The field of electronic structure includes the study of the ground and excited states of electrons which determine the properties of atoms, molecules, solids, and other condensed matter systems. In ab initio (first-principles) electronic structure methods, many properties can be calculated directly with a high degree of accuracy starting from the microscopic description of the system as defined by the Schrödinger equation, and with no experimental input. The region of applications of this field is vast and spans a wide range of problems in different majors such as physics, chemistry, materials science, earth sciences, and biology.
The purpose of this course is to give the students insight into the intellectual challenges in the theory of electrons in condensed matter and the wide scope of applications of electronic structure theory. It is the intention to cover not only the theoretical principles of electronic structure theory but also to provide a hands-on experience in modeling and simulations using an electronic structure package.
In the first part of the course, the emphasis will be on the theory, specifically, on the density functional theory (DFT) which in principle can provide the exact ground state of many-electron systems. DFT, with its favorable computational requirements, is the predominant method for systematic studies of various properties of condensed matter such as binding energy, crystal structure, magnetic properties, vibrations of the nuclei, ferroelectricity, optical properties, and many others. The shortcomings of this theory and also theoretical methods that go beyond DFT such as the GW approximation and quantum Monte Carlo methods will also be covered. In the second part of the course, the goal is to learn how to apply an ab initio DFT code in real applications – in practice, the modeling and simulation section will be “meshed” with the theory part. We will use ABINIT which is one of the most successful GNU-GPL free codes.
The course is appropriate for beginning and advanced graduate students with interests in modeling and simulations in engineering, physics and chemistry. It is most useful for those who are specializing in solid state physics, materials science, or quantum chemistry both in the theoretical and experimental tracks.
The background expected of students in this class is:
In the second part of the course, where the focus is on running and learning a computer simulation program, it would help if the students are familiar with LINUX or with running a computer code in other environments
The first part of the course will be drawn mostly from Richard Martin’s book “Electronic structure: Basic theory and practical methods.”
Other useful books include:
If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.
The University Counseling Center’s staff is dedicated to assisting students in their pursuit of personal and academic growth, to helping students gain a better understanding and appreciation of themselves, and to supporting students as they make important decisions about their lives. If you are in need of counseling services, please contact the University Counseling Center at 334 William Pitt Union (412) 648-7930 Refer to www.counseling.pitt.edu for details.
See http://www.pitt.edu/~provost/ai1.html for the University Guidelines on Academic Integrity. You are encouraged to discuss the homework problems with your classmates, however, the final work you turn in must be your own. Copying someone else’s work, in any way, is unacceptable. You should not borrow notes, homework, homework solutions, exams, or other materials from students who took this course in previous years. There is a distinction between discussing work, and merely copying someone else’s work. The idea here is that you should help each other to understand the problems and the concepts involved; you will learn more if you work on the assignments in groups and explain the methods to each other. On the other hand, if you simply copy what someone else has done then you are not increasing your understanding, and you are not being honest. You must put in your own effort on solving the problems. Exams, whether in class or take home, must be strictly each students individual effort. You must not discuss the exams with anyone but the instructor. Any violation of the Academic Integrity code will be prosecuted to the fullest extend of the code.
There will be a cumulative final exam at the end of the semester. There will be also homework sets which will be oriented toward basic knowledge of the key points in the course and are important for all students to master. Some of the problem sets are computational which are based on running ABINIT.
There will be a term paper or project that each student is expected to submit at the end of the semester. The topic can be chosen upon a mutual consent or from a provided list of topics. The term paper must fully describe some problem related to electronic structure with appropriate references to the literature. Students can also choose to do a computational project using ABINIT or any other density-functional code. All of the students are encouraged to choose a project which is closely related to their current research. However, the term paper or project does not have to be original research, but it must be original work on the part of the student.
Background Review ( 3 weeks)