CEM 993: Advanced Topics in Quantum Chemistry (Spring 2022)

ALGEBRAIC AND DIAGRAMMATIC METHODS FOR MANY-FERMION SYSTEMS

While we hope to return to in-person lecture format later in the semester, at least in the initial three weeks of Spring 2022, starting with a Zoom meeting on January 10, 2022, CEM 993 will be taught online. This will involve weekly interactions between students enrolled in the course and the course instructor at scheduled meeting times, with required attendance, and watching 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 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 begins on Monday, January 10, 2022, and ends on Friday, April 29, 2022. At least in the initial three weeks of the Spring 2022 Semester, course instruction will be based on the pre-recorded online lecture videos, which can be found on YouTube at https://www.youtube.com/results?search_query=Chem+580+Piecuch&sp=CAM%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 during the initial Zoom meeting on January 10, 2022.

If the in-person lecture format is permitted again, the schedule for the CEM 993 lectures in the Spring 2022 Semester will be as follows:

MWF 3:00–3:50 pm, Chemistry Bldg., Room 183, plus one extra hour per week, to be determined when the in-person classes are allowed.

Instructor:

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

Office telephone: 517-353-1151.

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/SS22/syllabus-CEM993-SS22.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 (Zoom link will be provided to the students by the course instructor). 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. At least in the initial three weeks of the Spring 2022 Semester, course instruction will be based on the pre-recorded online lecture videos, which can be found on YouTube at https://www.youtube.com/results?search_query=Chem+580+Piecuch&sp=CAM%253D, This 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 found by searching for ‘Chem 580 Piecuch’ on YouTube, 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.

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/SS22/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/SS22/MBPT-COURSE-SLIDES.pdf (introductory slides with the mini-course background information and content), https://www2.chemistry.msu.edu/courses/cem993/SS22/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/SS22/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. Additional handouts may be provided by the instructor to the students by email.

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. It is expected that students email their homework assignments as PDF files by 8:00 pm Eastern Time on the respective due dates. Late homeworks will not be accepted. Homework assignment solutions will be made available as PDF files and posted after the successive due dates. All homework assignments will contribute 35 % of the final grade.

Midterm exam:

There will be one midterm exam, contributing 30 % of the final grade. The date of the midterm exam will be announced in due time. The midterm exam booklet 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 in-person final exam has been scheduled by the Office of the Registrar on Wednesday, May 4, 2022, from 5:45 pm to 7:45 pm in Room 183 in the Chemistry Bldg. Because of the COVID-19 pandemic and university guidelines, adjustments to this schedule and/or the exam format may have to be made. They will be discussed with the students enrolled in CEM 993 in due time. The final exam will contribute 35 % of 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.