CEM 993: Advanced Topics in Quantum Chemistry (Spring 2021)

ALGEBRAIC AND DIAGRAMMATIC METHODS FOR MANY-FERMION SYSTEMS

In the Spring 2021 Semester, CEM 993 will be taught online. It will involve weekly interactions between students enrolled in the course and the course instructor at scheduled meeting times, with required attendance, and watching the pre-recorded lecture videos by the students, further elaborated on below, following the detailed schedule provided by the instructor in the beginning of the semester. CEM 993 will also include homework assignments, with deadlines for their completion, and testing in the form of midterm and final exams, as posted on the course website and communicated to the students via email. The Spring 2021 Semester begins on January 11 with a reading, reviewing, and reflection week that does not include any online or in-person class meetings. Formal instruction begins on January 19, 2020. The course instructor will contact the students enrolled in the course by email about determining the day and time of the weekly Zoom meetings and further organizational details.

Lectures:

Formal instruction at Michigan State University begins on Tuesday, January 19, 2021, and ends on Wednesday, April 21, 2021. Formal instruction will be based on the pre-recorded online lecture videos, which can be found on YouTube at https://www.youtube.com/results?q=Chem+580&sp=CAI%253D, following the detailed schedule provided by the instructor in the beginning of the semester, augmented with the additional materials described in the “Books and Other Useful Materials” section of this syllabus, and weekly Zoom meetings, to be determined in the beginning of the semester.

Instructor:

Professor Piotr Piecuch, Department of Chemistry, Michigan State University, Chemistry Bldg., Room 17 (inside Theory Suite, Room 19).

Office telephone: 517-353-1151 (when calling use the mobile phone number provided to students enrolled in the course by email).

Email: piecuch at chemistry dot msu dot edu.

Websites: https://www.chemistry.msu.edu/faculty-research/faculty-members/piotr-piecuch/ (department) and https://www2.chemistry.msu.edu/faculty/piecuch/ (group).

Course website:

https://www2.chemistry.msu.edu/courses/cem993/SS21/syllabus-CEM993-SS21.htm (this page).

Course contents:

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

Office hours, via Zoom:

Mondays, 5:00 – 6:00 pm Eastern time. For additional appointments by Zoom, contact the instructor by email. For questions about the course that do not require scheduled meetings, contact the instructor by email as well.

Books and other useful materials:

There is no single textbook for this class. Formal instruction is based on 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, available on YouTube at https://www.youtube.com/results?q=Chem+580&sp=CAI%253D (one can also find it by searching for ‘Chem 580’ on YouTube). This online lecture series was 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. Watching these lecture videos, following the detailed schedule provided by the instructor in the beginning of the semester, and taking good notes when doing so, is the best approach to learning the material.

There also are 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.

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 https://www2.chemistry.msu.edu/courses/cem993/SS21/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, will be very helpful too. These extended lecture notes consist of three PDF files, which can be downloaded from https://www2.chemistry.msu.edu/courses/cem993/SS21/MBPT-COURSE-SLIDES.pdf (introductory slides with the mini-course background information and content), https://www2.chemistry.msu.edu/courses/cem993/SS21/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 https://www2.chemistry.msu.edu/courses/cem993/SS21/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.

Homework assignments:

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 their MSU NetID information. All homework assignments contribute 35 % to the final grade. Late homework assignments will not be accepted.

Midterm exam:

There will be one midterm exam, contributing 30 % to the final grade. The date of the midterm exam will be announced in due time. The midterm exam booklets and 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 final exam will take place during the final examination session, Monday, April 26, through Friday, April 30, 2021. The specific date(s) and hours of the final exam will be announced in due time. The final exam will contribute 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

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 517-884-7273 or on the web at https://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 the instructor 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.