Fall 2008

Administrative Information

Class meets: MWF 10:10-11:05am in ST 129
Required Class Text: Quantum Chemistry, 2nd ed. by Donald A. McQuarrie (ISBN 13: 978-1-891389-50-4)
Useful (but not required): Applied Mathematics for Physical Chemistry, 3rd edition by James R. Barrante

Instructor: Dr. Jeremy Kua
Office: SCST 381
Phone: x7970 or (619) 260-7970
E-mail:
Office hours: Mon 1:30-3pm, Tue 2:30-4pm, Thu 10am-noon
Class web site:  http://home.sandiego.edu/~jkua/chem311fall08.html

Why should I care? What is the underlying structure of matter? Why is an atom stable? Why are some molecules stable but others not? What is a chemical bond, really? What controls ALL chemical reactions? Is truth indeed stranger than fiction? Is it possible to walk through walls? If you've ever asked yourself any of these questions, then this course will begin to answer some of them, but it will also bring up more nagging, but vitally interesting, questions!

Course goals: To understand the application of quantum mechanics to chemistry. The course will cover fundamentals of quantum mechanics, its application to atoms and molecules, chemical bonding, and a brief introduction to spectroscopy. We will also delve briefly into the use of computers in quantum chemical calculations.

Course requirements:
1. There will be three in-class exams and one Final Exam. There will be seven problem sets. Assigned problem set questions may come from the text and/or from me.

2. A good grasp of calculus is important for understanding the material and completing the problem sets and exams. It is your responsibility to refamiliarize yourself with your calculus text if you need a refresher. The text has Math Chapters that go over some of the mathematics. There is also Barrante's book (recommended, but not required).

3a. Collaboration is allowed, and even encouraged, on problem sets but each student must write up their own work. I am not as interested in whether you got the right answer but how you arrived at your answer. Intermediate steps must be shown.
3b. There will be NO collaboration on any exam. You do need to really understand the material deep down in your very own self.

4a. Grade breakdown is as follows:
                7 Problem Sets @ 2% each       14%
                3 Exams @ 17% each               51%
                Final Exam                                35%
4b. If you do better on the Final Exam than your cumulative grade in the class up to just before the Final, then your Final Exam grade will be your final grade. If not, the Final will just count for 35% of the grade.
4c. Tentative Grading Scale (subject to change by the instructor at any time)
                A        85-100%
                B        70-84%
                C        55-69%
                D        40-54%
                F         0-39%
Appended + and - will approximately constitute 3% widths at either end of the scale for A-D grades.

5a. Late problem sets will receive no credit (although I will go through your answers with comments) unless you have a good reason for turning it in late.
5b. There are no make-up exams. If you have a very good reason for missing an exam you have to let me know beforehand or as soon as possible. If I judge the reason to be valid and you did let me know beforehand or ASAP, an alternative will be available (probably in the form of an oral exam where I ask you anything I would have expected you to know on the exam).

6a. Students are most welcome to come in during office hours. Generally if my office door is wide open even if not during my office hours, you're more than welcome to stop by. Remember, I'm here to help you master the material. On the rare instances I'm super-busy right when you appear, I'll just ask you to come back a little later. I check my e-mail reasonably often during working hours so you can contact me that way too. (Don't expect replies on weekends and evenings.)
6b. I love talking about quantum mechanics and chemical bonding and the strangeness of the universe we live in. So if you have a wild thought or idea, I'll probably be interested in hearing it while giving you a dose of my wild ideas. Hopefully that will be obvious from class!

7a. All students are expected to adhere strictly to the Academic Integrity policy. Violations will be dealt with through the Dean of College of Arts and Sciences, in accordance with the University of San Diego policy on academic integrity.
7b. Use of a Solutions Manual or problem set solutions from previous years without authorization from the instructor is considered a breach of academic integrity.

Problem Set #1 is due Friday, Sept 12, 10:10am, in class.
Concept Question 1: What is the "quantum" in quantum mechanics?
Assigned problems: 1-19, 1-27, 1-39 (Old fat text: 1-17, 1-23, 1-26)
Concept Question 2: Why doesn't an electron collapse into the nucleus? (Hint: use Heisenberg's Uncertainty Principle)
Assigned problems: 2-2, 2-10, 2-26 (Old fat text: 2-2, 2-9, 2-18)

Problem Set #2 is due Monday, Sept 22, 10:10am, in class.
Assigned problems: 3-3, 3-9 (Old fat text: 3-3, 3-6)
Concept Question 1: What is the Born postulate and why is it useful?
Additional Problem: Calculate the probability of finding a particle in the middle third of a one-dimensional box for the n=1 and n=2 states. Comment on whether your results make sense.
Assigned problems: 3-22 (two typos: lower limit should be -a, not zero; and the normalization constant is sqrt(1/2a), not sqrt(1/a)), 3-26, 3-33 (ignore boundary condition proof) (Old fat text: 3-17, 3-20, 3-28)
[Feel free to use integral tables. Useful integrals and mathematical relationships can also be found in Problems B-8, 3-14 and 3-23.]

Problem Set #3 is due Wednesday, Oct 08, 10:10am, in class.
Concept Question: Sketch the first three energy levels, wavefunctions and probability distribution functions of the harmonic oscillator and comment on these features.
Assigned Problems: 5-13, 5-15, 5-21 (just for v=1), 5-22 (just check for orthogonality to v=0), 5-27 (for v=2), 5-42.
(Old fat text: 5-13 (do HI for 127-iodine with force constant 2309 N/m), 13-24, 5-15 (just for v=1), 5-16 (just check for orthogonality to v=0), 5-21 (for v=2), 13-33)
[Hint for 5-22 (old: 5-16): Where possible, you may use the properties of odd and even functions in the integrand to save time and crunching through math.]

Problem Set #4 is due Wednesday, Oct 22, 10:10am, in class.
Assigned problems: 4-12 (just the first expression), 6-6, 6-8, 6-15, 7-7, 7-9, 7-17. For 7-17, what is the most probable distance? Then calculate the average distance and compare it to the most probable distance.
(Old fat text: 4-17 (just the first expression), 5-35, 13-2, 13-12, 6-17, 6-20, 6-27 (and answer the same extra questions as for 7-17 in new text).
Not assigned, but you should know how to check that any two wavefunctions of the H atom are orthonormal.

Problem Set #5 is due Monday, Nov 10, 10:10am, in class.
Assigned problems: 8-2, 8-7 (then compare your result to the true ground state energy), 8-11 (using perturbation theory and the ground state wavefunction for the harmonic oscillator instead of the trial function), 8-12, 8-20.
Concept Question 1: Name one advantage and one disadvantage of using Slater-type orbitals.
Concept Question 2: What is the Hartree-Fock limit? What are the advantages and disadvantages of the Hartree-Fock approximation?

Problem Set #6 is due Monday, Nov 17, 10:10am, in class.
Assigned problems: 9-30, 9-46, 9-48, 10-6, 10-14
(Old fat text: 8-22, 8-32, 8-30, 9-3, 9-8)
Concept Question 1: What is the Born-Oppenheimer approximation? Why can it be used successfully?

Problem Set #7 is due Wednesday, Dec 10, 10:10am, in class.
Assigned problems: 11-7 (also write the overall term symbol), 11-13 (also draw the MO diagram and compare the bonding to the Lewis structure, 11-31 (just for psi1), 11-38
(Old fat text: 9-14, 9-17, 10-28, 10-31, with additions as described above)
Polygon-in-a-circle Question: Draw an energy diagram clearly indicating the energy levels (in terms of alpha and beta) of undistorted cyclooctatetraene, C8H8. Calculate the total pi-electronic energy and the delocalization energy of undistorted C8H8. Is this molecule expected to undergo Jahn-Teller distortion?

Approximate topic titles and associated sections of the text are in parenthesis. For those using the old fat textbook, most of the sections are closely aligned, although some parts from Chapter 13 have been incorporated into earlier chapters.
Blank lines delimit separate weeks.

03 Sep    Introduction, Failure of Classical Mechanics, Atomic Hydrogen Spectrum (1-1 to 1-5)
05 Sep    deBroglie hypothesis, Bohr's Atomic Theory (1-5 to 1-12)

08 Sep    Heisenberg Uncertainty Principle (1-13 to 1-14), Wave Equation (2-1 to 2-3)
10 Sep    Wave Equation (2-3 to 2-4)
12 Sep    Schrodinger Equation, Operators, Eigenvalue Problem (3-1 to 3-3)

15 Sep    Particle in a one-D box (3-4 to 3-6)
17 Sep    Particle in a three-D box (3-9), Expectation values, Heisenberg again (3-7 to 3-8)
19 Sep    Postulates of QM, Hermitian operators (4-1 to 4-6)

22 Sep    Postulates of QM (4-1 to 4-6)
24 Sep    Quantum Tunneling
26 Sep    Exam #1

29 Sep    Classical Harmonic Oscillator (5-1 to 5-4)
01 Oct    Quantum Harmonic Oscillator, Hermite polynomials (5-6, 5-8 to 5-9)
03 Oct    Infrared Spectroscopy (5-7,5-12)

06 Oct    Normal modes of vibration (5-11)
08 Oct    Angular Momentum, Rigid Rotor (6-1 to 6-2, 6-8)
10 Oct    Rotational Transitions (6-3 to 6-5)

13 Oct    Hydrogen Atom (7-1) and Spherical Harmonics (6-6 to 6-7)
15 Oct    Hydrogen Atom (7-1) and Spherical Harmonics (6-6 to 6-7)
17 Oct    FALL HOLIDAY (no class)

20 Oct    Hydrogen Atom Orbitals (7-2 to 7-3)
22 Oct    Electron Spin and Atomic Term Symbols (7-5 to 7-7)
24 Oct    Significance of Hydrogen

27 Oct    Exam #2
29 Oct    Variational Principle (7-9, 8-1)
31 Oct    Trial functions and the Secular Determinant (8-2 to 8-3)

03 Nov   Perturbation Theory (8-4 to 8-5)
05 Nov   Helium Atom, Hartree-Fock Equations (9-1 to 9-3)
07 Nov   Pauli Principle (9-4 to 9-5)

10 Nov   Term Symbols, Aufbau Principle, Hund's Rules (9-9 to 9-11)
12 Nov   Born-Oppenheimer Approximation, Hydrogen Molecule Ion (10-1 to 10-2, 10-4)
14 Nov   Energies of Molecular Orbitals (10-3, 10-5 to 10-6)

17 Nov   Homonuclear Diatomics, Molecular Orbital Theory (10-7, 11-1 to 11-2)
19 Nov   Molecular Term Symbols (11-4 to 11-5)
21 Nov   Exam #3

24 Nov   Electronic Transitions, Franck-Condon Principle
26 Nov   THANKSGIVING (no class)
28 Nov   THANKSGIVING (no class)

01 Dec   Huckel Theory for pi-systems (10-5 to 10-6)
03 Dec   Huckel Theory for pi-systems (10-5 to 10-6)
05 Dec   Hybrid Orbitals

08 Dec   Nature of the Chemical Bond
10 Dec   Nature of the Chemical Bond
12 Dec   Question and Answer time

Final Exam is Monday, Dec 15, 11am-1pm.