Course Code

P469

Credit

8

Prerequisite

P303 (Quantum Mechanics II)

Total Hours

42 Lectures + 14 Tutorials

Outcome of the Course

This course teaches the students important concepts and methods in density functional theory, with the aim to build their background for future research work in this area.

Approval

Syllabus

- Many-body problem: QM of electrons and nuclei, approximation methods for many electron systems, Born-Oppenheimer approximation, Hartree and HF theory, tight binding method, greens functions, electron correlation, Ci & many-body and Moller-plesset theory, complete active space methods, coupled cluster theory, density matrices, time-dependent approach to all the above formalism
- Foundations of Density Functional Theory(DFT): Hohenberg-Kohn (HK) theo-rem, degenerate ground states, variational DFT, N − and v− representability problem, Levy-Lieb constrained search, fractional particle number & derivative discontinuity, spin polarized systems, Exited states part i: Effective Single particle picture: Kohn-Sham (KS) construction, non-interacting v− representability, degenerate KS DFT, KS equations forspin polarized systems, interpretation of KS eigenvalues
- Exchange-Correlation (XC) Energy Functional: exact exchange formalism within DFT, exact representations of the energy functional, LDa, gga, meta-gga, weighted density approximation, self interaction correction (SiC), virial theorems, exact exchange formalism (OpM, KLi, HS), where DFT goes wrong, strengths of DFT, strong correlation: DFT+U, Rpa, gW, DFpT, DMFT, orbital free DFT, DFT- hybrid
- Crossover to Excited-States: time-dependent DFT: Runge-gross theorem, time- dependent KS equations, adiabatic LDa & TD XC potentials, linear response TDDFT, Excited states part ii, spin polarized TDDFT, frequency dependent XC kernel, TDCDFT, TDOEp, relativistic DFT, molecular orbital theories

Reference Books

- Density Functional Theory of atoms and Molecules by Robert G. Parr and Weitao Yang
- Density functional Theory by R.M. Dreizler and E.K.U. Gross
- Density Functional Theory by Eberhard Engel
- Primer in Density Functional Theory by C. Fiolhais, F. nogueira, Miguel and A. L. Marques
- Fundamentals of TDDFT by Miguel A. L. Marques et al.
- Time-dependent Density Functional Theory by Miguel A. L. Marques et al.
- Time-dependent Density Functional Theory by Carsten Ullrich
- Quantal Density Functional Theory I & II by Viraht Shani
- Recent advances in Density Functional Methods (Part I, II & III) by Delano P Chong
- Atomic and Electronic Structure of Solids by Ethimios Kaxiras
- Electronic Structure: Basic Theory and Practical Methods by Richard M. Martin
- Many-Body Quantum Theory in Condensed Matter Physics by H. Bruus and K. Flensberg
- Quantum Theory of the Electron Liquid by Gabriele Giuliani and Giovanni Vignale
- Molecular Electronic Structure Theory by T. U. Helgaker, P. Jorgensen and J. Olsen
- Electronic Structure Calculations for Solids and Molecules by J. Kohanoff
- Methods of Electronic Structure Calculations by M. Springborg
- Self Consistent Fields in Atoms by Norman March
- Computational Materials Science by J. G. Lee
- Density Functional Theory in Quantum Chemistry by Takao Tsuneda
- Material Modeling using DFT by Feliciano Giustino