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The Kohn-Sham approach to time-dependent density-functional theory (TDDFT) can be formulated, in principle exactly, by invoking the force-balance equation for the density, which leads to an explicit expression for the exchange-correlation…

The general expectation that, in principle, time-dependent density functional theory (TDDFT) be an exact formulation of the time-evolution of an interacting N-electron system is critically reexamined. It is demonstrated that the previous…

A recent paper (Phys. Rev A. 75, 022513 (2007), arXiv:cond-mat/0602020) challenges exact time-dependent density functional theory (TDDFT) on several grounds. We explain why these criticisms are either irrelevant or incorrect, and that TDDFT…

We present a variational formulation of Time-Dependent Density Functional Theory similar to the constrained-search variational formulation of ground-state density-function theory. The formulation is applied to justify the time-dependent…

Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence…

In their famous paper Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of $N$ interacting electrons, albeit limited at the time by certain troubling…

The Comment by Holas et al. [A. Holas, M. Cinal, and N. H. March, Phys. Rev. A 78, 016501 (2008)] on our recent paper [J. Schirmer and A. Dreuw, Phys. Rev. A 75, 022513 (2007)]. is an appropriate and valuable contribution. As a small…

In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such…

Given the time-evolution of an electron charge density, the local potential in Kohn-Sham time-dependent density functional theory (KS-TDDFT) can be modeled as a sum of instantaneous and dynamic contributions by assuming a certain form of…

Time-dependent density-functional theory (TDDFT) is deemed to be a formally rigorous way of dealing with the time-evolution of a many-electron system at the level of electron densities rather than the underlying wavefunctions, which in turn…

Floquet formulation of time-dependent density-functional theory is revisited in light of its recent criticism [Maitra and Burke, Chem. Phys. Lett. 359 (2002), 237]. It is shown that Floquet theory is well founded and its criticism has…

Reliable and robust convergence to the electronic ground state within density functional theory (DFT) Kohn-Sham (KS) calculations remains a thorny issue in many systems of interest. In such cases, charge sloshing can delay or completely…

We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids…

We provide a new formulation of Time-Dependent Density Functional Theory (TDDFT) based on the geometric structure of the set of states constrained to have a fixed density. Orbital-free TDDFT is formulated using a hydrodynamics equation…

The density functional theory (DFT) is a remarkably successful theory of electronic structure of matter. At the foundation of this theory lies the Kohn-Sham (KS) equation. In this paper, we describe the long-time behaviour of the…

An approximate solution to the time-dependent density functional theory (TDDFT) response equations for finite systems is developed, yielding corrections to the single-pole approximation. These explain why allowed Kohn-Sham transition…

This work continues a program to systematically generalize the Skyrme Hartree-Fock method for medium and heavy nuclei by applying effective field theory (EFT) methods to Kohn-Sham density functional theory (DFT). When conventional Kohn-Sham…

It is shown that the density-potential mapping and the ${\cal V}$-representability problems in the time-dependent current density functional theory (TDCDFT) are reduced to the solution of a certain many-body nonlinear Schr\"odinger equation…

Predictivity of the Kohn-Sham approach to dynamical problems, when regarded as an initial value problem in a time-dependent density functional framework, is analysed for a class of models for which the argument devised in the work of Maitra…

The practical success of density functional theory (DFT) is largely credited to the Kohn-Sham approach, which enables the exact calculation of the non-interacting electron kinetic energy via an auxiliary noninteracting system. Yet, the…