CEM 993: Advanced Topics in Quantum Chemistry (Spring 2023)

ALGEBRAIC AND DIAGRAMMATIC METHODS FOR MANY-FERMION SYSTEMS

CEM 993 has required lecture attendance and includes deadlines for completion of homework assignments. It also includes testing in the form of midterm and final exams.

Students enrolled in CEM 993, the CEM 993 instructor, and students who wish to attend the CEM 993 lectures without being enrolled in the course must follow the MSU COVID guidelines, as described on the Together We Will website.

Lectures:

MWF 4:10–5:00 pm, Chemistry Bldg., Room 183, plus one extra hour per week, from 5:00 to 6:00 pm each Wednesday (beginning with the January 11, 2023 class), also in Room 183.

Lectures begin on Monday, January 9, 2023, and end on Friday, April 28, 2023.

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/piecuch-piotr.aspx (department) and https://www2.chemistry.msu.edu/faculty/piecuch/ (group).

Course website:

https://www2.chemistry.msu.edu/courses/cem993/SS23/syllabus-CEM993-SS23.htm (this page).

Course contents:

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

Office hour:

Mondays, 6:00 – 7:00 pm. For additional appointments, 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. Thus, regular classroom attendance and taking accurate and thorough notes during the lectures will be essential for learning the material. For the students who must miss a class due to illness or other similarly serious circumstances, appropriate accommodations will be provided by the instructor.

The in-person lectures will be enhanced by 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 installment.

The lecture notes created by the instructor on an iPad during the Spring 2021 offering of CEM 993, which can be found in the homework section of this website (see the “Homework assignments” section below for further information) will be very useful too.

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 as well.

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/SS23/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/SS23/MBPT-COURSE-SLIDES.pdf (introductory slides with the mini-course background information and content), https://www2.chemistry.msu.edu/courses/cem993/SS23/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/SS23/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 ‘CEM 993’ or ‘Piecuch Piotr’ 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 Tuesday, May 2, 2023, from 5:45 pm to 7:45 pm in Room 183 in the Chemistry Bldg. 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.