  Helium Atom, Pauli Exclusion Principle, Slater Determinant, ManyElectron Problems: HartreeFock Selfconsistent Field Method  SAB 10.8, 10.9 Lv Ch. 11 
12  The BornOppenheimer Approximation, The Hydrogen Molecule Ion, Electronic Structure of Manyelectron Molecules: Molecular Orbital Theory, Huckel Theory  SAB 11.111.7 
13  Introduction to Computational Chemistry  Lv Ch. 15, 16.8, 17.1, 17.2 
14  The Interaction between Molecules and Radiation, Transition Probabilities, Selection Rules  SAB 13.1, 13.2, 14.1 
15  Rotational & Vibrational Spectroscopy of Molecules  SAB 13.413.9 
16  Electronic Spectroscopy of Diatomic Molecules, FranckCondon Principle  SAB 14.114.5 
17  Excited states, Electronic & Vibrational Relaxation, Fluorescence & Phosphorescence  SAB 14.614.8 
18  Why Quantum Mechanics? The Heisenberg Uncertainty Principle, The Timeindependent Schrödinger Equation, Operators  SAB 9.19.3 
Lecture  Topic 

Lecture 1  Introduction to Quantum Chemistry 1:53:51
Topic 1 Introduction to this course Topic 2 Historical review
Topic 3 What is quantum chemistry? 
Lecture 2  Wave Function and the Time Independent Schrödinger Equation 55:52
Topic 1 Time independent Schrödinger equation
Topic 2 Operators 
Lecture 3  Operators and Measurement 1:21:52
Topic 1 Operators
Topic 2 Superposition principle Topic 3 Measurement I 
Lecture 4  Measurement 44:47
Topic 1 Measurement II 
Lecture 5  A Particle in a Box I 1:49:07
Topic 1 Topic 1 A particle in a one dimensional box
Topic 2 A particle in a three dimensional box 
Lecture 6  A Particle in a Box II 58:14
Topic 1 Application of a particle in a box model Topic 2 Particles in a finite depth well and tunneling 
Lecture 7  Quantum Harmonic Oscillator 1:36:08
Topic 1 Harmonic oscillator I 
Lecture 8  Quantum Harmonic Oscillator and Ladder Operator 53:30
Topic 1 Harmonic oscillator II 
Lecture 9  Postulate of Quantum Mechanics and Dirac Notation 1:36:09
Topic 1 Postulate of quantum mechanics
Topic 2 Dirac notation 
Lecture 10  Quantum Dynamics 51:53
Topic 1 Quantum dynamics 
Lecture 11  Rigid Rotor and Spherical Harmonic 51:53
Topic 1 Rigid rotor and spherical harmonic 
Lecture 12  Angular Momentum in Quantum System 46:30
Topic 1 Angular momentum in quantum system 
Lecture 13  Hydrogenlike Atom I  1:38:16
Topic 1 The Hydrogenlike atom 
Lecture 14  Hydrogenlike Atom II  52:40
Topic 1 Electronic structure of hydrogenlike atom Topic 2 Atomic spectrum and ionization energy Topic 3 Electronic wave function II 
Lecture 15  Hydrogenlike Atom III  1:41:09
Topic 1 Electronic structure of hydrogenlike atom Topic 2 Atomic spectrum and selection rule Topic 3 Zeeman effects Topic 4 Electron spins Topic 5 Fine structure and hyperfine structure on spectrum 
Lecture 16  Approximation Methods 47:51
Topic 1 Approximation method Topic 2 Variational theory
Topic 3 Perturbation theory 
Lecture 17  Manyelectron Atoms – Helium Atom and Little on Spin Statistic 1:40:03
Topic 1 Helium atom (ground state)
Topic 2 Electron spin statistic 
Lecture 18  Required of Valid ManyElectron Wave Functions and Slater Determinant 50:23
Topic 1 Condition for a valid manyelectron wave functions Topic 2 Slater determinant Topic 3 Electron configuration 
Lecture 19  Manyelectron Atoms and Atomic Term Symbols 1:00:00
Topic 1 Manyelectron atoms Topic 2 Atomic term symbol 
Lecture 20  Wavefunction of H^{2+} Molecules 43:44
Topic 1 H^{2+} molecular orbital theory 
Lecture 21  Constructing Molecular Wavefunctions – MO theory, Configuration Interaction and Valence Bond Theory 1:38:44
Topic 1 Molecular orbital theory Topic 2 Post – HF method : Configuration interaction Topic 3 Valence bond theory I 
Lecture 22  Constructing Molecular Wavefunctions – Valence Bond Theory and Hückel Theory 52:26
Topic 1 Valence bond theory II Topic 2 Hückel theory 
Lecture 23  Computational Quantum chemistry 47:34
Topic 1 Computational Quantum chemistry 
Lecture 24  Molecular Spectroscopy I 1:38:16
Topic 1 Molecular spectroscopy

Lecture 25  Molecular Spectroscopy II 45:39
Topic 1 Hierarchy of molecular spectroscopy Topic 2 Population effects Topic 3 Einstein's A/B coefficients 
Lecture 26  Absorption of Light in Molecule 1:38:43
Topic 1 Absorption
Topic 2 Absorption of diatomic molecule 
Lecture 27  Vibrational Spectrum 52:02
Topic 1 Diatomic molecule vibrational spectrum and selection rule Topic 2 Anharmonicity and Morse potential model 
Lecture 28  Rotation – Vibration Spectrum and Normal Modes 1:43:51
Topic 1 Review of rotational and vibrational spectrum Topic 2 Rotation – vibration spectrum Topic 3 Polyatomic molecule 
Lecture 29  Electronic Spectroscopy I 49:05
Topic 1 Electronic spectroscopy I 
Lecture 30  Electronic Spectroscopy II 1:40:54
Topic 1 Electronic spectroscopy II
Topic 2 Example of electronic spectroscopy in real world Topic 3 Photophysics  Jablonski diagram 
2019© YuanChung Cheng's Research Group  鄭原忠老師理論物理化學研究室
國立臺灣大學化學系  Department of Chemistry, National Taiwan University