Density Functional Theory

• Introduction

• Foundations of Density Functional Theory: Existence Theorems

  • Hohenberg-Kohn theorem
  • Degenerate ground states
  • Variational equation, interacting v-representability
  • Fractional particle number, derivative discontinuity
  • Spin-polarized systems
  • Exited states: Part 1

• Effective Single-Particle Equations

  • Kohn-Sham equations
  • Noninteracting v-representability
  • Degenerate Kohn-Sham ground states
  • Kohn-Sham equations for spin-polarized systems
  • Interpretation of Kohn-Sham eigenvalues

• Exchange-Correlation Energy Functional

  • Definition of exact exchange within DFT
  • Exact representations of the xc-energy functional
  • Local density approximation
  • Nonlocal corrections to the LDA
  • Generalized gradient approximation
  • Weighted density approximation
  • Self-interaction correction

• Virial Theorems

• Optimized Potential Method: A Third Generation of Density Functional Theory

• Time-Dependent Density Functional Theory

  • Runge-Gross theorem
  • Time-dependent Kohn-Sham equations
  • Time-dependent local density approximation
  • Time-dependent linear response
  • Excited states: Part II
  • Spin-polarized time-dependent density functional theory

• Relativistic Density Functional Theory

• Appendix: Some basic commutators

• Bibliography