Density Functional Theory: Fundamentals and Applications

Physics 852: Density Functional Theory: Fundamentals and Applications

Course Information:

Time: Mon & Weds 10.00am –11.30 am

Place: Room 3209 Graduate Center CUNY

Instructor: Neepa T. Maitra

Dept of Physics and Astronomy, Hunter College, Rm 1214E North Building

Phone: 212-650-3518

Email: (best way to reach me)

Office hour: 11.30am—12.30pm Mon and Wed, location TBA

Pre-requisites:

Open to students with sufficient proficiency in quantum mechanics. Certainly open to those who have passed a graduate QM class; those who have passed upper-level undergraduate QM may have enough background to be decided on a case-by-case basis.

Recommended Reading:

There is no specific text for the course but there are several useful references we will be using (the relevant chapters of many of which are available on-line, or electronically through me):

Kieron Burke: “The ABC of DFT”, follow the links for DFT Book on http://chem.ps.uci.edu/~kieron/dft/

John P. Perdew and Stefan Kurth: “Density Functionals for Non-Relativistic Coulomb Systems”, in “A Primer in Density Functional Theory” Ed. C. Fiolhas, F. Nogueira, and M. Marques (Springer Lectures Notes in Physics, v.620, 2003).

Robert G. Parr and Weitao Yang, “Density Functional Theory of Atoms and Molecules”, (Oxford University Press, 1994).

Gabriele F. Giuliani and Giovanni Vignale, “Quantum Theory of the Electron Liquid”, (Cambridge University Press, 2005)

Reiner Dreizler and E. K. U. Gross, “Density Functional Theory” (Springer 1990)

In addition to these, journal articles will be recommended as we go along.

Grading:

Homework: 50%

There will be about 5 long problem sets, due about every two weeks.

Seminar Presentation: 50%

During the last few weeks, you will prepare a half-hour seminar on a topic, chosen mutually with me, on applications or development in DFT.

Course Syllabus:

1.The Many-Electron Problem

(N-electron interacting and non-interacting wavefunctions, 1- and 2-body probability densities, Overview of electronic structure methods and DFT)

2. Mathematical Necessities

(Functionals, one and two-body operators and expectation values, variational principle, Hellman-Feynman principle, virial theorem)

3. Hartree-Fock and Correlation

4. The Uniform Electron Gas

5. Hohenberg-Kohn Theorem

6. Kohn-Sham Scheme.

7. Exchange and Correlation Energy and Holes

8. Adiabatic Connection

9. Formal Properties of Functionals (Exact Conditions)

10. Local Density Approximation

11. Gradient Expansion and Generalized Gradient Approximations

12. Hybrids, Orbital Functionals, and Jacob’s Ladder

13. Performance and Challenges

14. Time-Dependent Density Functional Theory: The Runge-Gross Theorem

15. Linear Response and Excitation Spectra

16. Applications