Chemistry 311
Quantum Chemistry

Fall 2005

Administrative Information

Class meets: MWF 10:10-11:05am in ST 129
Required Class Text: Physical Chemistry: A Molecular Approach by Donald A. McQuarrie and John D. Simon
Recommended (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: M 1:30-3pm, Tu 2:30-3:30pm, W 1:30-3pm, Th 1:15-2:15pm
Class web site:  http://home.sandiego.edu/~jkua/chem311fall05.html

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 four in-class exams and one Final Exam. There will be nine problem sets (the lowest problem set grade will be dropped). 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 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.

4a. Grade breakdown is as follows:
                Problem Sets                             16%
                4 Exams @ 14% each               56%
                Final Exam                                28%

4b. 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).
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).

6. Students are most welcome to come in during office hours. Outside of my office hours, if I'm in my office and not swamped with work, I will be happy to answer questions and discuss coursework. Most of the time, if I'm in my office and the door is open, you're welcome to stop by. 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.)

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 without authorization from the instructor is considered a breach of academic integrity.

Homework Log

Problem Set #1 is due Wednesday, Sept 14, 10:10am, in class.
Assigned problems: 1-17, 1-21, 1-25, 2-2, 2-7, 2-9.

Problem Set #2 is due Wednesday, Sept 21, 10:10am in class.
Assigned problems: 3-3, 3-6, 3-8, 3-16, 3-20, 3-26.
Notes: For 3-20, you may use integrals from 3-10. I'd like to see how you derive general expressions for the expectation value of x, x^2, and sigma_x before you solve for the specific case of n=2.

Problem Set #3 is due Wednesday, October 5, 10:10am in class.
Assigned problems: 4-17 (prove first expression only), 5-13, 5-15 (prove for v=2 only), 5-16, 5-22, 5-35.
You may use Table 5-3.
Hint for 5-16: To save time, you may use the property of odd/even functions and definite integrals from the Table of Integrals.

Problem Set #4 is due Friday, October 14, 10:10am in class.
Assigned problems: 6-16 (just show 2s for and 2p(m=0)), 6-18, 6-20 (hint: integrate by parts), 6-24, 6-27 (In addition: What is the most probable distance? Calculate the average/expected value of r and compare it to the most probable distance.), 7-5.
General hint: useful integrals are in back flap of text book; wavefunctions for H-like atoms/ions can be found in Table 6-5.

Problem Set #5 is due Friday, October 28, 10:10am in class.
Assigned problems: 7-25, 7-26 (in addition, explain the steps you would take to solve for the minimum energy), 8-10, 8-22, 8-24, 8-30, 8-32.
Useful integral for 7-26: integral of x^m(1-x)^n dx from limits of 0 to 1 is equal to (m!n!)/(m+n+1)!

Problem Set #6 is due Monday, November 7, 10:10am in class.
Assigned problems: 9-8, 9-14, 9-25, 9-26, 10-3, 10-9, 10-12.
For 9-8 either ignore 1/R term everywhere or add it in everywhere (it makes no difference)
For 9-14, you may assume the ordering of the levels are all similar to N2.
For 9-26, flip the order of the last two levels. The nonbonding p(B) should be lower in energy than the antibonding 2p(B)+2p(F) terms.
For 10-9, use vectors (its easier!)

Problem Set #7 is due Monday, November 21, 10:10am in class.
Assigned problems: 10-28 (just solve for Psi_1), 10-31, 13-2, 13-12, 13-14, 13-24.

Problem Set #8 is due Tuesday, November 29, noon, in my office.
Assigned problems: 9-39, 13-29, 13-33, 13-42, 13-46.
For 13-29 you may assume that the ground electronic state minima is at zero energy. For 13-46, you may make use of Tables in Chapters 12-13.

Equations for Exam #4: chem311eqns.pdf.

Syllabus
(subject to change by the instructor at any time)

Approximate topic titles and associated sections of the text are in parenthesis.
Blank lines delimit separate weeks.

02 Sep    Introduction, Failure of Classical Mechanics, Atomic Hydrogen Spectrum (1-1 to 1-5)

05 Sep    LABOUR DAY
07 Sep    deBroglie hypothesis, Bohr's Atomic Theory (1-5 to 1-8)
09 Sep    Heisenberg Uncertainty Principle (1-9), Wave Equation (2-1 to 2-3)
        [note: shorter class due to Mass]

12 Sep    Wave Equation (2-4)
14 Sep    Schrodinger Equation Operators, Eigenvalue Problem (3-1 to 3-3, 4-6)
16 Sep    Particle in a one-D box (3-4 to 3-6)

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

26 Sep    Exam #1
28 Sep    Harmonic Oscillator (5-1 to 5-3)
30 Sep    Harmonic Oscillator (5-4 to 5-7)

03 Oct    Polar Coordinates, Rigid Rotor (5-8 to 5-9)
05 Oct    Hydrogen Atom (6-1 to 6-3)
07 Oct    Hydrogen Atom (6-3 to 6-5)

10 Oct    Hydrogen Atom (6-5 to 6-8)
12 Oct    Variational Principle (6-9, 7-1)
14 Oct    Trial functions and the Secular Determinant (7-2 to 7-3)

17 Oct    Perturbation Theory (7-4)
19 Oct    Exam#2
21 Oct    Helium Atom, Hartree-Fock Equations (8-1 to 8-3)

24 Oct    Pauli Principle, Koopmans' Approximation (8-4 to 8-7)
26 Oct    Term Symbols, Aufbau Principle, Hund's Rules (8-8 to 8-11)
28 Oct    Born-Oppenheimer Approximation, Hydrogen Molecule Ion (9-1 to 9-5)

31 Oct    Homonuclear Diatomics, Molecular Orbital Theory (9-4 to 9-7)
02 Nov   Molecular Orbital Theory (9-8 to 9-15)
04 Nov   Hybrid Orbitals (10-1 to 10-2)

07 Nov   MO Theory for Polyatomics (10-3 to 10-4)
09 Nov   Huckel Theory for pi-systems (10-5 to 10-6)
11 Nov   Exam#3

14 Nov   Rotational and Vibrational Spectroscopy (13-1 to 13-2)
16 Nov   Coupling of Rotation and Vibration (13-3 to 13-5, 13-8)
18 Nov   Electronic Spectra, Franck-Condon Principle, Selection Rules (13-6 to 13-7, 13-11 to 13-13)

21 Nov   Character Tables and Group Theory (12-2, 12-6)
23 Nov   Vibrations in polyatomics (13-9 to 13-10, 13-14)
25 Nov   THANKSGIVING (no class)

28 Nov   Electronic excitations (15-1 to 15-2)
30 Nov   Lasers (15-3 to 15-8)
02 Dec   Exam#4

05 Dec   NMR Spectroscopy (14)
07 Dec   Computational Chemistry
09 Dec   Nature of the Chemical Bond

12 Dec   Nature of the Chemical Bond

Final Exam is probably Monday, Dec 19, 11am-1pm.

Some links
Blackbody Radiation at Hyperphysics (Georgia State U)
Photoelectric Effect Animation at Lewison-Porter Central School
Bohr's Theory of the Hydrogen Atom from Walter Fendt's pages.
Experiments on Wave Interference at Colorado's Physics 2000 pages
Derivation of the Classical Wave Equation at Wolfgang Christian's web site, Davidson College.

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Last modified: 21 Jul 2005