Time-dependent density functional theory: Past, present, and future

In principle, we should not need the time-dependent extension of density-functional theory (TDDFT) for excitations, and in particular not for Molecular Dynamics (MD) studies: the theorem by Hohenberg and Kohn teaches us that for any observable that we wish to look at (including dynamical properties or observables dependent on excited states) there is a corresponding functional of the ground-state density. Yet the unavailability of such magic functionals in many cases (the the...

Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than possible otherwise. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certa...

Time-dependent density-functional theory (TDDFT) is widely used to describe electronic excitations in complex finite systems with large numbers of atoms, such as biomolecules and nanocrystals. The first part of this paper will give a simple and pedagogical explanation, using a two-level system, which shows how the basic TDDFT formalism for excitation energies works. There is currently an intense effort underway to develop TDDFT methodologies for the charge and spin dynamics i...

We propose a computationally efficient approach to the nonadiabatic time-dependent density functional theory (TDDFT) which is based on a representation of the frequency-dependent exchange correlation kernel as a response of a set of damped oscillators. The requirements to computational resources needed to implement our approach do not differ from those of the standard real-time TDDFT in the adiabatic local density approximation (ALDA). Thus, our result offers an exciting oppo...

This chapter is devoted to exact conditions in time-dependent density functional theory. Many conditions have been derived for the exact ground-state density functional, and several have played crucial roles in the construction of popular approximations. We believe that the reliability of the most fundamental approximation of any density functional theory, the local density approximation (LDA), is due to the exact conditions that it satisfies. Improved approximations should s...

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 Kohn-Sham method. Other promising applications to advance TDDFT are suggested.

The formalism of density functional theory (DFT) can be easily extended to the time dependent case (TDDFT). However, while in the static case the theory is well established and is expected to be, at least in principle, an exact approach for the determination of energy and density profiles of inhomogeneous systems, the applicability of TDDFT to the investigation of dynamic phenomena (for example propagation of collective phenomena) is less obvious especially in the microscopic...

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 representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays however the realization that Nature is not...

This article has been published as a chapter in "Chemical Reactivity Theory: A Density Functional View", ed. P. K. Chattaraj (CRC Press, New York, 2009), ch. 8, p. 105. In it, an overview of the relationship between time-dependent DFT and quantum hydrodynamics is presented, showing the role that Bohmian mechanics can play within the ab-initio methodology as both a numerical and an interpretative tool.

A introduction into density-functional theory and electronic structure methods is given, that aims at providing an intuitive understanding of the underlying concepts for the novice as well as an entry point towards the more advanced scientific literature.