P469 Density Functional Theory of Atoms, Molecules and Solids

Course No: 
P302 (Quantum Mechanics II)

(42 Lectures + 14 Tutorial)

  1. 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
  2. FoundationsofDensityFunctionalTheory(DFT):Hohenberg-Kohn(HK)theo-rem,degenerategroundstates,variationalDFT, 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,degenerateKSDFT,KSequationsforspinpolarizedsystems,interpretationofKSeigenvalues
  3. 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
  4. 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: 

1.      Density Functional Theory of atoms and Molecules by Robert G. Parr and Weitao Yang2.      Density functional Theory by R.M. Dreizler and E.K.U. Gross3.      Density Functional Theory by Eberhard Engel4.      Primer in Density Functional Theory by C. Fiolhais, F. nogueira, Miguel and A. L. Marques5.      Fundamentals of TDDFT by Miguel A. L. Marques et al.6.      Time-dependent Density Functional Theory by Miguel A. L. Marques et al.7.      Time-dependent Density Functional Theory by Carsten Ullrich8.      Quantal Density Functional Theory I & II by Viraht Shani9.      Recent advances in Density Functional Methods (Part I, II & III) by Delano P Chong10.  Atomic and Electronic Structure of Solids by Ethimios Kaxiras11.  Electronic Structure: Basic Theory and Practical Methods by Richard M. Martin12.  Many-Body Quantum Theory in Condensed Matter Physics by H. Bruus and K. Flensberg13.  Quantum Theory of the Electron Liquid by Gabriele Giuliani and Giovanni Vignale14.  Molecular Electronic Structure Theory by T. U. Helgaker, P. Jorgensen and J. Olsen15.  Electronic Structure Calculations for Solids and Molecules by J. Kohanoff16.  Methods of Electronic Structure Calculations by M. Springborg17.  Self Consistent Fields in Atoms by Norman March18.  Computational Materials Science by J. G. Lee19.  Density Functional Theory in Quantum Chemistry by Takao Tsuneda       20. Material Modeling using DFT by Feliciano Giustino

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