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Abstract/Syllabus:
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Trout, Bernhardt, 10.675J Computational Quantum Mechanics of Molecular and Extended Systems, Fall 2004. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (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°. 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.
Syllabus
Overview
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
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Learn a different approach to solving scientific and engineering problems: performing quantum mechanical calculations and understanding their scope, possibilities and limitations.
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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.)
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Gain a (partial) familiarity with the literature and be able to read it critically.
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Understand current research directions and possibilities.
Pre-requisites
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.
Textbook
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.
Software
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.
Hardware
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.
Grading
Table of Grading
| ACTIVITIES |
PERCENTAGES |
| Homework |
30% |
| Participation |
20% |
| Final Project |
50% |
Calendar
Table for Calendar Section
| LEC # |
TOPICS |
KEY DATES |
| 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) |
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Further Reading:
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Readings
Assigned readings of journal articles are included in the table below as well as readings from the required text:
Szabo, Attila, and Neil S. Ostlund. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. New York: McGraw-Hill, Inc., 1989. ISBN: 9780070627390.
A bibliography of recommended reference texts are listed below the table.
Table for Readings
| 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 |
Review quantum mechanics, Solution of hydrogen atom. |
| 3 |
Hartree-Fock Theory, Matrix Manipulations |
|
| 4 |
Mathematical Underpinnings, Dirac Notation, G03 Calculations |
Read SO, pp. 1-30. |
| 5 |
Electronic Classroom Tutorial |
|
| 6 |
Solution of Hartree-Fock Equations, Variational Principle, Mean Field Theory |
|
| 7 |
Solution of H-F Equations (cont.), Meaning of Eigenvalues, Basis Sets Introduction |
SO, pp. 108-122, 131-149. |
| 8 |
Gaussian Basis Sets |
|
| 9 |
Correlation, CI, MP Perturbation Theories |
SO, pp. 60-64, 320-326, 350-353; study graphs 375-376; skim SO chapter 4. |
| 10 |
Density Functional Theory (DFT) - Introduction |
Read handout on DFT.
DFT paper 1: Hohenberg, P., and W. Kohn. "Inhomogeneous Electron Gas." Physical Review 136, no. 3B (9 November, 1964): B864-B871.
DFT paper 2: Kohn, W., and L. J. Sham. "Self-Consistent Equations Including Exchange and Correlation Effects." Physical Review 140, no. 4A – 15 (November 1965): A1133-A1138. |
| 11 |
DFT: Solution of Kohn-Sham Equations and Exchange-Correlation Functionals |
|
| 12 |
Coupled-Cluster Theories, QCISD, G1, G2 |
Skim SO, chapter 5. |
| 13 |
G1, G2 (cont.), Comparison, NCSA Teams, Projects |
Read handouts
G2 Assessment: Curtiss, Larry A., Krishnan Raghavachari, Paul C. Redfern, and John A. Pople. "Assessment of Gaussian-2 and Density Functional Theories for the Computation of Enthalpies of Formation." The Journal of Chemical Physics 106, no. 3 (15 January 1997): 1063-1079.
G3 Theory: Curtiss, Larry A., Krishnan Raghavachari, Paul C. Redfern, Vitaly Rassolov, and John A. Pople. "Gaussian-3 (G3) Theory for Molecules Containing First and Second-row Atoms." The Journal of Chemical Physics 109, no. 18 (8 November 1998): 7764-7776. |
| 14 |
The Plane-wave Pseudopotential Method (PWPP) |
|
| 15 |
PWPP (cont.), Introduction to Classical Molecular Dynamics (MD) |
|
| 16 |
Car-Parrinello Molecular Dynamics - Method |
Original Car-Parrinello Paper: Car, R., and M. Parrinello. "Unified Approach for Molecular Dynamics and Density-Functional Theory." Physical Review Letter 55, no. 22–25 (November 1985): 2471-2474. |
| 17 |
Running the Car-Parrinello Code |
Review molecular dynamics from lecture 15 and 16. |
| 18 |
Car-Parrinello Molecular Dynamics - Applications |
|
| 19 |
Embedding, Reaction Field Methods, Solvation, Combined QM/MM |
|
| 20 |
Exploring Complex Free Energy Landscapes - Reactivity |
|
| 21 |
Computing Reaction Rate Constants |
|
| 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) |
|
Recommended Readings
Jensen, Frank. Introduction to Computational Chemistry. New York: John Wiley and Sons, 1998. ISBN: 9780471980858.
Hehre, Warren J., Leo Radom, Paul v.R. Schleyer, and J. A. Pople. Ab initio Molecular Orbital Theory. New York: John Wiley and Sons, 1986. ISBN: 9780471812418. [This is a classic text with a great amount of data, focussing on calculations performed with Gaussian.]
Parr, Robert G., and Weitao Yang. Density-Functional Theory of Atoms and Molecules. New York: Oxford University Press, 1989. ISBN: 9780195042795. [Classic book on density functional theory.]
Levine, Ira N. Quantum Chemistry. 5th ed. Upper Saddle River, NJ: Prentice Hall, 1999. ISBN: 9780136855125. [Introductory book on quantum mechanics with several good chapters on electronic structure calculations.]
Martin, Richard M. Electronic Structure: Basic Theory and Practical Methods. Cambridge, UK: Cambridge University Press, 2004. ISBN: 9780521782852. [Good recent book on electronic structure calculations from the physics standpoint, with a focus on density functional theory.]
Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. New York: John Wiley and Sons, 1977. ISBN: 9780471164326. [One of the many books on quantum mechanics.]
Hill, Terrell L. An Introduction to Statistical Thermodynamics. Reading, MA: Addison-Wesley Publishing Company, 1962. ASIN: B000NSP1SA. [Has basic statistical mechanical formulas used in Gaussian. A Dover edition is also available.]
McQuarrie, Donald A. Statistical Mechanics. New York: Harper Collins Publishers, Inc., 1976. ISBN: 9780060443665. [A more elaborate presentation than Hill's book.]
Ashcroft, Neil W., and N. David Mermin. Solid-State Physics. Fort Worth: Harcourt Brace College Publishers, 1987. ISBN: 9780030493461. [A classic text.]
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