EE5: Physical Chemistry 5 - Quantum Chemistry and Chemical Rate Theory

Department of Chemistry, University of Iceland

• Instructor: Hannes Jónsson , office in room 243 in VR-II
• Lectures: Tuesdays at 10:50-12:20 and Fridays at 9:10-10:40 in room 147 in building VR-II.
• Lab sessions, problem solving sessions and individual discussions on Thursday afternoons.

Course Description:

Methods for calculating the properties of chemicals and materials as well as the mechanism and rate of transitions, such as chemical reactions, diffusion and conformational changes. Quantum mechanical methods, in particular Hartree-Fock (HF), configuration interaction and density functional theory (DFT) will be applied to the calculation of electron wavefunctions for fixed coordinates of the nuclei. Transition state theory, classical and quantum mechanical, will be applied to the calculation of the rates of transformations from one stable arrangement of the atoms to anoher (chemical reactions, diffusion or conformational changes) . The course is to a large extent based on projects which involve calculations using computers (in some cases based on material covered in previous physical chemistry courses). A few of the projects are mandatory but most of them can be chosen by the student after approval of the instructor. Among possible projects are: Calculations of molecular structure and atomic structure of molecules or solids; determination of the mechanism and rate of transitions; calculations related to various types of spectroscopy. 20% of the grade is based on the projects and it is necessary to obtain a minimum grade in both the final exam and the grade for projects.

Topics Covered:

• Approximate methods: Variational and perturbation methods
• Systems with many electrons (HF, CI, MP2 and DFT methods)
• Spin, Angular momentum and addition of angular momenta
• Rate theory and calculations of rate constants, transition state theory, classical trajectories and quantum mechanical tunneling

Lecture Notes (not complete, they will be updated during the semester):

• Ia. Variational method
• Ib. Perturbation method
• Ic. Application of perturbation and variational methods: The van der Waals interaction

• IIa. Antisymmetry and Slater determinants
• IIb. Hartree-Fock and CI
• IIc. Møller-Plesset perturbation method
• IId. article by Kohn on Density functional theory (DFT)

• IIIa. Angular momentum and spin
• IIIb. Addition of angular momenta and spin-orbit coupling

• IV. Classical and quantum mechanical (tunneling) rates.

Other reading material:

• Roald Hoffmann, 'Solids and Surfaces: A Chemist's View of Bonding in Extended Structures'.
• Cohen-Tannoudji, Diu and Laloe (CDL), 'Quantum Mechanics' vol I and II.
• Szabo and Ostlund: 'Modern Quantum Chemistry'.
• K. Burke, 'The ABC of DFT', (http://dft.rutgers.edu/kieron/beta/)

Lab exercises (not complete, will be updated during the semester):

• lab1: Carry out the Huckel calculations described in the article by Farrell, see pdf file (due jan. 17.). Supporting material: Discussion of secular determinants and the Huckel method in the textbook from EE1 by McQuarrie. Assignment: Carry out calculations of the lowest absorption energy of the four dyes (x=0,1,2,3) using both Huckel method (with beta=2.60 eV) and the particle-in-a-box model and compare with the experimental measurements given in table 5 in the article by Farrell.

• lab2: Use Huckel method to calculate the energy levels of a closed ring of carbon atoms forming a conjugated chain of pi bonds. Write a function in Matlab for doing the calculation for a chain of N atoms and repeat for a few different values of N up to N=100. Plot energy as a function of the wave vector, k, and make a histogram of the density of states. (due Jan. 29).

• lab3: Carry out Hartree-Fock calculations on several diatomic molecules using the Spartan software. See instructions in pdf file (due Feb. 27.).

• lab4: Carry out ab intio calculations on methylene using the Spartan software. See instructions and an article which gives useful information (due March 5.).

• lab5: Carry out 5 exercises of your choice in this set of 39 exercises. Write clear and thoughtful answers to all the questions raised in the handout (due March 19.).

Homework assignments:

1.

Assigned Jan. 31, due Feb. 7: Assignment HD1.pdf

Solution to problem 1, problem 2, problem 3

2.

Assigned March 6., due March 12: Assignment HD2.pdf

Solution to problem 1, problem 2, problem 3

3.

Assigned March 26., due April 2: Assignment HD3.pdf

Solution to problem 2

4.

Assigned April 15., due April 22: Assignment HD4.pdf

Solution to problem 1 (Note: In this solution the Clebsch-Gordan coefficients are derived, but that is not necessary, it is OK to just look them up for example in Wickipedia).

Old Final Exam: