Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article explains what TDDFT is, and how it differs from ground-state DFT. We show the basic formalism, and illustrate with simple examples. We discuss its implementation and possible sources of error. We discuss many of the major successes and challenges of the theory, including weak fields, strong fields, continuum states, double excitations, charge transfer, high harmonic generation, multiphoton ionization, electronic quantum control, van der Waals interactions, transport through single molecules, currents, quantum defects, and, elastic electron-atom scattering.
ContentsVII. Beyond standard functionals 22 A. Double excitations 22 B. Polymers 23 C. Solids 23 D. Charge transfer 23 VIII. Other topics 23 A. Ground-state XC energy 23 B. Strong fields 24 C. Transport 25