Density Functional Theory

Density Functional Theory (DFT) provides a practical route for calculating the electronic structure of matter at all levels of aggregation. Five decades after its inception, it is now routinely used in many fields of research, from materials engineering to drug design. Time-dependent Density Functional Theory (TDDFT) has extended the success of DFT to time-dependent phenomena and excitations. Most applications are carried out in the linear-response regime to describe excitation and emission spectra, but the theory is applicable to a much broader class of problems, including strong-field phenomena, attosecond control of electron dynamics, nanoscale transport, and non-adiabatic dynamics of coupled electron-nuclear systems. The tutorial will provide an introduction to the basic formalism of DFT and TDDFT, an overview of state-of-the-art functionals and applications, and a discussion of the most pressing and challenging open questions.

Topics

• DFT: Basic theorems of ground-state DFT, with simple examples; exchange-correlation functionals and exact conditions such as scaling, self-interaction, and derivative discontinuities; exact exchange and beyond; the Jacob’s ladder of Density Functional approximations. Extensions to warm dense matter and ensembles may also be covered.

• TDDFT: Basic theorems of TDDFT, with simple examples; survey of time-dependent phenomena; memory dependence; linear response and excitation energies; optical processes in materials; multiple and charge-transfer excitations; strong-field processes; non-adiabatic electron-nuclear dynamics.