CEM 993: Advanced Topics in Quantum Chemistry (Spring 2020)

ALGEBRAIC AND DIAGRAMMATIC METHODS FOR MANY-FERMION SYSTEMS

Lectures:

MWF 3:00–3:50 pm, Chemistry Bldg., Room 183, plus one extra hour per week, from 5:10 to 6:10 pm each Wednesday (beginning with the 1/8/2020 class), also in Room 183.

Lectures begin on Monday, January 6, 2020, and end on Friday, April 24, 2020.

Instructor:

Professor Piotr Piecuch, Department of Chemistry, Michigan State University, Chemistry Bldg., Room 17 (enter through Room 19, Theory Suite), tel.: 517-353-1151, email: piecuch at chemistry.msu.edu, departmental and group websites: https://www.chemistry.msu.edu/faculty-research/faculty-members/piotr-piecuch/ and http://www2.chemistry.msu.edu/faculty/piecuch/.

Course Website:

http://www2.chemistry.msu.edu/courses/cem993/SS20/syllabus-CEM993.htm (this page).

Course Contents:

The detailed contents of the course can be downloaded from here.

Office Hour:

Mondays, 5:00–6:00 pm. For questions about the course that do not require meetings in my office, email or telephone contact will work as well.

Books and Other Useful Materials:

There is no single textbook for this class. Thus, regular classroom attendance and taking good lecture notes during our classes is the best approach to learning the material. There are, however, excellent lecture notes by Professor Josef Paldus, which are related to the material discussed in class. Downloading them from www.math.uwaterloo.ca/~paldus/resources.html is strongly recommended. They will also be provided, along with other useful materials, by the instructor in the beginning of and throughout the semester. Among other useful materials, which will become particularly helpful in the second half of the semester, when we will start discussing the details of the many-body perturbation theory (MBPT), are the lecture notes for the introductory talk on the single-reference MBPT prepared by Professor Piotr Piecuch for the Workshop of the Espace de Structure et de Réactions Nucléaires Théorique on “Many-Body Perturbation Theories in Modern Quantum Chemistry and Nuclear Physics,” March 26-30, 2018, CEA Saclay, Gif-sur-Yvette, France. The introductory slides preceding this talk and the talk itself can be downloaded from http://www2.chemistry.msu.edu/courses/cem993/SS20/MBPT-LECTURE-CEA-SACLAY-3-25-2018.pdf. An extended version of these lecture notes, prepared by Professor Piotr Piecuch for his mini-course on the single-reference MBPT offered in the College of Chemistry and Molecular Engineering of Peking University on November 12-14, 2019, should be quite helpful too. These extended lecture notes consist of three PDF files, which can be downloaded from http://www2.chemistry.msu.edu/courses/cem993/SS20/MBPT-COURSE-SLIDES.pdf (introductory slides with the mini-course background information and content), http://www2.chemistry.msu.edu/courses/cem993/SS20/PRELIMINARIES-COMPLETE-NOTES.pdf (preliminary material, including discussion of the molecular electronic Schrödinger equation, Slater determinants, configuration interaction wave function expansions, and elements of second quantization needed in MBPT), and http://www2.chemistry.msu.edu/courses/cem993/SS20/MBPT-COMPLETE-NOTES.pdf (the single-reference MBPT and its diagrammatic representation, including the underlying Rayleigh-Schrödinger perturbation theory, wave, reaction, and reduced resolvent operators, eigenfunction and eigenvalue expansions, renormalization terms and bracketing technique, rules for MBPT diagrams, MBPT diagrams in low orders, with a focus on the second-, third-, and fourth-order energy corrections and first- and second-order wave function contributions, linked, unlinked, connected, and disconnected diagrams, diagram cancellations in fourth-order energy and third-order wave function corrections, and linked and connected cluster theorems and their implications). Other books and sources of information will occasionally be used as well to discuss specific topics, including, for example, books on reserve. Please use the https://lib.msu.edu/resources/reserves/?ref=ql link and search for ‘CEM993’ or ‘Piecuch, P.’ for further information. Another way to facilitate and enhance learning is provided by the online lecture series of 44 videos, including 39 90-minute lectures, two 50-minute lectures, and one additional 4 hour 50 minute lecture split into three parts, which can also be watched on YouTube, recorded in 2016 at Washington University in St. Louis, where a course similar to CEM 993, called CEM 580/PHYSICS 580, was offered to graduate chemistry and physics students by the instructor of the present CEM 993 offering (if you do not want to use the above links, search for ‘Chem 580’ in YouTube). Watching these lecture videos (if need be, multiple times) should be helpful too.

Homeworks:

There will be six homework assignments, which will be successively added to the course website during the semester as PDF files. They will contain information about the relevant due dates. Students, who have registered for CEM 993, will be able to access them by clicking here and using the MSU NetID information. All homework assignments can contribute up to 35 % to the final grade. Late homeworks will not be accepted.

Midterm exam:

There will be one midterm exam, contributing up to 30 % to the final grade. The date of the midterm exam will be announced in due time. The solutions of the midterm exam problems will be made available in the same password-protected page where the homework assignments are posted.

Final exam:

The date, time, and place of the final exam are Wednesday, April 29, 2020, 5:45–7:45pm, Room 183 in Chemistry Bldg. The final exam will contribute up to 35 % to the final grade.

Grading scheme:

Assignments	35 % of the final grade
Midterm exam	30 % of the final grade
Final exam	35 % of the final grade
Total	100 %

Final grades will be assigned according to the following table:

85.0 – 100.0 %	4.0
70.0 – 84.9 %	3.5
55.0 – 69.9 %	3.0
45.0 – 54.9 %	2.5
35.0 – 44.9 %	2.0
30.0 – 34.9 %	1.5
25.0 – 29.9 %	1.0
20.0 – 24.9 %	0.5
0.0 – 19.9 %	0.0

Accommodations for Persons with Disabilities:

Michigan State University is committed to providing equal opportunity for participation in all programs, services, and activities. Requests for accommodations by persons with disabilities may be made by contacting the Resource Center for Persons with Disabilities at 517-884-RCPD (4-7273) or on the web at www.rcpd.msu.edu. Once your eligibility for an accommodation has been determined, you will be issued a Verified Individual Services Accommodation (“VISA”) form. Please present this form to Professor Piecuch at the start of the semester and/or at least two weeks prior to the accommodation date (test, final exam, homework, etc.). Requests received after this date will be honored whenever possible.