Quantum Chemistry Shangwu Ding Department of Chemistry National Sun Yat-sen University （ Updated Feb 2016 ） Course Introduction 課程介紹

授課老師 Professor: Dr. Shangwu Ding 丁尚武 Campus phone: 3917, Office: 理東

教材 : Peter Atkins, Julio de Paula, Physical Chemistry, 10 th Edition, 2014, Oxford University Press. ISBN 書商： 歐亞書局有限公司 231 台北縣新店市寶橋路 235 巷 118 號 5 樓 Phone: , FAX ： 聯絡人： 黃國雄先生 手機： ,

主要參考書： Thomas Engel, Phillip Reid, PHYSICAL CHEMISTRY, 3rd Edition, Prentice Hall, 2016, ISBN 或第 1 版 （ 2005 ）

課程網址： 含上述教材及參考書的講義投影片，作業及答案，學生提問及回答 等（限修課學生使用）

This course will cover basic quantum mechanics (atomic and molecular structure) and basic spectroscopies (Visible, UV, IR, Raman etc.). There are 7 chapters (see textbook). The following major topics will be taught in 48 lectures: 1. The Origins of Quantum Mechanics--From Classical to Quantum Mechanics 2. Dynamcis of Microscopic Systems -- The Schrödinger Equation 3. The Basics of Quantum Mechanics: Postulates, Operators (and Matrix), Uncertainty, Measurement 4. Using Quantum Mechanics on Simple Systems 5. The Particle in the Box and the Real World 6. Commuting and Noncommuting Operators and the Surprising effects of Entanglement 7. A Quantum Mechanical Model for the Vibration and Rotation of Molecules 8. The Vibrational and Rotational Spectroscopy of Diatomic Molecules 9. The Hydrogen Atom 10. Multielectron Atoms 11. Examples of Spectroscopy Involving Atoms 12. Chemical Bonding in H2+ and H2 13. Chemical Bonding in Diatomic Molecules 14. Molecular Shapes and Energy Levels for Polyatomic Molecules 15. Electronic Spectroscopy 16. Computational Chemistry 17. Molecular Symmetry 主要內容 The Content of the Course

The students are expected to have a good command of basic principles of quantum mechanics and how to apply them to solve basic problems important to chemistry, in particular, the theoretical background of atomic and molecular structure and spectra. The students are required to be familiar with the wavefunctions and energy levels of typical quantum mechanical systems such as particle-in-box, vibrator, rotor, hydrogen and hydrogen-like atoms, hydrogen molecule, heteronuclear diatomic molecules. The students will be able to apply group theory to determine the IR, Raman activity of a (simple) molecule or group. The students will learn basic knowledge and skills in doing computational quantum chemistry. 課程目標 Objectives of the Course

This course requires students to have taken basic and advanced calculus (including differential equations), matrix algebra, point group theory as well as general physics (classical Newtonian mechanics and electromagnetism). 特別提醒：此課程有較強的數學和物理的預備要求： 高等微積分（含微 分方程），矩陣代數，點群理論，普通物理學（力學，電磁學），如這 些方面有問題，請在修課前儘早補習，並及時接受輔導。 請好好利用課程網頁的資料： （含講義投影片， 作業，答案，參考資料等。請修課同學下載並盡量多花時間閱讀。） 另外，每禮拜我將提供 2-4 小時的數學及物理的補習及答疑，請在數理方 面感到有困難的同學盡量多參加。

1.Attendance ： 10% 2.Assignment ： 30% 3.Mid-term exam ： 20% 4.Final exam ： 40% 評分方式﹝評分標準及比例﹞ Grading Scheme Blackboard and Powerpoint Lectures + Discussion 授課方式 Teaching Methods

週次日期授課內容及主題 12016/02/22~2016/02/28 Week1 ： Introduction--The Origins of Quantum Mechanics 22016/02/29~2016/03/06 Week 2 ： Dynamics of Microscopic Systems--Schroedinger Equation 32016/03/07~2016/03/13 Week 3: The Principles of Quantum Mechanics--Operators (Hermiticity, Egenvalues, Commmutation), Superposition, Uncertainty, Measurement 42016/03/14~2016/03/20Week 4: Translation 52016/03/21~2016/03/27Week 5: Vibration 62016/03/28~2016/04/03Week 6: Rotation 72016/04/04~2016/04/10Week 7: Hydrogen Atom 82016/04/11~2016/04/17Week 8: Many-electron Atoms 92016/04/18~2016/04/24Week 9: Atomic Spectra + Mid-Term Exam /04/25~2016/05/01Week 10: Valence Bonding Theory and Molecular Orbital Theory /05/02~2016/05/08Week 11: Homonuclear Diatomic Molecules /05/09~2016/05/15Week 12: Heteronuclear Diatomic Molecules /05/16~2016/05/22Week 13: Ployatomic Molecules and Computational Chemistry /05/23~2016/05/29Week 14: General Features of Molecular Spectroscopy, Molecular Rotation /05/30~2016/06/05Week 15: Rotationall Spectroscopy of Diatomic Molecules /06/06~2016/06/12Week 16: Vibrational Spectroscopy of Diatomic Molecules /06/13~2016/06/19Week 17: Electronic Transitions and Electronic Spectra /06/20~2016/06/26Week 18: Review and Final Exam

時段 1: 時間：星期二 13 ： ： 00 地點： E4022 時段 2 ： 時間： 16 ： ： 00 地點： E4022 臨時聯絡人： 鄭人豪（博士生） ，校內分機： 3917 課業討論時間 Class Representative 班代 : ??? 校內： ； 手機：

A quick tour of the history of quantum chemistry (up to 1940) Greek atomic theory Dalton’s atomic theory Arrhenius’ ions Thomson’s electron Rutherford’s nucleus Planck’s quantum Einstein’s photon Bohr’s model de Brodgile’s wave Schrodinger’s wave equation Heisenberg’s observables and uncertainty principle Pauli’s exclusion principle Heitler-London’s hydrogen molecule Pauling’s chemical bond Herzberg’s molecular spectra

沒人睬我 一尺之棰 日取其半 萬世不竭 莊子

Ancient Greeks Matter cannot be divided infinitely; there should be a limit beyond which matter cannot be further broken. ATOM – unbreakable.

Democritus as right; Aristotle was wrong!

Svante Arrhenius: Dalton theory is flawed + - But I really did not know what is an ion

Thomson: Arrhenius was right, atoms do have structure! I now what Arrhenius’ ions mean

Ernest Rutherford: the atoms are mostly empty! The electrons and nucleus in the diagram are enlarged. A real atom is much more empty than this!

Electrons may be used as best ‘light’ to see tiniest possible things!

Niels Bohr: atoms are a tiny solar system I can explain these colors Quantum Transition

Erwin Schrodinger: I can calculate the spectrum of hydrogen atom Sorry, the law for microscopic objects is a little bit more complex than F = ma!

Werner Heisenberg ： only observables are meaningful in microscopic world; no ‘reality’ before measurement Any physical quantity must be treated as a differential operator (or matrix). Simultaneous measurements of two physical quantities may interfere with each other, leading to uncertainties:

Wolfgang Pauli: Electrons are Fermion Electron is bizarre; a pair of electrons is insane. One electron is fun; a pair of electrons is ecstasy.

This table tells us that our world at the fundamental level is quantum mechanical. Periodicity is a consequence of quantum mechanics. The ‘shell and subshell’ turned out to correspond to the physical quantities we can possibly measure of an atom (good quantum numbers)

Organic Chemistry Depends on Covalent Bonding. Without Covalent Bonding, There’d be no Organic Compounds. Covalent Bonding Had Been Very Mysterious Before Formed between two neutral atoms Saturation Directionality Resonance/Hybridization Etc. All these make no sense in classical physics!

Walter Heitler, Fritz London: hydrogen molecule exists, thanks to quantum mechanics. God modified the law in microscopic world so that molecules can form.

Linus Pauling ： I understand covalent bond. Organic chemistry would not have existed had the microscopic world obeyed Newtonian o Maxwell Laws.

Herzberg ： molecular vibration and rotation tell us a lot Electronic ground state Vibrational state Electronic first excited state Energy Nuclear Coordinate

The objectives of quantum chemistry The structure of atoms and molecules The dynamics of molecules The interactions between molecules It has achieved tremendous progress but it is still developing.