鄭原忠 OCW

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 time-independent quantum mechanics and approximation methods useful in physical chemistry, with an emphasis on the descriptions of many-electron systems and spectroscopy. The lectures will be divided into three parts: 1/3 with focus on basics of time-independent 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.

Description

Objective

Learning basic concepts of the quantum mechanic and its applications on the microscopic chemical system as the foundation of more advanced courses in chemistry.

Prerequisite

General chemistry, basic calculus. ( A little bit of linear algebra will be better.)

Planned topics

wavefunction, time-independent Schrödinger equation, quantum mechanical operators, particle in a box, harmonic oscillator, Hydrogen-like atoms, non-degenerate perturbation theory, variational theory, electronic structure of many-electron atoms, electronic structure of molecules, molecular spectroscopy.

Reference Book

Physical Chemistry, 4^th Edition by Robert J. Silbey, Robert A. Alberty, and Moungi G. Bawendi, Wiley [SAB].

Recommended reference book

Quantum Chemistry, 6^th Edition by Ira N. Levine, Pearson International [Lv].

Week	Topics	Reference
1	Why Quantum Mechanics? The Heisenberg Uncertainty Principle, The Time-independent Schrödinger Equation, Operators	SAB 9.1-9.3
2	The Superposition Principle & Expectation Values, Measurement	SAB 9.4-9.5 Lv Ch. 3
3	Particle in a One-Dimensional Box, Tunneling, Particle in a Three-Dimensional 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	Mid-term Exam (Tuesday)
9	The Schrödinger Equation for Hydrogen-like Atoms, Hydrogen-like Orbitals, Orbital Angular Momentum & Electron Spin	SAB 10.1-10.2, 10.4, 10.5 Lv 6.1-6.6, 6.8
10	Electronic Structures of Hydrogen-like Atoms, Atomic Terms, Variational Method	SAB 10.6 Lv Ch. 8, Ch. 9
11	Helium Atom, Pauli Exclusion Principle, Slater Determinant, Many-Electron Problems: Hartree-Fock Self-consistent Field Method	SAB 10.8, 10.9 Lv Ch. 11
12	The Born-Oppenheimer Approximation, The Hydrogen Molecule Ion, Electronic Structure of Many-electron Molecules: Molecular Orbital Theory, Huckel Theory	SAB 11.1-11.7
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 13.4-13.9
16	Electronic Spectroscopy of Diatomic Molecules, Franck-Condon Principle	SAB 14.1-14.5
17	Excited states, Electronic & Vibrational Relaxation, Fluorescence & Phosphorescence	SAB 14.6-14.8
18	Why Quantum Mechanics? The Heisenberg Uncertainty Principle, The Time-independent Schrödinger Equation, Operators	SAB 9.1-9.3

Lecture	Handout
Lecture 1	The Quantum World
Lecture 2	The Wave Function
Lecture 3	Operators and Observables
Lecture 4	Quantum Measurement
Lecture 5	A Particle in a Box
Lecture 6	Particle in a Box and the Real World
Lecture 7	Quantum Harmonic Oscillator
Lecture 8	Properties of Quantum Harmonic Oscillator
Lecture 9	Theories of Quantum Mechanics
Lecture 10	Numerical Solutions-Poorman's Quantum Mechanics Quantum Dynamics Demo (Slide)
Lecture 11	Quantum rigid rotor
Lecture 12	Properties of Quantum Angular Momentum
Lecture 13	Hydrogen-like Atom I
Lecture 14	Hydrogen-like atom-II Quantum Mechanics and Atomic Orbitals (Slide)
Lecture 15	Hydrogen-like Atom-II
Lecture 16	Variational Principle
Lecture 17	Many-electron System I –Helium Atom and Pauli Exclusion Principle
Lecture 18	Many-electron atoms Many-electron Atoms & Atomic Term Symbols (Slide)
Lecture 19	Many-electron Atoms
Lecture 20	Many-electron Molecules Introduction to Computational Quantum Chemistry (Slide)
Lecture 21	Valence Bond Theory WebMO Demo (Slide)
Lecture 22	Hückel MO Theory
Lecture 23	Computational Chemistry
Lecture 24	Light-Matter Interactions
Lecture 25	Overview of Molecular Spectroscopy
Lecture 26	Rotational and Vibrational Spectroscopy
Lecture 27	More on Vibrational Spectroscopy
Lecture 28	Motions of Polyatomic Molecule- Normal Mode
Lecture 29	Molecular Electronic Spectroscopy I
Lecture 30	Molecular Electronic Spectroscopy II
Lecture 31	Nuclear Magnetic Resonance