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 Computational Quantum Mechanics of Molecular and E  posted by  member7_php   on 2/15/2009  Add Courseware to favorites Add To Favorites  
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Trout, Bernhardt, 10.675J Computational Quantum Mechanics of Molecular and Extended Systems, Fall 2004. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 09 Jul, 2010). License: Creative Commons BY-NC-SA

Computational Quantum Mechanics of Molecular and Extended Systems

Fall 2004

Tetrahedral H-bonded water pentamer figure, O-O 0.282 nm, O--O 0.282 nm, O-O-O 109.47&deg. From Hydrogen Bonding in Water. (Image courtesy of Professor Martin Chaplin, London South Bank University. Used with permission.)

Course Highlights

This course features a complete set of assignments and downloadable lecture notes.

Course Description

The theoretical frameworks of Hartree-Fock theory and density functional theory are presented in this course as approximate methods to solve the many-electron problem. A variety of ways to incorporate electron correlation are discussed. The application of these techniques to calculate the reactivity and spectroscopic properties of chemical systems, in addition to the thermodynamics and kinetics of chemical processes, is emphasized. This course also focuses on cutting edge methods to sample complex hypersurfaces, for reactions in liquids, catalysts and biological systems.

*Some translations represent previous versions of courses.



The course teaches the art of quantum mechanical calculations from both the chemistry and physics point of view. It, thus, falls somewhere between a laboratory course and a lecture course. In a laboratory course, you must learn by doing, and it is more important that you learn how to run the equipment well and how to interpret the data than that you learn how a piece of equipment is constructed and what exactly is under its cover. Similarly, in this course, you will learn how to run various quantum codes correctly and how to interpret the output of the codes, but you will not necessarily need to know how each algorithm in the 100's of 1000's of lines of code works. On the other hand, you will learn the theories behind the computer codes, so that you will be able to interpret the output of the codes. You will also learn about applications of computational quantum mechanical methods, in order to understand their potential and scope. Finally, you will gain insight into the current research and development of these methods to know where the field is going and what to expect in the future.

Course Objectives

  1. Learn a different approach to solving scientific and engineering problems: performing quantum mechanical calculations and understanding their scope, possibilities and limitations.

  2. Be able to perform calculations during your research at MIT, in Practice School, and in your future work. (Several students of this class have published papers in major journals based on their projects.)

  3. Gain a (partial) familiarity with the literature and be able to read it critically.

  4. Understand current research directions and possibilities.


There are no specific prerequisites, just permission of the instructor. It is expected that students should be able relatively quickly to become comfortable with advanced concepts from mathematics and physics.


Szabo, Attila, and Neil S. Ostlund. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. New York: McGraw-Hill, Inc., 1989. ISBN: 9780070627390.

There is no suitable textbook for this course. The best one still seems to be Modern Quantum Chemistry by Szabo and Ostlund, which is "required" for the course. Introduction to Quantum Chemistry by Frank Jensen has similar material, but also includes a discussion of density functional theory and has a useful chapter, 12 "Transition State Theory and Statistical Mechanics." It also has helpful descriptions of many of the methods that Gaussian uses. It is "recommended" for the course. Finally, see the References document for other helpful books.


Gaussian03: Used to perform quantum mechanical calculations.

GaussView: GUI, used to create job files, run jobs, and visualize output.

CPMD: Car-Parrinello Molecular Dynamics Web site.


Sun and Linux® machines

NCSA (National Computational Science Alliance): SGI Origin 2000 (796 processors)

Homeworks and Final Project

There are five problem sets in this course. Each student is required to complete a final project.


Homework 30%
Participation 20%
Final Project 50%


1 Introduction, Textbook and Notes, Many Body Schrödinger Equation, Density Functional Theory, Examples and Inspiration  
2 Electronic Spin, Spin Orbitals, Molecular Orbital Theory, Valence Bond Theory  
3 Hartree-Fock Theory, Matrix Manipulations  
4 Mathematical Underpinnings, Dirac Notation, G03 Calculations  
5 Electronic Classroom Tutorial  
6 Solution of Hartree-Fock Equations, Variational Principle, Mean Field Theory Problem set 1 due
7 Solution of H-F Equations (cont.), Meaning of Eigenvalues, Basis Sets Introduction  
8 Gaussian Basis Sets Problem set 2 due
9 Correlation, CI, MP Perturbation Theories  
10 Density Functional Theory (DFT) - Introduction Problem set 3 due
11 DFT: Solution of Kohn-Sham Equations and Exchange-Correlation Functionals  
12 Coupled-Cluster Theories, QCISD, G1, G2 Problem set 4 due
13 G1, G2 (cont.), Comparison, NCSA Teams, Projects Initial choice of project and literature search due
14 The Plane-wave Pseudopotential Method (PWPP)  
15 PWPP (cont.), Introduction to Classical Molecular Dynamics (MD)  
16 Car-Parrinello Molecular Dynamics - Method  
17 Running the Car-Parrinello Code Project status report due
18 Car-Parrinello Molecular Dynamics - Applications  
19 Embedding, Reaction Field Methods, Solvation, Combined QM/MM Problem set 5 due
20 Exploring Complex Free Energy Landscapes - Reactivity  
21 Computing Reaction Rate Constants Project finalized
22 Student Final Project Presentations I  
23 Student Final Project Presentations II  
24 Design of Selective, Sulfur Resistant, Oxidation Automotive Catalysts (Presented by Course Teaching Assistant)   Tell A Friend