The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe...

An approximate solution to the time-dependent density-functional theory response equations for finite systems is developed, yielding corrections to the single-pole approximation. These explain why allowed Kohn-Sham transition frequencies and oscillator strengths are usually good approximations to the true values, and why sometimes they are not. The approximation yields simple expressions for Gö...

A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state |Psi0> and the particle-bath interaction operator, two external vector potentials A(r,t) and A'(r,t) that produce the same ensemble-averaged current density, j(r,t), must necessarily coincide up to a gauge transfor...

The exact time-dependent correlation energy in time-dependent density-functional theory is shown to sometimes become positive, which is impossible with most present TDDFT approximations. Both the correlation potential and energy can be strongly nonlocal in time. A new inequality is derived for the time-dependent exchange-correlation energy. The correlation energy appears to scale to a constant ...

Exact time-dependent density functionals remember both the entire history of the density and the initial wave function. We show that the two effects are intimately related, and all history dependence can be written as initial-state dependence, including that of the exchange-correlation kernel. For states that can be evolved from a ground state, all initial-state dependence is a dependence on a ...

A density-functional theory is established for inhomogeneous superfluids at finite temperature, subject to time-dependent external fields in isothermal conditions. After outlining parallelisms between a neutral superfluid and a charged superconductor, Hohenberg-KohnSham-type theorems are proved for gauge-invariant densities and a set of Bogolubov-Popov equations including exchange and correlati...

This chapter gives an overview of the description of the optical and dielectric properties of bulk insulators and semiconductors in time-dependent density-functional theory (TDDFT), with an emphasis on excitons. We review the linear-response formalism for periodic solids, discuss excitonic exchange-correlation kernels, calculate exciton binding energies for various materials, and compare the tr...